# LaTeX2HTML 2021 (Released January 1, 2021)
# Associate images original text with physical files.


$key = q//;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.91ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3741.png"
 ALT="$\displaystyle = - F\left(\frac{d^2}{d\hat{x}^2}
-\hat{k}^2-\frac{F''}{F}\right)...
...S^{-1} P\left(\frac{d^2}{d\hat{x}^{2}}-\hat{k}^{2}\right)^2\skew{3}\hat{\phi},$">|; 

$key = q/';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 0.67ex; vertical-align: 0.76ex; " SRC="|."$dir".q|img2405.png"
 ALT="$'$">|; 

$key = q/'equivdslashdhat{x};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3320.png"
 ALT="$'\equiv d/d\hat{x}$">|; 

$key = q/(0,,0,,E_z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1785.png"
 ALT="$(0, 0, E_z)$">|; 

$key = q/(0,,V_y,,0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2726.png"
 ALT="$(0, V_y,  0)$">|; 

$key = q/(1slash2),m,v_parallel^{2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.79ex; vertical-align: -1.04ex; " SRC="|."$dir".q|img553.png"
 ALT="$(1/2) m v_\parallel^{2}$">|; 

$key = q/(1slash2),m,v_perp^{2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.64ex; " SRC="|."$dir".q|img551.png"
 ALT="$(1/2) m v_\perp^{2}$">|; 

$key = q/(1slash2),m_i,V_s^{,2}=0.5,T_e,{rmeV};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img1607.png"
 ALT="$(1/2) m_i V_s^{ 2} = 0.5 T_e {\rm eV}$">|; 

$key = q/(1slash2),mu_{ss'},u_{ss'}^{2}simeqT;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.51ex; vertical-align: -0.76ex; " SRC="|."$dir".q|img822.png"
 ALT="$(1/2) \mu_{ss'} u_{ss'}^{2}\simeq T$">|; 

$key = q/(1slashmu_0,sigma),nabla^2{bfB};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3202.png"
 ALT="$(1/\mu_0 \sigma) \nabla^2{\bf B}$">|; 

$key = q/(2pi)^{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2527.png"
 ALT="$(2\pi)^{-1}$">|; 

$key = q/(3slash2),p_s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1030.png"
 ALT="$(3/2) p_s$">|; 

$key = q/(E_x,,-{rmi},E_x,,0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1831.png"
 ALT="$(E_x,  -{\rm i} E_x,  0)$">|; 

$key = q/(E_x,,0,,0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2484.png"
 ALT="$(E_x,  0,  0)$">|; 

$key = q/(E_x,,E_y,,0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1787.png"
 ALT="$(E_x,  E_y,  0)$">|; 

$key = q/(E_x,,{rmi},E_x,,0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1829.png"
 ALT="$(E_x,  {\rm i} E_x, 0)$">|; 

$key = q/(I,J)proptoexp(gamma,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.58ex; " SRC="|."$dir".q|img2913.png"
 ALT="$(I,J)\propto \exp(\gamma t)$">|; 

$key = q/(R_odotslashr_A)^2simeq1slash2500;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2856.png"
 ALT="$(R_\odot/r_A)^2\simeq 1/2500$">|; 

$key = q/(T_eslashm_e)^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1600.png"
 ALT="$(T_e/m_e)^{1/2}$">|; 

$key = q/(T_eslashm_i)^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2344.png"
 ALT="$(T_e/m_i)^{1/2}$">|; 

$key = q/(T_islashm_i)^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1561.png"
 ALT="$(T_i/m_i)^{1/2}$">|; 

$key = q/(V_x,,0,,V_z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2733.png"
 ALT="$(V_x, 0, V_z)$">|; 

$key = q/(dnslashdz)slash(k_0,n^2);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1947.png"
 ALT="$(dn/dz)/(k_0 n^2)$">|; 

$key = q/(dnslashdz)slash(k_0,n^2)ll1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1931.png"
 ALT="$(dn/dz)/(k_0 n^2)\ll 1$">|; 

$key = q/(dzslashdtheta)_{z_{rmmax}}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.66ex; " SRC="|."$dir".q|img710.png"
 ALT="$(dz/d\theta)_{z_{\rm max}}=0$">|; 

$key = q/(hat{delta}slashhat{W})^5;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3498.png"
 ALT="$(\hat{\delta}/\hat{W})^5$">|; 

$key = q/(hat{z}<0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2020.png"
 ALT="$(\hat{z}&lt;0)$">|; 

$key = q/(k+1),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1057.png"
 ALT="$(k+1) $">|; 

$key = q/(k-1),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1058.png"
 ALT="$(k-1) $">|; 

$key = q/(k_perp,,0,,k_parallel);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img2506.png"
 ALT="$(k_\perp, 0, k_\parallel)$">|; 

$key = q/(m_e,nslashtau_e),{bfU}simn,e,{bfj}slash(n,e^2,tau_eslashm_e);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.54ex; " SRC="|."$dir".q|img1169.png"
 ALT="$(m_e n/\tau_e) {\bf U}
\sim n e {\bf j}/(n e^2 \tau_e/m_e)$">|; 

$key = q/(m_eslashT_e)^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1572.png"
 ALT="$(m_e/T_e)^{1/2}$">|; 

$key = q/(m_eslashm_i)^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2345.png"
 ALT="$(m_e/m_i)^{1/2}$">|; 

$key = q/(n-1);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2650.png"
 ALT="$(n-1)$">|; 

$key = q/(partialphislashpartialxi)slash(partialphislashpartialhat{x});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3469.png"
 ALT="$(\partial \phi/\partial \xi)/(\partial\phi/\partial \hat{x})$">|; 

$key = q/(r,,theta,,phi);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2813.png"
 ALT="$(r, \theta, \phi)$">|; 

$key = q/(r,,theta,,varphi);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img435.png"
 ALT="$(r, \theta, \varphi)$">|; 

$key = q/(r,,theta,,z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2975.png"
 ALT="$(r, \theta, z)$">|; 

$key = q/(r_0,,theta,,phi_0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2826.png"
 ALT="$(r_0, \theta, \phi_0)$">|; 

$key = q/(rho_islashT_i),partialT_islashpartialx;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1256.png"
 ALT="$(\rho_i/T_i) \partial
T_i/\partial x$">|; 

$key = q/(rho_sslashlambda)^{|n|};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2469.png"
 ALT="$(\rho_s/\lambda)^{\vert n\vert}$">|; 

$key = q/(rhoslashl)^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1249.png"
 ALT="$(\rho/l)^2$">|; 

$key = q/(v_perp,,theta,,v_parallel);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img2352.png"
 ALT="$(v_\perp,  \theta,  v_\parallel)$">|; 

$key = q/(v_perp,costheta,,v_perp,sintheta,,v_parallel);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img2507.png"
 ALT="$(v_\perp \cos\theta, v_\perp \sin\theta, v_\parallel)$">|; 

$key = q/(varpi,,theta,,z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2933.png"
 ALT="$(\varpi, \theta, z)$">|; 

$key = q/(x,,y,,z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2974.png"
 ALT="$(x, y, z)$">|; 

$key = q/({bfE},,{bfB},,{mitOmega})rightarrowepsilon^{-1}({bfE},,{bfB},,{mitOmega});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img274.png"
 ALT="$({\bf E},  {\bf B},  {\mit\Omega})
\rightarrow \epsilon^{-1}({\bf E},  {\bf B},  {\mit\Omega})$">|; 

$key = q/({bfV}cdotnabla),{bfB}rightarrow0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3032.png"
 ALT="$({\bf V}\cdot\nabla) {\bf B} \rightarrow 0$">|; 

$key = q/({bfb}cdotnabla),{bfb};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img357.png"
 ALT="$({\bf b}\cdot\nabla) {\bf b}$">|; 

$key = q/({bfe}_+,{bfe}_-,{bfb});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1714.png"
 ALT="$({\bf e}_+, {\bf e}_-,{\bf b})$">|; 

$key = q/({bfe}_1,{bfe}_2,{bfb});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1707.png"
 ALT="$({\bf e}_1, {\bf e}_2, {\bf b})$">|; 

$key = q/({bfr}';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2363.png"
 ALT="$({\bf r}'$">|; 

$key = q/({bfr},,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2108.png"
 ALT="$({\bf r},  t)$">|; 

$key = q/({bfr},,{bfv});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img578.png"
 ALT="$({\bf r},  {\bf v})$">|; 

$key = q/({bfr};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2365.png"
 ALT="$({\bf r}$">|; 

$key = q/({mitGamma}+1)slash({mitGamma}-1);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3153.png"
 ALT="$({\mit\Gamma}+1)/({\mit\Gamma}-1)$">|; 

$key = q/({mitOmega},tau)^{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img217.png"
 ALT="$({\mit\Omega} \tau)^{-1}$">|; 

$key = q/+e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.23ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img30.png"
 ALT="$+e$">|; 

$key = q/+pi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.23ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1978.png"
 ALT="$+\pi$">|; 

$key = q/+pislash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3009.png"
 ALT="$+\pi/2$">|; 

$key = q/+y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1257.png"
 ALT="$+y$">|; 

$key = q/+z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.27ex; " SRC="|."$dir".q|img1922.png"
 ALT="$+z$">|; 

$key = q/-(E_y,B_x^{,ast}+E_y^{,ast},B_x)slash(4,mu_0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.95ex; " SRC="|."$dir".q|img1946.png"
 ALT="$-(E_y  B_x^{ \ast}
+E_y^{ \ast}  B_x)/(4 \mu_0)$">|; 

$key = q/-1.659times10^{-2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.14ex; " SRC="|."$dir".q|img3583.png"
 ALT="$-1.659\times 10^{-2}$">|; 

$key = q/-1leq{mitOmega}leq1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.22ex; " SRC="|."$dir".q|img3511.png"
 ALT="$-1\leq{\mit\Omega}\leq 1$">|; 

$key = q/-3.228times10^{-3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3585.png"
 ALT="$-3.228\times 10^{-3}$">|; 

$key = q/-6.410times10^{-3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3584.png"
 ALT="$-6.410\times 10^{-3}$">|; 

$key = q/-8.529times10^{-2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.14ex; " SRC="|."$dir".q|img3582.png"
 ALT="$-8.529\times 10^{-2}$">|; 

$key = q/-I;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img519.png"
 ALT="$-I$">|; 

$key = q/-c^2,n^2slash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2167.png"
 ALT="$-c^2 n^2/2$">|; 

$key = q/-e,{mitPhi};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img2312.png"
 ALT="$-e {\mit\Phi}$">|; 

$key = q/-e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img27.png"
 ALT="$-e$">|; 

$key = q/-gamma,a,skew{3}hat{phi};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3331.png"
 ALT="$-\gamma a \skew{3}\hat{\phi}$">|; 

$key = q/-infty<u<infty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.23ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img2545.png"
 ALT="$-\infty &lt; u&lt;\infty$">|; 

$key = q/-nablaT_e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1178.png"
 ALT="$-\nabla T_e$">|; 

$key = q/-pi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1979.png"
 ALT="$-\pi$">|; 

$key = q/-pislash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1968.png"
 ALT="$-\pi/2$">|; 

$key = q/-u_z(omega_0,z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2081.png"
 ALT="$-u_z(\omega_0,z)$">|; 

$key = q/-w_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1296.png"
 ALT="$-w_i$">|; 

$key = q/-y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1234.png"
 ALT="$-y$">|; 

$key = q/-z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.17ex; vertical-align: -0.27ex; " SRC="|."$dir".q|img1923.png"
 ALT="$-z$">|; 

$key = q/-{bfb}timesnablaT_e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1235.png"
 ALT="$-{\bf b}\times\nabla T_e$">|; 

$key = q/-{mitPi}_i^{2}slashomega^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.51ex; vertical-align: -0.76ex; " SRC="|."$dir".q|img2336.png"
 ALT="$-{\mit\Pi}_i^{2}/\omega^2$">|; 

$key = q/-{rmi},omega;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2259.png"
 ALT="$-{\rm i} \omega$">|; 

$key = q/0.25;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2866.png"
 ALT="$0.25$">|; 

$key = q/0.51;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img486.png"
 ALT="$0.51$">|; 

$key = q/0.6235;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3699.png"
 ALT="$0.6235$">|; 

$key = q/0.94;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.14ex; " SRC="|."$dir".q|img487.png"
 ALT="$0.94$">|; 

$key = q/0leqalphaleq1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.22ex; " SRC="|."$dir".q|img2927.png"
 ALT="$0\leq \alpha\leq 1$">|; 

$key = q/1-u_{r,A}slashu_r;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2878.png"
 ALT="$1-u_{r A}/u_r$">|; 

$key = q/1.000times10^{0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3586.png"
 ALT="$1.000\times 10^{0}$">|; 

$key = q/1.283times10^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3589.png"
 ALT="$1.283\times 10^2$">|; 

$key = q/1.5^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2848.png"
 ALT="$1.5^\circ$">|; 

$key = q/1.5times10^{11};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2750.png"
 ALT="$1.5\times 10^{11}$">|; 

$key = q/10;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img86.png"
 ALT="$10$">|; 

$key = q/10^4;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img91.png"
 ALT="$10^4 $">|; 

$key = q/10^6;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img95.png"
 ALT="$10^6$">|; 

$key = q/10^7;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img85.png"
 ALT="$10^7$">|; 

$key = q/10^{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img101.png"
 ALT="$10^{-1}$">|; 

$key = q/10^{-2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img96.png"
 ALT="$10^{-2}$">|; 

$key = q/10^{12};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img100.png"
 ALT="$10^{12}$">|; 

$key = q/10^{14},{rmm}^{-3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2753.png"
 ALT="$10^{14} {\rm m}^{-3}$">|; 

$key = q/10^{18};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img109.png"
 ALT="$10^{18}$">|; 

$key = q/10^{20};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img90.png"
 ALT="$10^{20}$">|; 

$key = q/10^{28};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img105.png"
 ALT="$10^{28}$">|; 

$key = q/1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img114.png"
 ALT="$1$">|; 

$key = q/1ggQggP^{2slash3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3746.png"
 ALT="$1\gg Q\gg P^{2/3}$">|; 

$key = q/1slash4;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1596.png"
 ALT="$1/4$">|; 

$key = q/1slashomega_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2062.png"
 ALT="$1/\omega_0$">|; 

$key = q/1slashr^{2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2858.png"
 ALT="$1/r^{2}$">|; 

$key = q/1times10^5;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img104.png"
 ALT="$1\times 10^5$">|; 

$key = q/2,a,B_0,skew{3}hat{mitPsi};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3466.png"
 ALT="$2 a B_0 \skew{3}\hat{\mit\Psi}$">|; 

$key = q/2,epsilon;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2286.png"
 ALT="$2 \epsilon$">|; 

$key = q/2,m_1slashm_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1193.png"
 ALT="$2 m_1/m_2$">|; 

$key = q/2,|{mitOmega}_e|;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img2494.png"
 ALT="$2 \vert{\mit\Omega}_e\vert$">|; 

$key = q/2.548times10^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3590.png"
 ALT="$2.548\times 10^2$">|; 

$key = q/20;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img829.png"
 ALT="$20$">|; 

$key = q/2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img110.png"
 ALT="$2$">|; 

$key = q/2pi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img238.png"
 ALT="$2\pi$">|; 

$key = q/2pislashk;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2105.png"
 ALT="$2\pi/k$">|; 

$key = q/2pislashk_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3550.png"
 ALT="$2\pi/k_1$">|; 

$key = q/2pislashk_p;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3715.png"
 ALT="$2\pi/k_p$">|; 

$key = q/2pislashomega;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2106.png"
 ALT="$2\pi/\omega$">|; 

$key = q/2pislash{mitOmega};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2894.png"
 ALT="$2\pi/{\mit\Omega}$">|; 

$key = q/2times10^3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img113.png"
 ALT="$2\times 10^3$">|; 

$key = q/2times10^5;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img87.png"
 ALT="$2\times 10^5$">|; 

$key = q/2times10^6;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2809.png"
 ALT="$2\times 10^6$">|; 

$key = q/2times10^{-3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img103.png"
 ALT="$2\times 10^{-3}$">|; 

$key = q/2times2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.10ex; " SRC="|."$dir".q|img1827.png"
 ALT="$2\times 2$">|; 

$key = q/3,|{mitOmega}_e|;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img2495.png"
 ALT="$3 \vert{\mit\Omega}_e\vert$">|; 

$key = q/3.3,T_e,{rmeV};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1608.png"
 ALT="$3.3 T_e {\rm eV}$">|; 

$key = q/3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img778.png"
 ALT="$3$">|; 

$key = q/3^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img468.png"
 ALT="$3^\circ$">|; 

$key = q/3times10^9;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2881.png"
 ALT="$3\times 10^9$">|; 

$key = q/3times10^{-14},M_odot;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2850.png"
 ALT="$3\times 10^{-14} M_\odot$">|; 

$key = q/3times10^{13};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2851.png"
 ALT="$3\times 10^{13}$">|; 

$key = q/4,h_0,(2slashalpha,h_0-1)^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2222.png"
 ALT="$4 h_0 (2/\alpha h_0-1)^{1/2}$">|; 

$key = q/4.959times10^1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.14ex; " SRC="|."$dir".q|img3588.png"
 ALT="$4.959\times 10^1$">|; 

$key = q/45^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2834.png"
 ALT="$45^\circ$">|; 

$key = q/4times10^6;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img99.png"
 ALT="$4\times 10^6$">|; 

$key = q/4times10^8;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img94.png"
 ALT="$4\times 10^8$">|; 

$key = q/50,R_odot;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2840.png"
 ALT="$50 R_\odot$">|; 

$key = q/500,{rmkm},{rms}^{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2752.png"
 ALT="$500 {\rm km} {\rm s}^{-1}$">|; 

$key = q/5;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img22.png"
 ALT="$5$">|; 

$key = q/5times10^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img116.png"
 ALT="$5\times 10^2$">|; 

$key = q/5times10^4;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img108.png"
 ALT="$5\times 10^4$">|; 

$key = q/5times10^9;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2853.png"
 ALT="$5\times 10^9$">|; 

$key = q/5times10^{-6};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img112.png"
 ALT="$5\times 10^{-6}$">|; 

$key = q/5times10^{10};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img89.png"
 ALT="$5\times 10^{10}$">|; 

$key = q/6,000;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img2852.png"
 ALT="$6,000$">|; 

$key = q/6.24times10^{18};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img35.png"
 ALT="$6.24\times 10^{18}$">|; 

$key = q/6.6,R_E;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img467.png"
 ALT="$6.6 R_E$">|; 

$key = q/6000;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2754.png"
 ALT="$6000$">|; 

$key = q/6times10^4;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img97.png"
 ALT="$6\times 10^4$">|; 

$key = q/6times10^7;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img102.png"
 ALT="$6\times 10^7$">|; 

$key = q/6times10^{10};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img111.png"
 ALT="$6\times 10^{10}$">|; 

$key = q/6times10^{11};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img92.png"
 ALT="$6\times 10^{11}$">|; 

$key = q/6times10^{15};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img106.png"
 ALT="$6\times 10^{15}$">|; 

$key = q/700,000;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img2887.png"
 ALT="$700,000$">|; 

$key = q/7times10^0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img88.png"
 ALT="$7\times 10^0$">|; 

$key = q/7times10^6,,{rmm}^{-3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2849.png"
 ALT="$7\times 10^6  {\rm m}^{-3}$">|; 

$key = q/7times10^{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img98.png"
 ALT="$7\times 10^{-1}$">|; 

$key = q/7times10^{-5};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img93.png"
 ALT="$7\times 10^{-5}$">|; 

$key = q/7times10^{-7};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img115.png"
 ALT="$7\times 10^{-7}$">|; 

$key = q/7times10^{-9};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img107.png"
 ALT="$7\times 10^{-9}$">|; 

$key = q/8.227times10^{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3581.png"
 ALT="$8.227\times 10^{-1}$">|; 

$key = q/9.645times10^{0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.14ex; " SRC="|."$dir".q|img3587.png"
 ALT="$9.645\times 10^{0}$">|; 

$key = q/90^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.14ex; " SRC="|."$dir".q|img122.png"
 ALT="$90^\circ$">|; 

$key = q/=-U,{bfe}_z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3272.png"
 ALT="$=-U {\bf e}_z$">|; 

$key = q/=rho,(-cosgamma,{bfe}_1+singamma,{bfe}_2);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img503.png"
 ALT="$= \rho (-\cos\gamma {\bf e}_1+ \sin\gamma {\bf e}_2)$">|; 

$key = q/A';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img2030.png"
 ALT="$A'$">|; 

$key = q/A;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img179.png"
 ALT="$A$">|; 

$key = q/ABC;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img702.png"
 ALT="$ABC$">|; 

$key = q/A_t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1132.png"
 ALT="$A_t$">|; 

$key = q/A_v;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1131.png"
 ALT="$A_v$">|; 

$key = q/B(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img423.png"
 ALT="$B(z)$">|; 

$key = q/B;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img476.png"
 ALT="$B$">|; 

$key = q/B^{2}slash(2,mu_0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img143.png"
 ALT="$B^{2}/(2 \mu_0)$">|; 

$key = q/B_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img540.png"
 ALT="$B_0$">|; 

$key = q/B_E=mu_0M_Eslash(4pi,R_E^{3})=3.11times10^{-5},{rmT};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.51ex; vertical-align: -0.77ex; " SRC="|."$dir".q|img445.png"
 ALT="$B_E= \mu_0 M_E/(4\pi  R_E^{3}) = 3.11\times 10^{-5} {\rm T}$">|; 

$key = q/B_ast;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.73ex; vertical-align: -0.35ex; " SRC="|."$dir".q|img3627.png"
 ALT="$B_\ast$">|; 

$key = q/B_ast=B_0,hat{B}_ast;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3637.png"
 ALT="$B_\ast=B_0 \hat{B}_\ast$">|; 

$key = q/B_m;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img459.png"
 ALT="$B_m$">|; 

$key = q/B_phi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2862.png"
 ALT="$B_\phi$">|; 

$key = q/B_pm;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3011.png"
 ALT="$B_\pm$">|; 

$key = q/B_r;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img2859.png"
 ALT="$B_r$">|; 

$key = q/B_rproptor^{-2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img2870.png"
 ALT="$B_r\propto r^{-2}$">|; 

$key = q/B_rslash!sqrt{mu_0,rho};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.80ex; " SRC="|."$dir".q|img2879.png"
 ALT="$B_r/\!\sqrt{\mu_0 \rho}$">|; 

$key = q/B_theta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2988.png"
 ALT="$B_\theta$">|; 

$key = q/B_x(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1914.png"
 ALT="$B_x(z)$">|; 

$key = q/B_x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1948.png"
 ALT="$B_x$">|; 

$key = q/B_z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2987.png"
 ALT="$B_z$">|; 

$key = q/B_z=V_z=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3251.png"
 ALT="$B_z=V_z=0$">|; 

$key = q/B_{0,y}=+B_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3282.png"
 ALT="$B_{0 y}=+B_0$">|; 

$key = q/B_{0,y}=-B_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3280.png"
 ALT="$B_{0 y}=-B_0$">|; 

$key = q/B_{0,y}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3284.png"
 ALT="$B_{0 y}=0$">|; 

$key = q/B_{0,y}slashB_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3286.png"
 ALT="$B_{0 y}/B_0$">|; 

$key = q/B_{0tmspace+thinmuskip{.1667em}y}slashB_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img6.png"
 ALT="$B_{0\tmspace +\thinmuskip {.1667em}y}/B_0$">|; 

$key = q/B_{rmeq};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.75ex; " SRC="|."$dir".q|img527.png"
 ALT="$B_{\rm eq}$">|; 

$key = q/B_{rmeq}=B_EslashL^3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.51ex; vertical-align: -0.75ex; " SRC="|."$dir".q|img455.png"
 ALT="$B_{\rm eq}=B_E/L^3$">|; 

$key = q/B_{rmmax};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img426.png"
 ALT="$B_{\rm max}$">|; 

$key = q/B_{rmmin};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img424.png"
 ALT="$B_{\rm min}$">|; 

$key = q/B_{x,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img3080.png"
 ALT="$B_{x 2}$">|; 

$key = q/B_{y,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3081.png"
 ALT="$B_{y 2}$">|; 

$key = q/B_{y,2}<B_{y,1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3178.png"
 ALT="$B_{y 2}&lt;B_{y 1}$">|; 

$key = q/B_{y,2}>B_{y,1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3177.png"
 ALT="$B_{y 2}&gt;B_{y 1}$">|; 

$key = q/B_{y,2}neq0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3196.png"
 ALT="$B_{y 2}\neq 0$">|; 

$key = q/B_{y,2}rightarrow-B_{y,1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3179.png"
 ALT="$B_{y 2}\rightarrow -B_{y 1}$">|; 

$key = q/Bslash!sqrt{mu_0,rho};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.80ex; " SRC="|."$dir".q|img2880.png"
 ALT="$B/\!\sqrt{\mu_0 \rho}$">|; 

$key = q/C(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img386.png"
 ALT="$C(t)$">|; 

$key = q/C;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img388.png"
 ALT="$C$">|; 

$key = q/C_pm;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3007.png"
 ALT="$C_\pm$">|; 

$key = q/C_s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img586.png"
 ALT="$C_s$">|; 

$key = q/C_{s's};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1040.png"
 ALT="$C_{s's}$">|; 

$key = q/C_{ss'}(f_s,f_{s'});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img848.png"
 ALT="$C_{ss'}(f_s,f_{s'})$">|; 

$key = q/C_{ss'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1039.png"
 ALT="$C_{ss'}$">|; 

$key = q/D;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img1998.png"
 ALT="$D$">|; 

$key = q/D_pm;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3008.png"
 ALT="$D_\pm$">|; 

$key = q/Df_1slashDt;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2360.png"
 ALT="$D f_1/Dt$">|; 

$key = q/E(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2264.png"
 ALT="$E(t)$">|; 

$key = q/E;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img2032.png"
 ALT="$E$">|; 

$key = q/E=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2034.png"
 ALT="$E=0$">|; 

$key = q/E_0,exp[,{rmi},(k,x-omega,t)];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.58ex; " SRC="|."$dir".q|img2303.png"
 ALT="$E_0 \exp[ {\rm i} 
(k x-\omega t)]$">|; 

$key = q/E_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img512.png"
 ALT="$E_0$">|; 

$key = q/E_parallel;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img220.png"
 ALT="$E_\parallel$">|; 

$key = q/E_pm;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img1715.png"
 ALT="$E_\pm$">|; 

$key = q/E_x,(1,,-{rmi},SslashD,,0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1856.png"
 ALT="$E_x (1, -{\rm i} S/D,  0)$">|; 

$key = q/E_x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1789.png"
 ALT="$E_x$">|; 

$key = q/E_x=-sigmaslashepsilon_0=-e,n,deltaxslashepsilon_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img47.png"
 ALT="$E_x= -\sigma/\epsilon_0 =- e n \delta x/\epsilon_0$">|; 

$key = q/E_x=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1818.png"
 ALT="$E_x=0$">|; 

$key = q/E_y(hat{z});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1975.png"
 ALT="$E_y(\hat{z})$">|; 

$key = q/E_y(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2059.png"
 ALT="$E_y(t)$">|; 

$key = q/E_y(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1913.png"
 ALT="$E_y(z)$">|; 

$key = q/E_y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1790.png"
 ALT="$E_y$">|; 

$key = q/E_y=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1817.png"
 ALT="$E_y=0$">|; 

$key = q/E_z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1791.png"
 ALT="$E_z$">|; 

$key = q/E_z=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1816.png"
 ALT="$E_z=0$">|; 

$key = q/EllB,v;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img419.png"
 ALT="$E\ll B v$">|; 

$key = q/Ellm_e,nu_e,v_{t,e}slashe;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1655.png"
 ALT="$E\ll m_e \nu_e v_{t e}/e$">|; 

$key = q/F(0)<0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3144.png"
 ALT="$F(0)&lt;0$">|; 

$key = q/F(1)<0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3148.png"
 ALT="$F(1)&lt;0$">|; 

$key = q/F(hat{x})=tanh(hat{x});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3319.png"
 ALT="$F(\hat{x})=\tanh(\hat{x})$">|; 

$key = q/F(mathaccentV{hat}05E{x})=qopnamerelaxo{tanh}(mathaccentV{hat}05E{x});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img8.png"
 ALT="$F(\mathaccentV {hat}05E{x})=\qopname \relax o{tanh}(\mathaccentV {hat}05E{x})$">|; 

$key = q/F(omega);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2063.png"
 ALT="$F(\omega)$">|; 

$key = q/F(omega)slashn^{1slash2}(omega,z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2073.png"
 ALT="$F(\omega)/n^{1/2}(\omega,z)$">|; 

$key = q/F(x)=tanh(xslasha);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3306.png"
 ALT="$F(x)=\tanh(x/a)$">|; 

$key = q/F({bfk});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2111.png"
 ALT="$F({\bf k})$">|; 

$key = q/F;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img1875.png"
 ALT="$F$">|; 

$key = q/F=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2035.png"
 ALT="$F=0$">|; 

$key = q/F[({mitGamma}+1)slash({mitGamma}-1)]>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3145.png"
 ALT="$F[({\mit\Gamma}+1)/({\mit\Gamma}-1)]&gt;0$">|; 

$key = q/F^{2}geq0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.22ex; " SRC="|."$dir".q|img1753.png"
 ALT="$F^{2}\geq 0$">|; 

$key = q/F_0'(U);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.79ex; " SRC="|."$dir".q|img2535.png"
 ALT="$F_0'(U)$">|; 

$key = q/F_0'(U_0)=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.79ex; " SRC="|."$dir".q|img2534.png"
 ALT="$F_0'(U_0)=0$">|; 

$key = q/F_0(U);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2537.png"
 ALT="$F_0(U)$">|; 

$key = q/F_0(U_0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2540.png"
 ALT="$F_0(U_0)$">|; 

$key = q/F_0(u);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2241.png"
 ALT="$F_0(u)$">|; 

$key = q/F_0(u)rightarrow0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2543.png"
 ALT="$F_0(u)\rightarrow 0$">|; 

$key = q/F_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2318.png"
 ALT="$F_0$">|; 

$key = q/F_1(u,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2242.png"
 ALT="$F_1(u,t)$">|; 

$key = q/F_1(u,t=0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2274.png"
 ALT="$F_1(u,t=0)$">|; 

$key = q/F_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img2248.png"
 ALT="$F_1$">|; 

$key = q/F_{0,e};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2339.png"
 ALT="$F_{0 e}$">|; 

$key = q/Fequivtanh(hat{x})rightarrow0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3333.png"
 ALT="$F\equiv\tanh(\hat{x})\rightarrow 0$">|; 

$key = q/Frightarrow0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3332.png"
 ALT="$F\rightarrow 0$">|; 

$key = q/Fslashn^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2068.png"
 ALT="$F/n^{1/2}$">|; 

$key = q/G(u);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2272.png"
 ALT="$G(u)$">|; 

$key = q/G;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img1062.png"
 ALT="$G$">|; 

$key = q/G=6.67times10^{-11},{rmm}^{3},{rms}^{-2},{rmkg}^{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.58ex; " SRC="|."$dir".q|img2756.png"
 ALT="$G= 6.67\times 10^{-11} {\rm m}^{3} {\rm s}^{-2} {\rm kg}^{-1}$">|; 

$key = q/G_{s'}({bfv});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img809.png"
 ALT="$G_{s'}({\bf v})$">|; 

$key = q/G_{s'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img908.png"
 ALT="$G_{s'}$">|; 

$key = q/Gamma(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3404.png"
 ALT="$\Gamma(z)$">|; 

$key = q/H(hat{x},xi);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3592.png"
 ALT="$H(\hat{x},\xi)$">|; 

$key = q/H(mathaccentV{hat}05E{x},xi);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img23.png"
 ALT="$H(\mathaccentV {hat}05E{x},\xi )$">|; 

$key = q/H(v);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img942.png"
 ALT="$H(v)$">|; 

$key = q/H({bfp},{bfq},t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img393.png"
 ALT="$H({\bf p}, {\bf q}, t)$">|; 

$key = q/H;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img394.png"
 ALT="$H$">|; 

$key = q/H_{s'}(zeta);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img903.png"
 ALT="$H_{s'}(\zeta)$">|; 

$key = q/H_{s'}({bfv});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img808.png"
 ALT="$H_{s'}({\bf v})$">|; 

$key = q/I(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2890.png"
 ALT="$I(t)$">|; 

$key = q/I(t)=I(0),exp(gamma,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.58ex; " SRC="|."$dir".q|img2897.png"
 ALT="$I(t) = I(0) \exp(\gamma t)$">|; 

$key = q/I;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img338.png"
 ALT="$I$">|; 

$key = q/I_0=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1631.png"
 ALT="$I_0=1$">|; 

$key = q/I_1(y);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1995.png"
 ALT="$I_1(y)$">|; 

$key = q/I_1(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2001.png"
 ALT="$I_1(z)$">|; 

$key = q/I_1,hat{W}slash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3614.png"
 ALT="$I_1 \hat{W}/2$">|; 

$key = q/I_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img2019.png"
 ALT="$I_1$">|; 

$key = q/I_2=3slash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1632.png"
 ALT="$I_2=3/2$">|; 

$key = q/I_4=15slash4;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1633.png"
 ALT="$I_4=15/4$">|; 

$key = q/I_m;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img20.png"
 ALT="$I_m$">|; 

$key = q/I_n(lambda_e)slashlambda_erightarrow0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2490.png"
 ALT="$I_n(\lambda_e)/\lambda_e
\rightarrow 0$">|; 

$key = q/I_n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img19.png"
 ALT="$I_n$">|; 

$key = q/I_{-2}=2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img1630.png"
 ALT="$I_{-2}=2$">|; 

$key = q/I_{-n}(lambda_s)=I_n(lambda_s);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2519.png"
 ALT="$I_{-n}(\lambda_s)=I_n(\lambda_s)$">|; 

$key = q/I_{pm1}(lambda_e)slashlambda_erightarrow1slash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2488.png"
 ALT="$I_{\pm 1}(\lambda_e)/\lambda_e \rightarrow
1/2$">|; 

$key = q/J(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2902.png"
 ALT="$J(t)$">|; 

$key = q/J;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img495.png"
 ALT="$J$">|; 

$key = q/J=-(B_0slasha),(1+hat{J});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3477.png"
 ALT="$J=-(B_0/a) (1+\hat{J})$">|; 

$key = q/J_0(x);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3273.png"
 ALT="$J_0(x)$">|; 

$key = q/J_1(hat{x}),cosxi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3541.png"
 ALT="$J_1(\hat{x}) \cos\xi$">|; 

$key = q/J_1(hat{x});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3577.png"
 ALT="$J_1(\hat{x})$">|; 

$key = q/J_1(y);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1987.png"
 ALT="$J_1(y)$">|; 

$key = q/J_1(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1999.png"
 ALT="$J_1(z)$">|; 

$key = q/J_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3299.png"
 ALT="$J_1$">|; 

$key = q/J_m(hat{x});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3540.png"
 ALT="$J_m(\hat{x})$">|; 

$key = q/J_n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2389.png"
 ALT="$J_n$">|; 

$key = q/K=1slash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1589.png"
 ALT="$K=1/2$">|; 

$key = q/K_1(y);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1996.png"
 ALT="$K_1(y)$">|; 

$key = q/K_1(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2002.png"
 ALT="$K_1(z)$">|; 

$key = q/K_m(k);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3576.png"
 ALT="$K_m(k)$">|; 

$key = q/K_{13}=K_{31}=K_{23}=K_{32}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2438.png"
 ALT="$K_{13} = K_{31} = K_{23}=K_{32}=0$">|; 

$key = q/K_{alphabeta};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2430.png"
 ALT="$K_{\alpha\beta}$">|; 

$key = q/K_{ss'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img661.png"
 ALT="$K_{ss'}$">|; 

$key = q/L';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img2912.png"
 ALT="$L'$">|; 

$key = q/L,L'>M^{2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img2915.png"
 ALT="$L L'&gt;M^{2}$">|; 

$key = q/L;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img52.png"
 ALT="$L$">|; 

$key = q/L=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1858.png"
 ALT="$L=0$">|; 

$key = q/L=a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img3041.png"
 ALT="$L=a$">|; 

$key = q/L=pislashk;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3647.png"
 ALT="$L=\pi/k$">|; 

$key = q/L=r_{rmeq}slashR_E;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.75ex; " SRC="|."$dir".q|img442.png"
 ALT="$L=r_{\rm eq}/R_E$">|; 

$key = q/Lll10;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img451.png"
 ALT="$L \ll 10$">|; 

$key = q/Lrightarrowinfty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img1850.png"
 ALT="$L\rightarrow\infty$">|; 

$key = q/Lsim10^{4},{rmkm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3673.png"
 ALT="$L\sim 10^{4} {\rm km}$">|; 

$key = q/Lsim3.5times10^6;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2883.png"
 ALT="$L\sim 3.5\times 10^6$">|; 

$key = q/M;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img2892.png"
 ALT="$M$">|; 

$key = q/M_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1015.png"
 ALT="$M_0$">|; 

$key = q/M_1-1ll1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3125.png"
 ALT="$M_1-1 \ll 1$">|; 

$key = q/M_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3124.png"
 ALT="$M_1$">|; 

$key = q/M_1<1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3105.png"
 ALT="$M_1&lt;1$">|; 

$key = q/M_1=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3106.png"
 ALT="$M_1=1$">|; 

$key = q/M_1=V_1slashV_{S,1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3102.png"
 ALT="$M_1= V_1/V_{S 1}$">|; 

$key = q/M_1>1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3104.png"
 ALT="$M_1&gt;1$">|; 

$key = q/M_1gg1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3126.png"
 ALT="$M_1\gg 1$">|; 

$key = q/M_1neq1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3108.png"
 ALT="$M_1\neq 1$">|; 

$key = q/M_1rightarrowinfty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3131.png"
 ALT="$M_1\rightarrow \infty$">|; 

$key = q/M_2<1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3128.png"
 ALT="$M_2 &lt; 1$">|; 

$key = q/M_2=V_2slash({mitGamma},p_2slashrho_2)^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3127.png"
 ALT="$M_2=V_2/({\mit\Gamma} p_2/\rho_2)^{1/2}$">|; 

$key = q/M_A^{2}slash(u_r,r^{2});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.75ex; " SRC="|."$dir".q|img2869.png"
 ALT="$M_A^{2}/(u_r r^{2})$">|; 

$key = q/M_Agg1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img2875.png"
 ALT="$M_A\gg 1$">|; 

$key = q/M_E=8.05times10^{22}~{rmA,m}^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img436.png"
 ALT="$M_E = 8.05\times 10^{22}&nbsp;{\rm A m}^2$">|; 

$key = q/M_odot=2times10^{30},{rmkg};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.58ex; " SRC="|."$dir".q|img2757.png"
 ALT="$M_\odot=2\times 10^{30} {\rm kg}$">|; 

$key = q/M_{13}=M_{31}=M_{23}=M_{32}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2449.png"
 ALT="$M_{13} = M_{31} = M_{23}=M_{32}=0$">|; 

$key = q/N(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2142.png"
 ALT="$N(z)$">|; 

$key = q/N;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img1113.png"
 ALT="$N$">|; 

$key = q/N=N(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2132.png"
 ALT="$N=N(z)$">|; 

$key = q/O;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img701.png"
 ALT="$O$">|; 

$key = q/P-n^2=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1853.png"
 ALT="$P-n^2 =0$">|; 

$key = q/P;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img1724.png"
 ALT="$P$">|; 

$key = q/P_z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2040.png"
 ALT="$P_z$">|; 

$key = q/Pgg1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img3752.png"
 ALT="$P\gg 1$">|; 

$key = q/Pll1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img3751.png"
 ALT="$P\ll 1$">|; 

$key = q/Q;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img13.png"
 ALT="$Q$">|; 

$key = q/Q>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3395.png"
 ALT="$Q&gt;0$">|; 

$key = q/Q^{5slash4}propto{mitDelta}'slashS^{1slash3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3446.png"
 ALT="$Q^{5/4} \propto {\mit\Delta}'/S^{1/3}$">|; 

$key = q/Qll1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3427.png"
 ALT="$Q\ll 1$">|; 

$key = q/QllP^{-1slash3},P^{2slash3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3748.png"
 ALT="$Q\ll P^{-1/3}, P^{2/3}$">|; 

$key = q/Qrightarrow1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3428.png"
 ALT="$Q\rightarrow 1$">|; 

$key = q/R';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img2911.png"
 ALT="$R'$">|; 

$key = q/R'rightarrow0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2919.png"
 ALT="$R'\rightarrow 0$">|; 

$key = q/R;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img1723.png"
 ALT="$R$">|; 

$key = q/R=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1857.png"
 ALT="$R=0$">|; 

$key = q/R_E=6.37times10^6,{rmm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img443.png"
 ALT="$R_E = 6.37\times 10^6 {\rm m}$">|; 

$key = q/R_odot;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2811.png"
 ALT="$R_\odot$">|; 

$key = q/Requivp_2slashp_1rightarrowinfty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3130.png"
 ALT="$R\equiv p_2/p_1\rightarrow\infty$">|; 

$key = q/Rneq1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.21ex; " SRC="|."$dir".q|img3110.png"
 ALT="$R\neq 1$">|; 

$key = q/Rrightarrow0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2920.png"
 ALT="$R\rightarrow 0$">|; 

$key = q/Rrightarrowinfty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img1836.png"
 ALT="$R\rightarrow\infty$">|; 

$key = q/S,hat{gamma};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3322.png"
 ALT="$S \hat{\gamma}$">|; 

$key = q/S;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img2151.png"
 ALT="$S$">|; 

$key = q/S=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img2158.png"
 ALT="$S=0$">|; 

$key = q/S=k_xslashk_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2187.png"
 ALT="$S=k_x/k_0$">|; 

$key = q/S=tau_Rslashtau_H;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3644.png"
 ALT="$S=\tau_R/\tau_H$">|; 

$key = q/S^{,2slash3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3669.png"
 ALT="$S^{ 2/3}$">|; 

$key = q/S^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3654.png"
 ALT="$S^{1/2}$">|; 

$key = q/S^{1slash3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3449.png"
 ALT="$S^{1/3}$">|; 

$key = q/S_c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img3047.png"
 ALT="$S_c$">|; 

$key = q/Sgg1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3415.png"
 ALT="$S\gg 1$">|; 

$key = q/Srightarrowinfty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img1776.png"
 ALT="$S\rightarrow \infty$">|; 

$key = q/Ssim10^{11};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3241.png"
 ALT="$S\sim 10^{11}$">|; 

$key = q/Ssim10^{8};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3240.png"
 ALT="$S\sim 10^{8}$">|; 

$key = q/T(r);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2759.png"
 ALT="$T(r)$">|; 

$key = q/T({rmeV});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img82.png"
 ALT="$T({\rm eV})$">|; 

$key = q/T;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img38.png"
 ALT="$T$">|; 

$key = q/T<T_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2781.png"
 ALT="$T&lt;T_0$">|; 

$key = q/T=T(x);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1644.png"
 ALT="$T=T(x)$">|; 

$key = q/T_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2773.png"
 ALT="$T_0$">|; 

$key = q/T_0simeq5.8times10^6;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2780.png"
 ALT="$T_0\simeq 5.8\times 10^6$">|; 

$key = q/T_e,T_irightarrow0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1441.png"
 ALT="$T_e, T_i\rightarrow 0$">|; 

$key = q/T_e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img158.png"
 ALT="$T_e$">|; 

$key = q/T_e=T_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1189.png"
 ALT="$T_e=T_i$">|; 

$key = q/T_e>T_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1190.png"
 ALT="$T_e&gt;T_i$">|; 

$key = q/T_e^{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.65ex; " SRC="|."$dir".q|img1181.png"
 ALT="$T_e^{-1}$">|; 

$key = q/T_eggT_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2347.png"
 ALT="$T_e\gg T_i$">|; 

$key = q/T_esimT_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1207.png"
 ALT="$T_e\sim T_i$">|; 

$key = q/T_esimeqT_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1497.png"
 ALT="$T_e\simeq T_i$">|; 

$key = q/T_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img161.png"
 ALT="$T_i$">|; 

$key = q/T_i=T_e=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img206.png"
 ALT="$T_i=T_e=0$">|; 

$key = q/T_i=T_e=T;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img194.png"
 ALT="$T_i=T_e=T$">|; 

$key = q/T_illT_e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2.png"
 ALT="$T_i\ll T_e$">|; 

$key = q/T_s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img831.png"
 ALT="$T_s$">|; 

$key = q/T_{alphabeta};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2440.png"
 ALT="$T_{\alpha\beta}$">|; 

$key = q/T_{parallel,i}<T_{perp,i};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img2642.png"
 ALT="$T_{\parallel i}&lt; T_{\perp i}$">|; 

$key = q/T_{parallel,i}=T_{perp,i};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img2639.png"
 ALT="$T_{\parallel i}=T_{\perp i}$">|; 

$key = q/T_{parallel,s};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img2610.png"
 ALT="$T_{\parallel s}$">|; 

$key = q/T_{perp,s};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2609.png"
 ALT="$T_{\perp s}$">|; 

$key = q/T_{s'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img832.png"
 ALT="$T_{s'}$">|; 

$key = q/Tsim1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img2808.png"
 ALT="$T\sim 1$">|; 

$key = q/Tsim2times10^{6};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2769.png"
 ALT="$T\sim 2\times 10^{6}$">|; 

$key = q/U(0,!sqrt{2},Q^{1slash4},p);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3400.png"
 ALT="$U(0,\!\sqrt{2} Q^{1/4} p)$">|; 

$key = q/U(a,x);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3401.png"
 ALT="$U(a,x)$">|; 

$key = q/U;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img1208.png"
 ALT="$U$">|; 

$key = q/U=(1slasha,k,tau_R),hat{U};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3479.png"
 ALT="$U=(1/a k \tau_R) \hat{U}$">|; 

$key = q/U=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img1188.png"
 ALT="$U=0$">|; 

$key = q/U=U_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2533.png"
 ALT="$U=U_0$">|; 

$key = q/U=omegaslashk;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2524.png"
 ALT="$U=\omega/k$">|; 

$key = q/U_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2536.png"
 ALT="$U_0$">|; 

$key = q/U_0=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2552.png"
 ALT="$U_0=0$">|; 

$key = q/U_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3301.png"
 ALT="$U_1$">|; 

$key = q/U_e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2561.png"
 ALT="$U_e$">|; 

$key = q/U_parallel;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img2679.png"
 ALT="$U_\parallel$">|; 

$key = q/U_parallel=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img420.png"
 ALT="$U_\parallel = 0$">|; 

$key = q/U_{0,parallel};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img301.png"
 ALT="$U_{0 \parallel}$">|; 

$key = q/U_{ss'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img601.png"
 ALT="$U_{ss'}$">|; 

$key = q/UsimV_esimV_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1475.png"
 ALT="$U\sim V_e\sim V_i$">|; 

$key = q/Usimdelta,V_esimdelta,V_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1488.png"
 ALT="$U \sim \delta V_e\sim \delta V_i$">|; 

$key = q/Uslash({mitOmega},a)=1.3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3044.png"
 ALT="$U/({\mit\Omega} a)=1.3$">|; 

$key = q/V,,Brightarrow0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img2923.png"
 ALT="$V, B\rightarrow 0$">|; 

$key = q/V;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img196.png"
 ALT="$V$">|; 

$key = q/V<V_S,costheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2744.png"
 ALT="$V&lt;V_S \cos\theta$">|; 

$key = q/V=omegaslashk;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2745.png"
 ALT="$V=\omega/k$">|; 

$key = q/V=|{bfV}(a)|=({mitOmega}^{2},a^2+U^{2})^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3040.png"
 ALT="$V=\vert{\bf V}(a)\vert= ({\mit\Omega}^{2} a^2+U^{2})^{1/2}$">|; 

$key = q/V>V_S,costheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2743.png"
 ALT="$V&gt;V_S  \cos\theta$">|; 

$key = q/V_+;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3210.png"
 ALT="$V_+$">|; 

$key = q/V_+>V_S,costheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2746.png"
 ALT="$V_+&gt; V_S \cos\theta$">|; 

$key = q/V_+geqV_-;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img2732.png"
 ALT="$V_+\geq V_-$">|; 

$key = q/V_-;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3211.png"
 ALT="$V_-$">|; 

$key = q/V_-<V_S,costheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2747.png"
 ALT="$V_-&lt;V_S \cos\theta$">|; 

$key = q/V_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3134.png"
 ALT="$V_1$">|; 

$key = q/V_1>V_{S,1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3133.png"
 ALT="$V_1 &gt; V_{S 1}$">|; 

$key = q/V_A;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img1544.png"
 ALT="$V_A$">|; 

$key = q/V_A=B_astslash!sqrt{mu_0,rho};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.80ex; " SRC="|."$dir".q|img3646.png"
 ALT="$V_A = B_\ast/\!\sqrt{\mu_0 \rho}$">|; 

$key = q/V_A=Bslash!sqrt{mu_0,n_e,m_i};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.80ex; " SRC="|."$dir".q|img515.png"
 ALT="$V_A = B/\!\sqrt{\mu_0 n_e m_i}$">|; 

$key = q/V_AggV_S;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2737.png"
 ALT="$V_A\gg V_S$">|; 

$key = q/V_Allc;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img1815.png"
 ALT="$V_A\ll c$">|; 

$key = q/V_Asim100,{rmkm},{rms}^{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3672.png"
 ALT="$V_A\sim 100 {\rm km} {\rm s}^{-1}$">|; 

$key = q/V_S;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1543.png"
 ALT="$V_S$">|; 

$key = q/V_S<V_A;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2749.png"
 ALT="$V_S&lt;V_A$">|; 

$key = q/V_S^{2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.51ex; vertical-align: -0.78ex; " SRC="|."$dir".q|img3205.png"
 ALT="$V_S^{2}$">|; 

$key = q/V_alpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1215.png"
 ALT="$V_\alpha$">|; 

$key = q/V_e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1209.png"
 ALT="$V_e$">|; 

$key = q/V_e=V_i=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1172.png"
 ALT="$V_e=V_i =0$">|; 

$key = q/V_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1560.png"
 ALT="$V_i$">|; 

$key = q/V_i=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1186.png"
 ALT="$V_i=0$">|; 

$key = q/V_isim(T_eslashm_i)^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1562.png"
 ALT="$V_i\sim (T_e/m_i)^{1/2}$">|; 

$key = q/V_s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1564.png"
 ALT="$V_s$">|; 

$key = q/V_s=(T_eslashm_i)^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1591.png"
 ALT="$V_s=(T_e/m_i)^{1/2}$">|; 

$key = q/V_sslashv_{t,s};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img923.png"
 ALT="$V_s/v_{t s}$">|; 

$key = q/V_x=V_z=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1821.png"
 ALT="$V_x=V_z=0$">|; 

$key = q/V_y=V_z=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1823.png"
 ALT="$V_y=V_z=0$">|; 

$key = q/V_{+,1}=(V_{S,1}^{2}+V_{A,1}^{2})^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.57ex; vertical-align: -0.80ex; " SRC="|."$dir".q|img3152.png"
 ALT="$V_{+ 1} = (V_{S 1}^{2} + V_{A 1}^{2})^{1/2}$">|; 

$key = q/V_{+,2}=(V_{S,2}^{2}+V_{A,2}^{2})^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.57ex; vertical-align: -0.80ex; " SRC="|."$dir".q|img3237.png"
 ALT="$V_{+ 2}=(V_{S 2}^{2}+V_{A 2}^{2})^{1/2}$">|; 

$key = q/V_{A,1}=B_1slash(mu_0,rho_1)^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3151.png"
 ALT="$V_{A 1}=B_1/(\mu_0 \rho_1)^{1/2}$">|; 

$key = q/V_{S,1}<V_{A,1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3191.png"
 ALT="$V_{S 1}&lt;V_{A 1}$">|; 

$key = q/V_{S,1}=({mitGamma},p_1slashrho_1)^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3103.png"
 ALT="$V_{S 1}=({\mit\Gamma} p_1/\rho_1)^{1/2}$">|; 

$key = q/V_{S,1}>V_{A,1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3192.png"
 ALT="$V_{S 1}&gt; V_{A 1}$">|; 

$key = q/V_{x,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img3082.png"
 ALT="$V_{x 2}$">|; 

$key = q/V_{y,1}=B_{y,1}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3194.png"
 ALT="$V_{y 1}=B_{y 1} =0$">|; 

$key = q/V_{y,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3083.png"
 ALT="$V_{y 2}$">|; 

$key = q/V_{y,2}neq0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3195.png"
 ALT="$V_{y 2}\neq 0$">|; 

$key = q/Vsimc;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img1442.png"
 ALT="$V\sim c$">|; 

$key = q/Vsimdelta,v_t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2681.png"
 ALT="$V\sim \delta v_t$">|; 

$key = q/Vsimdelta^{-1},v_t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2678.png"
 ALT="$V\sim \delta^{-1} v_t$">|; 

$key = q/VslashL;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1436.png"
 ALT="$V/L$">|; 

$key = q/Vslash{rme};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img201.png"
 ALT="$V/{\rm e}$">|; 

$key = q/W;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img2042.png"
 ALT="$W$">|; 

$key = q/W<0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img2045.png"
 ALT="$W&lt;0$">|; 

$key = q/W=4,hat{mitPsi}^{1slash2},a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3657.png"
 ALT="$W=4 \hat{\mit\Psi}^{1/2} a$">|; 

$key = q/W=a,hat{W};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3536.png"
 ALT="$W=a \hat{W}$">|; 

$key = q/W_{ss'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img934.png"
 ALT="$W_{ss'}$">|; 

$key = q/W_{ss}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img964.png"
 ALT="$W_{ss}=0$">|; 

$key = q/Wlla;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3658.png"
 ALT="$W\ll a$">|; 

$key = q/X;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img1870.png"
 ALT="$X$">|; 

$key = q/X=4,hat{x}slashhat{W};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3507.png"
 ALT="$X=4 \hat{x}/\hat{W}$">|; 

$key = q/X=ssqrt{2,({mitOmega}-cosxi)};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.73ex; vertical-align: -0.74ex; " SRC="|."$dir".q|img3514.png"
 ALT="$X=s\sqrt{2 ({\mit\Omega}-\cos\xi)}$">|; 

$key = q/Y_1(y);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1988.png"
 ALT="$Y_1(y)$">|; 

$key = q/Y_1(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2000.png"
 ALT="$Y_1(z)$">|; 

$key = q/Z';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img2420.png"
 ALT="$Z'$">|; 

$key = q/Z(zeta);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2322.png"
 ALT="$Z(\zeta)$">|; 

$key = q/Z,e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img160.png"
 ALT="$Z e$">|; 

$key = q/Z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img2419.png"
 ALT="$Z$">|; 

$key = q/Z_r;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img2618.png"
 ALT="$Z_r$">|; 

$key = q/[A,B]equivnablaAtimesnablaBcdot{bfe}_z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3270.png"
 ALT="$[A,B]\equiv \nabla A\times \nabla B\cdot{\bf e}_z$">|; 

$key = q/[A]_1^2equivA_2-A_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.77ex; " SRC="|."$dir".q|img3079.png"
 ALT="$[A]_1^2\equiv A_2-A_1$">|; 

$key = q/[S]_1^2<0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.77ex; " SRC="|."$dir".q|img3122.png"
 ALT="$[S]_1^2&lt;0$">|; 

$key = q/[S]_1^2=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.77ex; " SRC="|."$dir".q|img3120.png"
 ALT="$[S]_1^2=0$">|; 

$key = q/[S]_1^2>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.77ex; " SRC="|."$dir".q|img3123.png"
 ALT="$[S]_1^2&gt;0$">|; 

$key = q/[phi,psi];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3467.png"
 ALT="$[\phi,\psi]$">|; 

$key = q/_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1273.png"
 ALT="$_0$">|; 

$key = q/_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.00ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img1276.png"
 ALT="$_1$">|; 

$key = q/_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.00ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img1277.png"
 ALT="$_2$">|; 

$key = q/_3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1282.png"
 ALT="$_3$">|; 

$key = q/_4;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.00ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img1283.png"
 ALT="$_4$">|; 

$key = q/_s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 0.72ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1081.png"
 ALT="$_s$">|; 

$key = q/a,hat{z};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.73ex; vertical-align: -0.27ex; " SRC="|."$dir".q|img1993.png"
 ALT="$a \hat{z}$">|; 

$key = q/a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img205.png"
 ALT="$a$">|; 

$key = q/a<r<infty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.23ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img2792.png"
 ALT="$a&lt;r&lt;\infty$">|; 

$key = q/a<r<r_c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2782.png"
 ALT="$a&lt;r&lt;r_c$">|; 

$key = q/a>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1950.png"
 ALT="$a&gt;0$">|; 

$key = q/a>y_+>y_->0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img558.png"
 ALT="$a&gt;y_+&gt;y_-&gt;0$">|; 

$key = q/a>y_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img565.png"
 ALT="$a&gt;y_0$">|; 

$key = q/a_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3389.png"
 ALT="$a_0$">|; 

$key = q/a_s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img865.png"
 ALT="$a_s$">|; 

$key = q/a_{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3388.png"
 ALT="$a_{-1}$">|; 

$key = q/alpha,(T_e,j_betaslashn,e),{bfi};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1262.png"
 ALT="$\alpha (T_e j_\beta/n e) {\bf i}$">|; 

$key = q/alpha,(nabla,T_e)_beta,{bfi};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1261.png"
 ALT="$\alpha (\nabla T_e)_\beta {\bf i}$">|; 

$key = q/alpha,h_0<1slash4;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2218.png"
 ALT="$\alpha h_0&lt;1/4$">|; 

$key = q/alpha,h_0<2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2223.png"
 ALT="$\alpha h_0&lt;2$">|; 

$key = q/alpha,h_0=1slash4;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2219.png"
 ALT="$\alpha h_0=1/4$">|; 

$key = q/alpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img537.png"
 ALT="$\alpha$">|; 

$key = q/alpha=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2929.png"
 ALT="$\alpha=0$">|; 

$key = q/alpha=90^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.14ex; " SRC="|."$dir".q|img456.png"
 ALT="$\alpha=90^\circ$">|; 

$key = q/alpha=k_{ss'}slash(E_{ss'},b);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img713.png"
 ALT="$\alpha=k_{ss'}/(E_{ss'} b)$">|; 

$key = q/alpha>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2928.png"
 ALT="$\alpha&gt;0$">|; 

$key = q/alpha_{rmeq};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.75ex; " SRC="|."$dir".q|img454.png"
 ALT="$\alpha_{\rm eq}$">|; 

$key = q/arightarrowhat{delta}_{rmSP},a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3710.png"
 ALT="$a\rightarrow \hat{\delta}_{\rm SP} a$">|; 

$key = q/asim7times10^5,{rmkm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2767.png"
 ALT="$a\sim 7\times 10^5 {\rm km}$">|; 

$key = q/b+db;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img724.png"
 ALT="$b+db$">|; 

$key = q/b;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img723.png"
 ALT="$b$">|; 

$key = q/b>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1970.png"
 ALT="$b&gt;0$">|; 

$key = q/b_{rmmax}=(sum_sn_s,e_s^{2}slashepsilon_0,T_s)^{-1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img837.png"
 ALT="$b_{\rm max} =(\sum_s n_s e_s^{2}/\epsilon_0 T_s)^{-1/2}$">|; 

$key = q/b_{rmmax}ggb_{rmmin};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img830.png"
 ALT="$b_{\rm max}\gg b_{\rm min}$">|; 

$key = q/b_{rmmin};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img824.png"
 ALT="$b_{\rm min}$">|; 

$key = q/bar{B};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img1318.png"
 ALT="$\bar{B}$">|; 

$key = q/bar{F}_1(u,p);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2265.png"
 ALT="$\bar{F}_1(u,p)$">|; 

$key = q/bar{F}_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img2250.png"
 ALT="$\bar{F}_1$">|; 

$key = q/bar{V}_e=(8,T_eslashpi,m_e)^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1597.png"
 ALT="$\bar{V}_e=(8 T_e/\pi m_e)^{1/2}$">|; 

$key = q/bar{W}=2,hat{W}slashpi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3600.png"
 ALT="$\bar{W}=2 \hat{W}/\pi$">|; 

$key = q/bar{l}_e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1317.png"
 ALT="$\bar{l}_e$">|; 

$key = q/bar{l}_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1383.png"
 ALT="$\bar{l}_i$">|; 

$key = q/bar{n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img1315.png"
 ALT="$\bar{n}$">|; 

$key = q/bar{psi}(-p)=bar{psi}(p);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3384.png"
 ALT="$\bar{\psi}(-p)=\bar{\psi}(p)$">|; 

$key = q/bar{rho}_e=bar{v}_eslash(ebar{B}slashm_e);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1319.png"
 ALT="$\bar{\rho}_e =\bar{ v}_e/(e\bar{B}/m_e)$">|; 

$key = q/bar{rho}_i=bar{v}_islash(ebar{B}slashm_i);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1384.png"
 ALT="$\bar{\rho}_i =\bar{ v}_i/(e\bar{B}/m_i)$">|; 

$key = q/bar{u}_{ss'}^{2}lesssimT_sslashm_s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.51ex; vertical-align: -0.76ex; " SRC="|."$dir".q|img838.png"
 ALT="$\bar{u}_{ss'}^{2}\lesssim T_s/m_s$">|; 

$key = q/bar{v}_e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.73ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1316.png"
 ALT="$\bar{v}_e$">|; 

$key = q/bar{v}_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.73ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1382.png"
 ALT="$\bar{v}_i$">|; 

$key = q/beta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img141.png"
 ALT="$\beta$">|; 

$key = q/beta_1=2,mu_0,p_1slashB_1^{2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.77ex; " SRC="|."$dir".q|img3139.png"
 ALT="$\beta_1= 2 \mu_0 p_1/B_1^{2}$">|; 

$key = q/beta_s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img145.png"
 ALT="$\beta_s$">|; 

$key = q/c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img866.png"
 ALT="$c$">|; 

$key = q/c^2,k_perp^2slashomega^2gg1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.64ex; " SRC="|."$dir".q|img2482.png"
 ALT="$c^2 k_\perp^2/\omega^2\gg 1$">|; 

$key = q/c_s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2590.png"
 ALT="$c_s$">|; 

$key = q/c_s=(T_eslashm_i)^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2587.png"
 ALT="$c_s=(T_e/m_i)^{1/2}$">|; 

$key = q/cdots;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 0.28ex; vertical-align: 0.37ex; " SRC="|."$dir".q|img2279.png"
 ALT="$\cdots$">|; 

$key = q/chi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img641.png"
 ALT="$\chi$">|; 

$key = q/chi=-{mitOmega}_s,(t'-t)+theta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2505.png"
 ALT="$\chi=-{\mit\Omega}_s (t'-t)+\theta$">|; 

$key = q/chi=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img758.png"
 ALT="$\chi=0$">|; 

$key = q/chi_t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1135.png"
 ALT="$\chi_t$">|; 

$key = q/chi_v;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1134.png"
 ALT="$\chi_v$">|; 

$key = q/chi_{rmmax};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img768.png"
 ALT="$\chi_{\rm max}$">|; 

$key = q/chi_{rmmin};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img769.png"
 ALT="$\chi_{\rm min}$">|; 

$key = q/chirightarrowchi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img647.png"
 ALT="$\chi\rightarrow\chi$">|; 

$key = q/chisimnu,l^{2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1130.png"
 ALT="$\chi\sim\nu l^{2}$">|; 

$key = q/cos(m,xi);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3528.png"
 ALT="$\cos(m \xi)$">|; 

$key = q/cosxi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3526.png"
 ALT="$\cos\xi$">|; 

$key = q/cosxi<0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3625.png"
 ALT="$\cos\xi&lt;0$">|; 

$key = q/cosxi>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3626.png"
 ALT="$\cos\xi&gt;0$">|; 

$key = q/cslashn;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1924.png"
 ALT="$c/n$">|; 

$key = q/dB_rslashdr;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3015.png"
 ALT="$dB_r/dr$">|; 

$key = q/dBslashdt=partialBslashpartialt+U_{0,parallel},{bfb}cdotnablaB+{bfv}_EcdotnablaB;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img380.png"
 ALT="$dB/dt=\partial B/\partial t + U_{0 \parallel} {\bf b}\cdot\nabla B + {\bf v}_E\cdot\nabla B$">|; 

$key = q/dHslashdt=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img861.png"
 ALT="$dH/dt =0$">|; 

$key = q/d[S]_1^2slashdrgeq0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.77ex; " SRC="|."$dir".q|img3119.png"
 ALT="$d[S]_1^2/dr\geq 0$">|; 

$key = q/d^2phislashdz^{2}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1928.png"
 ALT="$d^2\phi/dz^{2}=0$">|; 

$key = q/d^3{bfu}_{ss'}=d^3{bfu}_{ss'}';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.51ex; vertical-align: -0.76ex; " SRC="|."$dir".q|img610.png"
 ALT="$d^3{\bf u}_{ss'}=d^3{\bf u}_{ss'}'$">|; 

$key = q/d_eslashdhat{t}equivpartialslashpartialhat{t}+widehat{bfV}_ecdotwidehat{nabla};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.62ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1378.png"
 ALT="$d_e/d\hat{t}\equiv\partial /\partial\hat{t} +
\widehat{\bf V}_e\cdot\widehat{\nabla}$">|; 

$key = q/d_islashdhat{t}equivpartialslashpartialhat{t}+widehat{bfV}_icdotwidehat{nabla};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.62ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1420.png"
 ALT="$d_i/d\hat{t}\equiv\partial /\partial\hat{t} +
\widehat{\bf V}_i\cdot\widehat{\nabla}$">|; 

$key = q/delimiter"426830Aqopnamerelaxo{cos}xidelimiter"526930Bslashdelimiter"426830A1delimiter"526930B;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img18.png"
 ALT="$\delimiter ''426830A \qopname \relax o{cos}\xi \delimiter ''526930B /\delimiter ''426830A 1\delimiter ''526930B $">|; 

$key = q/delta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img140.png"
 ALT="$\delta$">|; 

$key = q/delta_ast;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.35ex; " SRC="|."$dir".q|img3628.png"
 ALT="$\delta_\ast$">|; 

$key = q/delta_ast=a,hat{delta}_ast;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.35ex; " SRC="|."$dir".q|img3639.png"
 ALT="$\delta_\ast=a \hat{\delta}_\ast$">|; 

$key = q/delta_e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1376.png"
 ALT="$\delta_e$">|; 

$key = q/delta_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1418.png"
 ALT="$\delta_i$">|; 

$key = q/delta_p;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3722.png"
 ALT="$\delta_p$">|; 

$key = q/delta_{rmSP};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3721.png"
 ALT="$\delta_{\rm SP}$">|; 

$key = q/deltalla;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img207.png"
 ALT="$\delta\ll a$">|; 

$key = q/deltarho_{rmext};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img64.png"
 ALT="$\delta\rho_{\rm ext}$">|; 

$key = q/deltarho_{rmext}=q,delta({bfr});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.56ex; " SRC="|."$dir".q|img69.png"
 ALT="$\delta\rho_{\rm ext} = q \delta({\bf r})$">|; 

$key = q/deltarightarrow0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img2677.png"
 ALT="$\delta\rightarrow 0$">|; 

$key = q/deltasimzetasimmull1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1503.png"
 ALT="$\delta\sim \zeta\sim\mu\ll 1$">|; 

$key = q/deltaslashasim{calS}^{-1slash4};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3689.png"
 ALT="$\delta/a\sim {\cal S}^{-1/4}$">|; 

$key = q/deltax;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img45.png"
 ALT="$\delta x$">|; 

$key = q/deltax=(deltax)_0,cos,({mitPi},t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img49.png"
 ALT="$\delta x = (\delta x)_0 \cos ({\mit\Pi} t)$">|; 

$key = q/deltax_islashdeltax_e=-Z,m_eslashm_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img166.png"
 ALT="$\delta x_i/\delta x_e=- Z m_e/m_i$">|; 

$key = q/delta{mitPhi}({bfr});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img63.png"
 ALT="$\delta{\mit\Phi}({\bf r})$">|; 

$key = q/delta{mitPhi};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img170.png"
 ALT="$\delta{\mit\Phi}$">|; 

$key = q/dgammaslashdtsimeq{mitOmega}={calO}(epsilon^{-1});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img292.png"
 ALT="$d\gamma/dt \simeq {\mit\Omega} = {\cal O}(\epsilon^{-1})$">|; 

$key = q/dhat{psi}slashdhat{x};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3349.png"
 ALT="$d\hat{\psi}/d\hat{x}$">|; 

$key = q/displaystyle(m_s+m_{s'})int{bfU}_{ss'},C_{ss'},d^3{bfv}_s={bf0}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img658.png"
 ALT="$\displaystyle (m_s+m_{s'}) \int {\bf U}_{ss'} C_{ss'} d^3{\bf v}_s = {\bf0}.$">|; 

$key = q/displaystyle(omega^2-k^2,V_A^{2},cos^2theta)left[omega^4-omega^2,k^2,(V_A^{2}+V_S^{2})+k^4,V_A^{2},V_S^{2},cos^2thetaright]=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.29ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img2724.png"
 ALT="$\displaystyle (\omega^2 - k^2 V_A^{2} \cos^2\theta)\left[
\omega^4 - \omega^2 k^2 (V_A^{2}+V_S^{2}) + k^4 V_A^{2} V_S^{2} \cos^2\theta
\right] = 0.$">|; 

$key = q/displaystyle(q+s),q,s={rmi},m,{mitOmega},tau_R,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.56ex; " SRC="|."$dir".q|img3027.png"
 ALT="$\displaystyle (q+s) q s = {\rm i} m {\mit\Omega} \tau_R,$">|; 

$key = q/displaystyle(t),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img231.png"
 ALT="$\displaystyle (t),$">|; 

$key = q/displaystyle(t)=rho,[-cos({mitOmega},t+gamma_0),{bfe}_1+sin({mitOmega},t+gamma_0),{bfe}_2],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img232.png"
 ALT="$\displaystyle (t) = \rho  [-\cos({\mit\Omega}  t+\gamma_0) {\bf e}_1
+\sin({\mit\Omega} t + \gamma_0) {\bf e}_2],$">|; 

$key = q/displaystyle(tau_b)_esimeq5.62times10^{-2}frac{L}{sqrt{{calE}({rmMeV})}},(1-0.43sinalpha_{rmeq}),,,{rmseconds}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.19ex; vertical-align: -2.30ex; " SRC="|."$dir".q|img475.png"
 ALT="$\displaystyle (\tau_b)_e \simeq 5.62\times 10^{-2}\frac{L}{\sqrt{{\cal E}({\rm MeV})}}  (1- 0.43 \sin\alpha_{\rm eq})   {\rm seconds}.$">|; 

$key = q/displaystyle(tau_b)_psimeq2.41,frac{L}{sqrt{{calE}({rmMeV})}},(1-0.43sinalpha_{rmeq}),,,{rmseconds},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.19ex; vertical-align: -2.30ex; " SRC="|."$dir".q|img474.png"
 ALT="$\displaystyle (\tau_b)_p \simeq 2.41 \frac{L}
{\sqrt{{\cal E}({\rm MeV})}}  (1- 0.43 \sin\alpha_{\rm eq})   {\rm seconds},$">|; 

$key = q/displaystyle({bfR},{bfU},t,gamma),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img281.png"
 ALT="$\displaystyle ({\bf R}, {\bf U}, t, \gamma),$">|; 

$key = q/displaystyle({bfZ},t,tau),dtau=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img252.png"
 ALT="$\displaystyle ({\bf Z}, t, \tau) d\tau = 0,$">|; 

$key = q/displaystyle({bfZ},t,tau).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img248.png"
 ALT="$\displaystyle ({\bf Z}, t, \tau).$">|; 

$key = q/displaystyle({bfZ},t,tau)rangleequivfrac{1}{2pi}oint;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img251.png"
 ALT="$\displaystyle ({\bf Z}, t, \tau)\rangle\equiv
\frac{1}{2\pi}\oint$">|; 

$key = q/displaystyle({bfb}cdotnabla),{bfb}=-{bfb}times(nablatimes{bfb})simeqfrac{nabla_perpB}{B}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img479.png"
 ALT="$\displaystyle ({\bf b}\cdot\nabla) {\bf b} =-{\bf b}\times(\nabla\times
{\bf b})\simeq \frac{\nabla_\perp B}{B}.$">|; 

$key = q/displaystyle({bfv}times{bfB}_0)cdotnabla_vf_0=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2351.png"
 ALT="$\displaystyle ({\bf v}\times{\bf B}_0)\cdot\nabla_v f_0 = 0.$">|; 

$key = q/displaystyle+[delta^{-2}],e,n,({bfE}+{bfV}_etimes{bfB});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1458.png"
 ALT="$\displaystyle + [\delta^{-2}] e  n 
({\bf E} + {\bf V}_e\times {\bf B})$">|; 

$key = q/displaystyle+[zeta^{-1}],nablacdot{bfq}_{Te}+nablacdot{bfq}_{Ue};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1499.png"
 ALT="$\displaystyle + [\zeta^{-1}] \nabla\cdot{\bf q}_{Te} +\nabla\cdot{\bf q}_{Ue}$">|; 

$key = q/displaystyle+delta_e,zeta_e^{-1},widehat{nabla}cdotwidehat{bfq}_{Te}+(1+lambda_e^{2}),delta_e,widehat{nabla}cdotwidehat{bfq}_{Ue};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.79ex; vertical-align: -0.65ex; " SRC="|."$dir".q|img1372.png"
 ALT="$\displaystyle +\delta_e \zeta_e^{-1}  \widehat{\nabla}\cdot\widehat{\bf q}_{Te}
+(1+\lambda_e^{2}) \delta_e \widehat{\nabla}\cdot\widehat{\bf q}_{Ue}$">|; 

$key = q/displaystyle+m,n,{bfg};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1099.png"
 ALT="$\displaystyle + m n {\bf g}$">|; 

$key = q/displaystyle,(;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img327.png"
 ALT="$\displaystyle  ($">|; 

$key = q/displaystyle,,{bfb}cdot(;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img326.png"
 ALT="$\displaystyle   {\bf b}\cdot($">|; 

$key = q/displaystyle,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 0.17ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img504.png"
 ALT="$\displaystyle  $">|; 

$key = q/displaystyle-[delta^{-2}],e,n,({bfE}+{bfV}_itimes{bfB});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1464.png"
 ALT="$\displaystyle - [\delta^{-2}] e  n 
({\bf E} + {\bf V}_i\times {\bf B})$">|; 

$key = q/displaystyle-e,langle{bfu}times(;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img332.png"
 ALT="$\displaystyle -e  \langle {\bf u} \times ($">|; 

$key = q/displaystyle-frac{e}{m_e},{bfE}cdotnabla_vf_e=C_e.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.41ex; vertical-align: -1.96ex; " SRC="|."$dir".q|img1650.png"
 ALT="$\displaystyle -\frac{e}{m_e} {\bf E}\cdot \nabla_v f_e = C_e.
$">|; 

$key = q/displaystyle-frac{partial{bfB}_t}{partialt}+nablatimes({bfV}_ptimes{bfB}_t)=eta,nablatimes{bfj}_p,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2966.png"
 ALT="$\displaystyle -\frac{\partial {\bf B}_t}{\partial t} +\nabla\times({\bf V}_p\times
{\bf B}_t) = \eta \nabla\times {\bf j}_p,$">|; 

$key = q/displaystyle-frac{partial{bfB}}{partialt}+nablatimes({bfV}times{bfB});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2703.png"
 ALT="$\displaystyle -\frac{\partial{\bf B}}{\partial t}+ \nabla\times(
{\bf V} \times {\bf B})$">|; 

$key = q/displaystyle-frac{partial{bfB}}{partialt}+nablatimes({bfV}times{bfB}_0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2706.png"
 ALT="$\displaystyle -\frac{\partial{\bf B}}{\partial t}+ \nabla\times(
{\bf V} \times {\bf B}_0)$">|; 

$key = q/displaystyle-k^2,{mitPhi}=frac{e}{epsilon_0}int!f_1,d^3{bfv},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img2235.png"
 ALT="$\displaystyle -k^2 {\mit\Phi} = \frac{e}{\epsilon_0} \int\! f_1 d^3{\bf v},$">|; 

$key = q/displaystyle-lambda_i,hat{n},(widehat{bfE}+widehat{bfV}_itimeswidehat{bfB});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.57ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1413.png"
 ALT="$\displaystyle -\lambda_i \hat{n} (\widehat{\bf E} + \widehat{\bf V}_i
\times\widehat{\bf B})$">|; 

$key = q/displaystyle-left[frac{partialf_s({bfr},{bfv}_s,t)}{partialt}right]_{ss'}d^3{bfr},d^3{bfv}_s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.58ex; vertical-align: -2.31ex; " SRC="|."$dir".q|img617.png"
 ALT="$\displaystyle -\left[\frac{\partial f_s({\bf r},{\bf v}_s,t)}{\partial t}\right]_{ss'} d^3{\bf r} d^3{\bf v}_s$">|; 

$key = q/displaystyle-omega,rho+rho_0,{bfk}cdot{bfV};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2709.png"
 ALT="$\displaystyle -\omega \rho + \rho_0 {\bf k}\cdot{\bf V}$">|; 

$key = q/displaystyle-omega,rho_0,{bfV}+p,{bfk}-frac{({bfk}times{bfB})times{bfB}_0}{mu_0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img2710.png"
 ALT="$\displaystyle -\omega \rho_0 {\bf V} + p {\bf k} - \frac{ ({\bf k}\times{\bf B})\times
{\bf B}_0}{\mu_0}$">|; 

$key = q/displaystyle-omegaleft(frac{p}{p_0}-frac{{mitGamma},rho}{rho_0}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2712.png"
 ALT="$\displaystyle -\omega\left(\frac{p}{p_0} - \frac{{\mit\Gamma} \rho}{\rho_0}\right)$">|; 

$key = q/displaystyle-{rmi},(omega-{bfk}cdot{bfv}),f_1+{rmi},frac{e}{m_e},{mitPhi},{bfk}cdotnabla_vf_0=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.41ex; vertical-align: -1.96ex; " SRC="|."$dir".q|img2234.png"
 ALT="$\displaystyle -{\rm i} (\omega - {\bf k}\cdot{\bf v})  f_1
+ {\rm i} \frac{e}{m_e} {\mit\Phi}  {\bf k}\cdot\nabla_v f_0 = 0,$">|; 

$key = q/displaystyle-{rmi},omega,m_i,n_e,{bfV};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1688.png"
 ALT="$\displaystyle -{\rm i} \omega m_i  n_e {\bf V}$">|; 

$key = q/displaystyle0leqRleqinfty,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img3112.png"
 ALT="$\displaystyle 0\leq R \leq \infty,$">|; 

$key = q/displaystyle1+frac{1}{(k,lambda_D)^2}-frac{{mitPi}_i^{2}}{omega^{2}}=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img2341.png"
 ALT="$\displaystyle 1 + \frac{1}{(k \lambda_D)^2} - \frac{{\mit\Pi}_i^{2}}{\omega^{2}} = 0,$">|; 

$key = q/displaystyle1+frac{e^2}{epsilon_0,m_e,k^2}intfrac{{bfk}cdotnabla_vf_0}{omega-{bfk}cdot{bfv}},d^3{bfv}=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img2236.png"
 ALT="$\displaystyle 1 + \frac{e^2}{\epsilon_0 m_e k^2} \int\frac{ {\bf k}\cdot\nabla_v f_0}
{\omega - {\bf k}\cdot{\bf v}} d^3{\bf v} = 0.$">|; 

$key = q/displaystyle1+sum_sfrac{2,{mitPi}_s^{2}}{(k_parallel,v_s)^2}left[1+xi_0,Z(xi_0)right]=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.91ex; vertical-align: -2.62ex; " SRC="|."$dir".q|img2517.png"
 ALT="$\displaystyle 1 + \sum_s\frac{2 {\mit\Pi}_s^{2}}{(k_\parallel v_s)^2}\left[1+\xi_0 Z(\xi_0)\right]=0,$">|; 

$key = q/displaystyle1+sum_sfrac{2,{mitPi}_s^{2}}{(k_perp,v_s)^2}left[1-xi_0,{rme}^{-lambda_s}!sum_{n=-infty,infty}frac{I_n(lambda_s)}{xi_n}right]=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.64ex; vertical-align: -2.80ex; " SRC="|."$dir".q|img2518.png"
 ALT="$\displaystyle 1+\sum_s \frac{2 {\mit\Pi}_s^{2}}{(k_\perp v_s)^2}\left[1-\xi_0...
... e}^{-\lambda_s}\!\sum_{n=-\infty,\infty}\frac{I_n(\lambda_s)}{\xi_n}\right]=0,$">|; 

$key = q/displaystyle1-b^{2},z_{rmmax}^{2}-left(frac{k_{ss'}}{E_{ss'}}right)z_{rmmax}=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img711.png"
 ALT="$\displaystyle 1-b^{2} z_{\rm max}^{2}- \left(\frac{k_{ss'}}{E_{ss'}}\right)z_{\rm max}=0.$">|; 

$key = q/displaystyle1-frac{1}{x}-frac{3,y^{2}}{x^2}+{rmi},epsilon(x,y)=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img2651.png"
 ALT="$\displaystyle 1-\frac{1}{x} - \frac{3 y^{2}}{x^2} + {\rm i} \epsilon(x,y) = 0,
$">|; 

$key = q/displaystyle1-frac{Z'(zeta)}{2,(k,lambda_D)^2}=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img2657.png"
 ALT="$\displaystyle 1- \frac{Z'(\zeta) }{2 (k \lambda_D)^2}= 0,
$">|; 

$key = q/displaystyle1-frac{Z'(zeta_e)}{2,(k,lambda_{D,e})^2}-frac{Z'(zeta_i)}{2,(k,lambda_{D,i})^2}=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img2661.png"
 ALT="$\displaystyle 1-\frac{Z'(\zeta_e)}{2 (k \lambda_{D e})^2} - \frac{Z'(\zeta_i)}{2 (k \lambda_{D i})^2} = 0,
$">|; 

$key = q/displaystyle1-frac{{{mitPi}}_e^{2}}{omega^2}-frac{k^2,c^2}{omega^2}=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img1788.png"
 ALT="$\displaystyle 1 - \frac{ {{\mit\Pi}}_e^{2}}{\omega^2} - \frac{k^2 c^2}{\omega^2} = 0.$">|; 

$key = q/displaystyle1-frac{{{mitPi}}_e^{2}}{omega^2}=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img1786.png"
 ALT="$\displaystyle 1- \frac{{{\mit\Pi}}_e^{2}}{\omega^2} = 0.$">|; 

$key = q/displaystyle1-zeta_{rmmax}^{2}-alpha,zeta_{rmmax}=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.51ex; vertical-align: -0.66ex; " SRC="|."$dir".q|img714.png"
 ALT="$\displaystyle 1-\zeta_{\rm max}^{2} -\alpha \zeta_{\rm max} = 0.$">|; 

$key = q/displaystyle10,{rmeV}<T_e,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img843.png"
 ALT="$\displaystyle 10 {\rm eV} &lt;T_e,$">|; 

$key = q/displaystyle1=frac{Z'(zeta_e)}{2,(k,lambda_{D,e})^{2}}+frac{Z'(zeta_i)}{2,(k,lambda_{D,i})^{2}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img2575.png"
 ALT="$\displaystyle 1= \frac{Z'(\zeta_e)}{2 (k \lambda_{D e})^{2}} + \frac{Z'(\zeta_i)}{2 (k \lambda_{D i})^{2}},$">|; 

$key = q/displaystyle1=frac{{mitPi}_e^{2}}{(omega-k,U_e+{rmi},k,v_e)^2}+frac{{mitPi}_i^{2}}{(omega+{rmi},k,v_i)^2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img2563.png"
 ALT="$\displaystyle 1 = \frac{{\mit\Pi}_e^{2}}{(\omega-k U_e + {\rm i} k v_e)^2} + \frac{{\mit\Pi}_i^{2}}{(\omega+{\rm i} k v_i)^2},$">|; 

$key = q/displaystyle2,frac{d^2skew{3}hat{mitPhi}}{dy^2}=-{rme}^{-skew{3}hat{mitPhi}}+left(1+frac{skew{3}hat{mitPhi}}{K}right)^{-1slash2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.02ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1581.png"
 ALT="$\displaystyle 2 \frac{d^2 \skew{3}\hat{\mit\Phi}}{dy^2} = - {\rm e}^{-\skew{3}\hat{\mit\Phi}}+ \left(1+\frac{\skew{3}\hat{\mit\Phi}}{K}\right)^{-1/2},$">|; 

$key = q/displaystyle2={mitPi}_e^{2}left[frac{1}{(k,V-zeta)^{2}}+frac{1}{(k,V+zeta)^{2}}right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2669.png"
 ALT="$\displaystyle 2 = {\mit\Pi}_e^{2}\left[\frac{1}{(k V - \zeta)^{2}}+ \frac{1}{(k V+\zeta)^{2}}\right],
$">|; 

$key = q/displaystyle2pi,e,langle(;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img405.png"
 ALT="$\displaystyle 2\pi e \langle ($">|; 

$key = q/displaystyle:nabla{bfV}+nablacdot{bfq};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1101.png"
 ALT="$\displaystyle :\nabla{\bf V} + \nabla\cdot{\bf q}$">|; 

$key = q/displaystyle=(0,,B_1,,0),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3135.png"
 ALT="$\displaystyle = (0, B_1, 0),$">|; 

$key = q/displaystyle=(0,,B_2,,0).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3136.png"
 ALT="$\displaystyle = (0, B_2, 0).$">|; 

$key = q/displaystyle=(1+2,skew{3}hat{mitPhi})^{-1slash2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1616.png"
 ALT="$\displaystyle = (1+2 \skew{3}\hat{\mit\Phi})^{-1/2},$">|; 

$key = q/displaystyle=(1+2,skew{3}hat{mitPhi})^{1slash2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1614.png"
 ALT="$\displaystyle = (1+2 \skew{3}\hat{\mit\Phi})^{1/2},$">|; 

$key = q/displaystyle=(1+lambda_e^{2}),delta_e,zeta_e,widehat{bfF}_U+delta_e,widehat{bfF}_T,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.79ex; vertical-align: -0.65ex; " SRC="|."$dir".q|img1370.png"
 ALT="$\displaystyle = (1+\lambda_e^{2}) \delta_e \zeta_e \widehat{\bf F}_U + \delta_e
 \widehat{\bf F}_T,$">|; 

$key = q/displaystyle=(B_1,,0,,0),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3089.png"
 ALT="$\displaystyle = (B_1, 0, 0),$">|; 

$key = q/displaystyle=(B_2,,0,,0).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3091.png"
 ALT="$\displaystyle = (B_2, 0, 0).$">|; 

$key = q/displaystyle=(V_1,,0,,0),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3085.png"
 ALT="$\displaystyle = (V_1, 0, 0),$">|; 

$key = q/displaystyle=(V_2,,0,,0),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3087.png"
 ALT="$\displaystyle = (V_2, 0, 0),$">|; 

$key = q/displaystyle=(k,a)^{2slash3},{calS}^{-1slash3},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3684.png"
 ALT="$\displaystyle = (k a)^{2/3} {\cal S}^{-1/3},$">|; 

$key = q/displaystyle=(omega-k_parallel,v_parallel),frac{partialf_{0,s}}{partialv_perp}+k_parallel,v_perp,frac{partialf_{0,s}}{partialv_parallel},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.19ex; vertical-align: -2.19ex; " SRC="|."$dir".q|img2401.png"
 ALT="$\displaystyle =(\omega-k_\parallel v_\parallel) \frac{\partial f_{0 s}}{\par...
..._\perp}
+ k_\parallel v_\perp \frac{\partial f_{0 s}}{\partial v_\parallel},$">|; 

$key = q/displaystyle=(v_{1}^{2}-r,cos^2theta_1,V_{A,1}^{2})^{2}left(left[({mitGamma}+1)-({mitGamma}-1),rright]v_{1}^{2}-2,r,V_{S,1}^{2}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.23ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img3169.png"
 ALT="$\displaystyle =(v_{1}^{2}-r \cos^2\theta_1 V_{A 1}^{2})^{2}\left(
\left[({\mit\Gamma}+1)-({\mit\Gamma}-1) r\right]
v_{1}^{2}- 2 r V_{S 1}^{2}\right)$">|; 

$key = q/displaystyle=-(1+lambda_i^{2}),delta_i,zeta_i,mu,widehat{bfF}_U-delta_i,widehat{bfF}_T,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.79ex; vertical-align: -0.65ex; " SRC="|."$dir".q|img1414.png"
 ALT="$\displaystyle = -(1+\lambda_i^{2}) \delta_i \zeta_i \mu \widehat{\bf F}_U
- \delta_i
 \widehat{\bf F}_T,$">|; 

$key = q/displaystyle=-0.71,n,nabla_parallelT_e-frac{3,n}{2,|{mitOmega}_e|,tau_e},{bfb}timesnabla_perpT_e.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.98ex; " SRC="|."$dir".q|img1295.png"
 ALT="$\displaystyle = - 0.71 n \nabla_\parallel T_e
-\frac{3 n}{2 \vert{\mit\Omega}_e\vert \tau_e} {\bf b}\times\nabla_\perp T_e.$">|; 

$key = q/displaystyle=-2,c^2,{bfk},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img2136.png"
 ALT="$\displaystyle = - 2 c^2 {\bf k},$">|; 

$key = q/displaystyle=-2,pi^{1slash2},zeta,{rme}^{-zeta^{2}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.73ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2623.png"
 ALT="$\displaystyle = -2 \pi^{1/2} \zeta {\rm e}^{-\zeta^{2}}.$">|; 

$key = q/displaystyle=-4pi,f_{s'}({bfv}),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img811.png"
 ALT="$\displaystyle = -4\pi f_{s'}({\bf v}),$">|; 

$key = q/displaystyle=-4pi,v^{2},f_{s'}(v),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img895.png"
 ALT="$\displaystyle =-4\pi v^{2} f_{s'}(v),$">|; 

$key = q/displaystyle=-A+{rmi},frac{pi}{2},{rmsgn}(epsilon),D=-A-{rmi},{rmsgn}(epsilon),B,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.01ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img2012.png"
 ALT="$\displaystyle = -A +{\rm i} \frac{\pi}{2} {\rm sgn}(\epsilon) D = -A - {\rm i} 
{\rm sgn}(\epsilon) B,$">|; 

$key = q/displaystyle=-A,sin(k,z-omega,t).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1764.png"
 ALT="$\displaystyle = -A \sin (k z-\omega  t).$">|; 

$key = q/displaystyle=-B(r_0,theta,phi_0),frac{{mitOmega},r_0}{u_s},frac{r_0}{r},sintheta.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img2831.png"
 ALT="$\displaystyle = - B(r_0,\theta,\phi_0) \frac{{\mit\Omega} r_0}{u_s}
 \frac{r_0}{r} \sin\theta.$">|; 

$key = q/displaystyle=-B_0,a,lnleft[coshleft(frac{x}{a}right)right]+psi_1(x),{rme}^{,{rmi},k,y+gamma,t},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.35ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img3291.png"
 ALT="$\displaystyle = -B_0 a \ln\left[\cosh\left(\frac{x}{a}\right)\right] + \psi_1(x) {\rm e}^{ {\rm i} k y+\gamma t},$">|; 

$key = q/displaystyle=-Fleft(frac{d^2}{dhat{x}^2}-hat{k}^2-frac{F''}{F}right)hat{psi},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3318.png"
 ALT="$\displaystyle = - F\left(\frac{d^2}{d\hat{x}^2}
-\hat{k}^2-\frac{F''}{F}\right)\hat{\psi},$">|; 

$key = q/displaystyle=-R',J,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img2910.png"
 ALT="$\displaystyle = - R' J,$">|; 

$key = q/displaystyle=-T_e,frac{dn_e}{dx}+e,n_e,frac{d{mitPhi}}{dx},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1557.png"
 ALT="$\displaystyle = - T_e \frac{dn_e}{dx} + e n_e \frac{d{\mit\Phi}}{dx},$">|; 

$key = q/displaystyle=-T_i,frac{dn_i}{dx}-e,n_i,frac{d{mitPhi}}{dx},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1555.png"
 ALT="$\displaystyle = - T_i \frac{dn_i}{dx} - e n_i \frac{d{\mit\Phi}}{dx},$">|; 

$key = q/displaystyle=-[delta^{-1},zeta,mu^2],w_i,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1448.png"
 ALT="$\displaystyle = -[\delta^{-1} \zeta \mu^2] w_i,$">|; 

$key = q/displaystyle=-[delta^{-2},zeta,mu^2],w_i+[zeta],w_U+w_T,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1461.png"
 ALT="$\displaystyle =-[\delta^{-2} \zeta \mu^2]  w_i
+[\zeta] w_U + w_T,$">|; 

$key = q/displaystyle=-[delta^{-2},zeta],{bfF}_U-[delta^{-2}],{bfF}_T,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1465.png"
 ALT="$\displaystyle = -[\delta^{-2} \zeta]  {\bf F}_U - [\delta^{-2}] {\bf F}_T,$">|; 

$key = q/displaystyle=-[zeta],{bfF}_U-{bfF}_T,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1450.png"
 ALT="$\displaystyle =- [\zeta] {\bf F}_U
-{\bf F}_T,$">|; 

$key = q/displaystyle=-[zeta],{bfF}_U.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1440.png"
 ALT="$\displaystyle =- [\zeta] {\bf F}_U.$">|; 

$key = q/displaystyle=-delta_e^{-1},zeta_e,mu^2,widehat{w}_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.51ex; vertical-align: -0.65ex; " SRC="|."$dir".q|img1373.png"
 ALT="$\displaystyle = -\delta_e^{-1} \zeta_e \mu^2 \widehat{w}_i$">|; 

$key = q/displaystyle=-e,(n-n_0).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1903.png"
 ALT="$\displaystyle = - e (n-n_0).$">|; 

$key = q/displaystyle=-e,n,{bfE}-nablap,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1899.png"
 ALT="$\displaystyle =-e n {\bf E}-\nabla p,$">|; 

$key = q/displaystyle=-frac{1}{2,T},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img877.png"
 ALT="$\displaystyle = -\frac{1}{2 T},$">|; 

$key = q/displaystyle=-frac{1}{pi}left[1-left(ln|hat{z}|+2,gamma-1right)hat{z},right]+{calO}left(hat{z}^{2}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img2009.png"
 ALT="$\displaystyle = -\frac{1}{\pi}\left[
1 -\left(\ln\vert\hat{z}\vert + 2 \gamma-1\right)\hat{z} \right]+ {\cal O}\left(\hat{z}^{2}\right),$">|; 

$key = q/displaystyle=-frac{2}{pi},B,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img2013.png"
 ALT="$\displaystyle = - \frac{2}{\pi} B,$">|; 

$key = q/displaystyle=-frac{B_0}{a},cosh^{-2}left(frac{x}{a}right)+J_1(x),{rme}^{,{rmi},k,y+gamma,t},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img3293.png"
 ALT="$\displaystyle = -\frac{B_0}{a} \cosh^{-2}\left(\frac{x}{a}\right)+J_1(x) {\rm e}^{ {\rm i} k y+\gamma t},$">|; 

$key = q/displaystyle=-frac{e,B_0}{m_e},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.85ex; vertical-align: -1.96ex; " SRC="|."$dir".q|img1695.png"
 ALT="$\displaystyle = -\frac{e B_0}{m_e},$">|; 

$key = q/displaystyle=-frac{n,T_e}{2,|{mitOmega}_e|},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.98ex; " SRC="|."$dir".q|img1285.png"
 ALT="$\displaystyle = -\frac{n T_e}{2 \vert{\mit\Omega}_e\vert} ,$">|; 

$key = q/displaystyle=-frac{nabla{mitPi}_e^{2}}{2,omega},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img2141.png"
 ALT="$\displaystyle = - \frac{\nabla{\mit\Pi}_e^{2}}{2 \omega},$">|; 

$key = q/displaystyle=-frac{partial{bfB}}{partialt},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2684.png"
 ALT="$\displaystyle = - \frac{\partial{\bf B}}{\partial t},$">|; 

$key = q/displaystyle=-frac{partial{calM}slashpartialt}{partial{calM}slashpartialomega}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img2129.png"
 ALT="$\displaystyle =-\frac{\partial{\cal M}/\partial t }
{\partial{\cal M}/\partial\omega}.$">|; 

$key = q/displaystyle=-frac{partial{calM}slashpartial{bfk}}{partial{calM}slashpartialomega},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img2127.png"
 ALT="$\displaystyle =-\frac{\partial{\cal M}/\partial {\bf k} }
{\partial{\cal M}/\partial\omega},$">|; 

$key = q/displaystyle=-frac{v_perp}{{mitOmega}},left(sinleft[{mitOmega},(t-t')+theta,right]-sinthetaright),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.01ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img2372.png"
 ALT="$\displaystyle = -\frac{v_\perp}{{\mit\Omega}} \left(\sin\left[{\mit\Omega} (t-t')
+\theta \right] -\sin\theta\right),$">|; 

$key = q/displaystyle=-frac{{mitPi}_i^{2}}{omega^2}-frac{{mitPi}_e^{2}}{omega^2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img1880.png"
 ALT="$\displaystyle = -\frac{{\mit\Pi}_i^{2}}{\omega^2} - \frac{{\mit\Pi}_e^{2}}{\omega^2}.$">|; 

$key = q/displaystyle=-hat{x},frac{d^2hat{psi}}{dhat{x}^2}+hat{gamma},S^{-1},P,frac{d^4skew{3}hat{phi}}{dhat{x}^{4}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3744.png"
 ALT="$\displaystyle = -\hat{x} \frac{d^2\hat{\psi}}{d\hat{x}^2}+ \hat{\gamma} S^{-1} P \frac{d^4\skew{3}\hat{\phi}}{d\hat{x}^{4}}.$">|; 

$key = q/displaystyle=-hat{x},frac{d^2hat{psi}}{dhat{x}^2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3340.png"
 ALT="$\displaystyle = -\hat{x} \frac{d^2\hat{\psi}}{d\hat{x}^2}.$">|; 

$key = q/displaystyle=-hat{z}+{calO}left(hat{z}^{2}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.23ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img2007.png"
 ALT="$\displaystyle = - \hat{z} + {\cal O}\left(\hat{z}^{2}\right),$">|; 

$key = q/displaystyle=-intC_{ss'},d^3{bfv}_s,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img654.png"
 ALT="$\displaystyle = - \int C_{ss'} d^3{\bf v}_s,$">|; 

$key = q/displaystyle=-intfrac{1}{2},m_{s'},v_{s'}^{2},C_{s's},d^3{bfv}_{s'}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img1004.png"
 ALT="$\displaystyle =- \int\frac{1}{2} m_{s'} v_{s'}^{2} C_{s's} d^3{\bf v}_{s'}.$">|; 

$key = q/displaystyle=-intm_{s'},{bfv}_{s'},C_{s's},d^3{bfv}_{s'},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img1002.png"
 ALT="$\displaystyle = -\int m_{s'} {\bf v}_{s'} C_{s's} d^3{\bf v}_{s'},$">|; 

$key = q/displaystyle=-k_{ss'},frac{{bfr}_{ss'}}{|{bfr}_{ss'}|^{3}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.98ex; " SRC="|."$dir".q|img667.png"
 ALT="$\displaystyle = -k_{ss'} \frac{{\bf r}_{ss'}}{\vert{\bf r}_{ss'}\vert^{3}},$">|; 

$key = q/displaystyle=-kappa_parallel^e,nablaT_e-0.71,frac{T_e}{e},{bfj},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img1197.png"
 ALT="$\displaystyle = -\kappa_\parallel^e \nabla T_e -
0.71 \frac{T_e}{e} {\bf j},$">|; 

$key = q/displaystyle=-kappa_parallel^e,nabla_parallelT_e-kappa_perp^e,nabla_perpT_e-kappa_times^e,{bfb}timesnabla_perpT_e,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.94ex; " SRC="|."$dir".q|img1309.png"
 ALT="$\displaystyle =-\kappa_\parallel^e \nabla_\parallel T_e -\kappa_\perp^e 
\nabla_\perp T_e
-\kappa_\times^e {\bf b}\times\nabla_\perp T_e,$">|; 

$key = q/displaystyle=-kappa_parallel^i,nablaT_i,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.79ex; vertical-align: -0.94ex; " SRC="|."$dir".q|img1199.png"
 ALT="$\displaystyle = -\kappa_\parallel^i \nabla T_i,$">|; 

$key = q/displaystyle=-kappa_parallel^i,nabla_parallelT_i-kappa_perp^i,nabla_perpT_i+kappa_times^i,{bfb}timesnabla_perpT_i,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.79ex; vertical-align: -0.94ex; " SRC="|."$dir".q|img1240.png"
 ALT="$\displaystyle = -\kappa_\parallel^i \nabla_\parallel T_i -\kappa_\perp^i 
\nabla_\perp T_i
+\kappa_\times^i {\bf b}\times\nabla_\perp T_i,$">|; 

$key = q/displaystyle=-left(frac{2,{bfl}}{u_{ss'}^{2}}right)_alpha.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.69ex; vertical-align: -2.51ex; " SRC="|."$dir".q|img777.png"
 ALT="$\displaystyle = - \left(\frac{2 {\bf l}}{u_{ss'}^{2}}\right)_\alpha.$">|; 

$key = q/displaystyle=-left[{rme}^{-skew{3}hat{mitPhi}}+(1+2,skew{3}hat{mitPhi})^{1slash2}-2right]^{1slash2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.74ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img1610.png"
 ALT="$\displaystyle = -\left[{\rm e}^{-\skew{3}\hat{\mit\Phi}}+(1+2 \skew{3}\hat{\mit\Phi})^{1/2}-2\right]^{1/2},$">|; 

$key = q/displaystyle=-n_{s'},F_1(zeta),frac{v_alpha}{v^{3}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img911.png"
 ALT="$\displaystyle = - n_{s'} F_1(\zeta) \frac{v_\alpha}{v^{3}},$">|; 

$key = q/displaystyle=-nabla{mitOmega},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img2124.png"
 ALT="$\displaystyle = -\nabla{\mit\Omega},$">|; 

$key = q/displaystyle=-nabla{mitPi}_e^{2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.51ex; vertical-align: -0.65ex; " SRC="|."$dir".q|img2138.png"
 ALT="$\displaystyle = -\nabla{\mit\Pi}_e^{2},$">|; 

$key = q/displaystyle=-w_i+frac{{bfj}cdot{bfF}}{n,e}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img1224.png"
 ALT="$\displaystyle = -w_i + \frac{ {\bf j}\cdot {\bf F} }{n  e}.$">|; 

$key = q/displaystyle=-w_i+frac{{bfj}cdot{bfF}}{n,e}=-w_i+frac{j^{2}}{sigma_parallel}-0.71,frac{{bfj}cdotnablaT_e}{e}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.19ex; " SRC="|."$dir".q|img1162.png"
 ALT="$\displaystyle = -w_i + \frac{ {\bf j}\cdot {\bf F} }{n  e}= -w_i +
\frac{j^{2}}{\sigma_\parallel} -
0.71 \frac{{\bf j}\cdot \nabla T_e}{e}.$">|; 

$key = q/displaystyle=-w_i+w_U+w_T.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1314.png"
 ALT="$\displaystyle = -w_i+w_U + w_T.$">|; 

$key = q/displaystyle=-{bfF},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img1152.png"
 ALT="$\displaystyle =- {\bf F},$">|; 

$key = q/displaystyle=-{bfF}_U-{bfF}_T,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1380.png"
 ALT="$\displaystyle =- {\bf F}_U -{\bf F}_T,$">|; 

$key = q/displaystyle=-{bfV}times{bfB}_0+frac{{bfj}times{bfB}_0}{n_e,e}+frac{m_e}{n_e,e^2}frac{partial{bfj}}{partialt},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.96ex; " SRC="|."$dir".q|img1687.png"
 ALT="$\displaystyle = - {\bf V}\times{\bf B}_0 +\frac{{\bf j}\times{\bf B}_0}{n_e e}
+\frac{m_e}{n_e e^2}\frac{\partial{\bf j}}{\partial t},$">|; 

$key = q/displaystyle=-{bfV}times{bfB}_0+frac{{bfj}times{bfB}_0}{n_e,e}-{rmi},frac{omega,m_e}{n_e,e^2},{bfj}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.96ex; " SRC="|."$dir".q|img1689.png"
 ALT="$\displaystyle = - {\bf V}\times{\bf B}_0 +\frac{{\bf j}\times{\bf B}_0}{n_e e}
-{\rm i} \frac{\omega m_e}{n_e e^2} {\bf j}.$">|; 

$key = q/displaystyle=-{mitOmega},r,sintheta,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img2818.png"
 ALT="$\displaystyle = - {\mit\Omega} r \sin\theta,$">|; 

$key = q/displaystyle=-{rmi},(m,{mitOmega}-k,U),B_r;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2981.png"
 ALT="$\displaystyle = -{\rm i} (m {\mit\Omega}-k  U) B_r$">|; 

$key = q/displaystyle=-{rmi},k_0,n^2,{bfE},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2174.png"
 ALT="$\displaystyle = -{\rm i} k_0 n^2 {\bf E},$">|; 

$key = q/displaystyle=-{rmi},mu_0,{bfj}-frac{omega}{c^2},{bfE},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img1672.png"
 ALT="$\displaystyle = - {\rm i} \mu_0 {\bf j} - \frac{\omega}{c^2} {\bf E},$">|; 

$key = q/displaystyle=-{rmi},mu_0,{bfj}-frac{omega}{c^2},{bfE}=-frac{omega}{c^2},{bfK}cdot{bfE},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img2394.png"
 ALT="$\displaystyle = -{\rm i} \mu_0 {\bf j} - \frac{\omega}{c^2} {\bf E}
=-\frac{\omega}{c^2} {\bf K}\cdot{\bf E},$">|; 

$key = q/displaystyle=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img682.png"
 ALT="$\displaystyle =0,$">|; 

$key = q/displaystyle=0.51,frac{n,T_e}{{mitOmega}_e^{2},tau_e},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.18ex; " SRC="|."$dir".q|img1279.png"
 ALT="$\displaystyle = 0.51  \frac{n T_e}{{\mit\Omega}_e^{2} \tau_e},$">|; 

$key = q/displaystyle=0.71,frac{T_e}{e},{bfj}_parallel-frac{3,T_e}{2,|{mitOmega}_e|,tau_e,e},{bfb}times{bfj}_perp.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.98ex; " SRC="|."$dir".q|img1311.png"
 ALT="$\displaystyle = 0.71 \frac{T_e}{e} {\bf j}_\parallel-
\frac{3 T_e}{2 \vert{\mit\Omega}_e\vert \tau_e e} {\bf b}\times{\bf j}_\perp.$">|; 

$key = q/displaystyle=0.73,n,tau_e,T_e,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1217.png"
 ALT="$\displaystyle = 0.73 n \tau_e T_e,$">|; 

$key = q/displaystyle=0.96,n,tau_i,T_i,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1219.png"
 ALT="$\displaystyle = 0.96 n \tau_i T_i,$">|; 

$key = q/displaystyle=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1102.png"
 ALT="$\displaystyle = 0.$">|; 

$key = q/displaystyle=1+frac{{mitPi}_i^{2}}{{mitOmega}_i^{2}}+frac{{mitPi}_e^{2}}{{mitOmega}_e^{2}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.43ex; " SRC="|."$dir".q|img1879.png"
 ALT="$\displaystyle = 1+\frac{{\mit\Pi}_i^{2}}{{\mit\Omega}_i^{2}}+ \frac{{\mit\Pi}_e^{2}}{{\mit\Omega}_e^{2}},$">|; 

$key = q/displaystyle=1+hat{J},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img3486.png"
 ALT="$\displaystyle = 1 + \hat{J},$">|; 

$key = q/displaystyle=1+{mitGamma},M_1^{2},(1-r^{-1})=frac{({mitGamma}+1),r-({mitGamma}-1)}{({mitGamma}+1)-({mitGamma}-1),r}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img3101.png"
 ALT="$\displaystyle = 1+ {\mit \Gamma} M_1^{2} (1-r^{-1})= \frac{({\mit \Gamma}+1) r-({\mit\Gamma}-1)}{({\mit\Gamma}+1)-({\mit\Gamma}-1) r}.$">|; 

$key = q/displaystyle=1,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img3093.png"
 ALT="$\displaystyle = 1,$">|; 

$key = q/displaystyle=1-frac{{{mitPi}}_e^{2}}{omega^2}-frac{{{mitPi}}_i^{2}}{omega^2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img1728.png"
 ALT="$\displaystyle = 1 - \frac{{{\mit\Pi}}_e^{2}}{\omega^2}-\frac{{{\mit\Pi}}_i^{2}}{\omega^2}.$">|; 

$key = q/displaystyle=1-sum_sfrac{{mitPi}_s^{2}}{(k_parallel,v_s)^2},,Z'left(frac{omega}{k_parallel,v_s}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.91ex; vertical-align: -2.62ex; " SRC="|."$dir".q|img2448.png"
 ALT="$\displaystyle = 1 - \sum_s \frac{{\mit\Pi}_s^{2}}
{(k_\parallel v_s)^2}   Z'\left(\frac{\omega}{k_\parallel v_s}\right),$">|; 

$key = q/displaystyle=1-sum_sfrac{{mitPi}_s^{2}}{omega^2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.91ex; vertical-align: -2.62ex; " SRC="|."$dir".q|img2437.png"
 ALT="$\displaystyle = 1-\sum_s\frac{{\mit\Pi}_s^{2}}{\omega^2},$">|; 

$key = q/displaystyle=1.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3501.png"
 ALT="$\displaystyle = 1.$">|; 

$key = q/displaystyle=2,H_{s'}({bfv}),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img813.png"
 ALT="$\displaystyle = 2 H_{s'}({\bf v}),$">|; 

$key = q/displaystyle=2,frac{n,T_i}{m_i,{mitOmega}_i^{2},tau_i}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.30ex; vertical-align: -2.43ex; " SRC="|."$dir".q|img1244.png"
 ALT="$\displaystyle = 2  \frac{n T_i}{m_i {\mit\Omega}_i^{2} \tau_i}.$">|; 

$key = q/displaystyle=2,omega,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img2134.png"
 ALT="$\displaystyle = 2 \omega,$">|; 

$key = q/displaystyle=2,v^{2},H_{s'}(v).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img897.png"
 ALT="$\displaystyle =2 v^{2} H_{s'}(v).$">|; 

$key = q/displaystyle=2,v_{t,{s'}}^{2},zeta,H_{s'}(zeta),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.51ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img901.png"
 ALT="$\displaystyle =2 v_{t {s'}}^{2} \zeta H_{s'}(\zeta),$">|; 

$key = q/displaystyle=23-lnleft(n_e^{1slash2},T_e^{-3slash2}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.23ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img844.png"
 ALT="$\displaystyle =23 - \ln\left(n_e^{1/2} T_e^{-3/2}\right)$">|; 

$key = q/displaystyle=24-lnleft(n_e^{1slash2},T_e^{-1}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.23ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img842.png"
 ALT="$\displaystyle = 24 - \ln\left(n_e^{1/2} T_e^{-1}\right)$">|; 

$key = q/displaystyle=2sqrt{a,hat{z}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img1990.png"
 ALT="$\displaystyle =2\sqrt{a \hat{z}},$">|; 

$key = q/displaystyle=2sqrt{hat{z}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img1982.png"
 ALT="$\displaystyle = 2\sqrt{\hat{z}},$">|; 

$key = q/displaystyle=3.2,,frac{n,tau_e,T_e}{m_e},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.85ex; vertical-align: -1.96ex; " SRC="|."$dir".q|img1201.png"
 ALT="$\displaystyle = 3.2  \frac{n \tau_e T_e}{m_e},$">|; 

$key = q/displaystyle=3.9,,frac{n,tau_i,T_i}{m_i},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.85ex; vertical-align: -1.96ex; " SRC="|."$dir".q|img1203.png"
 ALT="$\displaystyle = 3.9  \frac{n \tau_i T_i}{m_i},$">|; 

$key = q/displaystyle=4.7,frac{n,T_e}{m_e,{mitOmega}_e^{2},tau_e},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.18ex; " SRC="|."$dir".q|img1242.png"
 ALT="$\displaystyle = 4.7 \frac{n T_e}{m_e {\mit\Omega}_e^{2} \tau_e},$">|; 

$key = q/displaystyle=;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 0.61ex; vertical-align: 0.21ex; " SRC="|."$dir".q|img254.png"
 ALT="$\displaystyle =$">|; 

$key = q/displaystyle=A',left[{rmsgn}(epsilon)+1right],hat{z}^{1slash4},expleft[+{rmi}left(2sqrt{hat{z}}-frac{3}{4},piright)right];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2028.png"
 ALT="$\displaystyle = A' \left[{\rm sgn}(\epsilon) + 1\right] \hat{z}^{1/4} 
\exp\left[
+{\rm i}\left(2\sqrt{\hat{z}} - \frac{3}{4} \pi\right)\right]$">|; 

$key = q/displaystyle=A,cos(k,z-omega,t),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1762.png"
 ALT="$\displaystyle =A \cos(k z-\omega  t),$">|; 

$key = q/displaystyle=B(r_0,theta,phi_0)left(frac{r_0}{r}right)^2,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.74ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img2828.png"
 ALT="$\displaystyle = B(r_0,\theta,\phi_0)\left(\frac{r_0}{r}\right)^2,$">|; 

$key = q/displaystyle=B_0,tanhleft(frac{x}{a}right),{bfe}_y,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.29ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img3276.png"
 ALT="$\displaystyle = B_0 \tanh\left(\frac{x}{a}\right) {\bf e}_y,$">|; 

$key = q/displaystyle=B_rpm{rmi},B_theta,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2990.png"
 ALT="$\displaystyle = B_r \pm {\rm i} B_\theta,$">|; 

$key = q/displaystyle=B_t(varpi,z,t),{bfe}_theta,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2946.png"
 ALT="$\displaystyle = B_t(\varpi,z,t) {\bf e}_\theta,$">|; 

$key = q/displaystyle=B_x(z),exp(-{rmi},omega,t),{bfe}_x,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.58ex; " SRC="|."$dir".q|img2179.png"
 ALT="$\displaystyle = B_x(z) \exp(-{\rm i} \omega t) {\bf e}_x,$">|; 

$key = q/displaystyle=B_x(z),{rme}^{,{rmi},(k_x,x-omega,t)},{bfe}_x+B_z(z),{rme}^{,{rmi},(k_x,x-omega,t)},{bfe}_z,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2183.png"
 ALT="$\displaystyle = B_x(z) {\rm e}^{ {\rm i} (k_x x-\omega t)} {\bf e}_x + B_z(z) {\rm e}^{ {\rm i} (k_x x-\omega t)} {\bf e}_z,$">|; 

$key = q/displaystyle=B_y(z),{rme}^{,{rmi},(k_x,x-omega,t)},{bfe}_y,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.68ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2192.png"
 ALT="$\displaystyle = B_y(z) {\rm e}^{ {\rm i} (k_x x-\omega t)} {\bf e}_y,$">|; 

$key = q/displaystyle=E_x(z),{rme}^{,{rmi},(k_x,x-omega,t)},{bfe}_x+E_z(z),{rme}^{,{rmi},(k_x,x-omega,t)},{bfe}_z,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2191.png"
 ALT="$\displaystyle = E_x(z) {\rm e}^{ {\rm i} (k_x x-\omega t)} {\bf e}_x+E_z(z) {\rm e}^{ {\rm i} (k_x x-\omega t)} {\bf e}_z,$">|; 

$key = q/displaystyle=E_y(z),exp(-{rmi},omega,t),{bfe}_y,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2177.png"
 ALT="$\displaystyle = E_y(z) \exp(-{\rm i} \omega t) {\bf e}_y,$">|; 

$key = q/displaystyle=E_y(z),{rme}^{,{rmi},(k_x,x-omega,t)},{bfe}_y,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.68ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2182.png"
 ALT="$\displaystyle = E_y(z) {\rm e}^{ {\rm i} (k_x x-\omega t)} {\bf e}_y,$">|; 

$key = q/displaystyle=I,A,{bfn},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img337.png"
 ALT="$\displaystyle = I A {\bf n},$">|; 

$key = q/displaystyle=I,pi,rho^2,{bfb}=frac{m,u_perp^{2}}{2,B},{bfb}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.85ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img341.png"
 ALT="$\displaystyle = I \pi \rho^2 {\bf b} = \frac{m u_\perp^{2}}{2 B} {\bf b}.$">|; 

$key = q/displaystyle=K_{22}=1-frac{1}{2}sum_sfrac{{mitPi}_s^{2}}{omega^2}left(frac{omega}{omega-{mitOmega}_s}+frac{omega}{omega+{mitOmega}_s}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.91ex; vertical-align: -2.62ex; " SRC="|."$dir".q|img2433.png"
 ALT="$\displaystyle = K_{22} = 1-\frac{1}{2}\sum_s\frac{{\mit\Pi}_s^{2}}{\omega^2}
\l...
...\omega}{\omega-{\mit\Omega}_s} +
\frac{\omega}{\omega + {\mit\Omega}_s}\right),$">|; 

$key = q/displaystyle=L,I+M,J,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img2904.png"
 ALT="$\displaystyle = L I + M  J,$">|; 

$key = q/displaystyle=L,nabla,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img1334.png"
 ALT="$\displaystyle = L \nabla,$">|; 

$key = q/displaystyle=L.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1757.png"
 ALT="$\displaystyle = L.$">|; 

$key = q/displaystyle=M,I+L',J,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img2906.png"
 ALT="$\displaystyle = M I + L' J,$">|; 

$key = q/displaystyle=P,R,L.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1749.png"
 ALT="$\displaystyle = P R L.$">|; 

$key = q/displaystyle=P.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1760.png"
 ALT="$\displaystyle = P.$">|; 

$key = q/displaystyle=R,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img1756.png"
 ALT="$\displaystyle = R,$">|; 

$key = q/displaystyle=R,L,sin^2theta+P,S,(1+cos^2theta),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1747.png"
 ALT="$\displaystyle = R L \sin^2\theta + P S (1+\cos^2\theta),$">|; 

$key = q/displaystyle=S,sin^2theta+P,cos^2theta,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img1745.png"
 ALT="$\displaystyle = S \sin^2\theta + P \cos^2\theta,$">|; 

$key = q/displaystyle=U_1(x),{rme}^{,{rmi},k,y+gamma,t},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3297.png"
 ALT="$\displaystyle = U_1(x) {\rm e}^{ {\rm i} k y+\gamma t},$">|; 

$key = q/displaystyle=V_sleft[1-frac{2,e}{m_i,V_s^{,2}},({mitPhi}-{mitPhi}_s)right]^{1slash2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1569.png"
 ALT="$\displaystyle = V_s\left[1- \frac{2 e}{m_i V_s^{ 2}} ({\mit\Phi}-{\mit\Phi}_s)\right]^{1/2},$">|; 

$key = q/displaystyle=V_t(varpi,z,t),{bfe}_theta.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2948.png"
 ALT="$\displaystyle = V_t(\varpi,z,t) {\bf e}_\theta.$">|; 

$key = q/displaystyle=[delta^{-1},zeta,mu^2],w_i.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1452.png"
 ALT="$\displaystyle =[\delta^{-1} \zeta \mu^2]  w_i.$">|; 

$key = q/displaystyle=[delta^{-2},zeta,mu^2],W_i.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1467.png"
 ALT="$\displaystyle = [\delta^{-2} \zeta \mu^2] W_i.$">|; 

$key = q/displaystyle=[delta^{-2},zeta,mu^2],w_i.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1502.png"
 ALT="$\displaystyle = [\delta^{-2} \zeta \mu^2] w_i.$">|; 

$key = q/displaystyle=[delta^{-2},zeta],{bfF}_U+[delta^{-2}],{bfF}_T,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1459.png"
 ALT="$\displaystyle =[\delta^{-2} \zeta]  {\bf F}_U + [\delta^{-2}] 
{\bf F}_T,$">|; 

$key = q/displaystyle=[phi,psi]+frac{eta}{mu_0},(J-J_0),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img3264.png"
 ALT="$\displaystyle = [\phi,\psi]+\frac{\eta}{\mu_0} (J-J_0),$">|; 

$key = q/displaystyle=[zeta],{bfF}_U+{bfF}_T,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1446.png"
 ALT="$\displaystyle = [\zeta] {\bf F}_U + {\bf F}_T,$">|; 

$key = q/displaystyle=[zeta],{bfF}_U,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1438.png"
 ALT="$\displaystyle = [\zeta] {\bf F}_U,$">|; 

$key = q/displaystyle=c,S,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img2153.png"
 ALT="$\displaystyle = c S,$">|; 

$key = q/displaystyle=cos^2theta_1,V_{A,1}^{2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.66ex; " SRC="|."$dir".q|img3174.png"
 ALT="$\displaystyle = \cos^2\theta_1 V_{A 1}^{2},$">|; 

$key = q/displaystyle=delta_i^{-1},zeta_i,mu,widehat{w}_i.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.51ex; vertical-align: -0.65ex; " SRC="|."$dir".q|img1416.png"
 ALT="$\displaystyle = \delta_i^{-1} \zeta_i \mu \widehat{w}_i.$">|; 

$key = q/displaystyle=delta_{alphabeta}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img799.png"
 ALT="$\displaystyle = \delta_{\alpha\beta}.$">|; 

$key = q/displaystyle=eta,{bfj}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3244.png"
 ALT="$\displaystyle =\eta {\bf j}.$">|; 

$key = q/displaystyle=frac{({bfk}cdot{bfV}),{bfB}_0-({bfk}cdot{bfB}_0),{bfV}}{omega}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img2718.png"
 ALT="$\displaystyle = \frac{ ({\bf k}\cdot{\bf V}) {\bf B}_0
- ({\bf k}\cdot{\bf B}_0) {\bf V}}{\omega}.$">|; 

$key = q/displaystyle=frac{({mitGamma}+1),M_1^{2}}{2+({mitGamma}-1),M_1^{2}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.80ex; vertical-align: -2.44ex; " SRC="|."$dir".q|img3100.png"
 ALT="$\displaystyle = \frac{({\mit \Gamma}+1) M_1^{2}}{2+({\mit\Gamma}-1) M_1^{2}},$">|; 

$key = q/displaystyle=frac{({rmi},E_xslashE_y)-({mitOmega}_eslashomega)}{1-({mitOmega}_eslashomega),({rmi},E_xslashE_y)}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.26ex; " SRC="|."$dir".q|img1884.png"
 ALT="$\displaystyle = \frac{({\rm i} E_x/E_y)-({\mit\Omega}_e/\omega)}{1-({\mit\Omega}_e/\omega) ({\rm i} E_x/E_y)}.$">|; 

$key = q/displaystyle=frac{({rmi},E_xslashE_y)-({mitOmega}_islashomega)}{1-({mitOmega}_islashomega),({rmi},E_xslashE_y)},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.26ex; " SRC="|."$dir".q|img1882.png"
 ALT="$\displaystyle = \frac{({\rm i} E_x/E_y)- ({\mit\Omega}_i/\omega)}{1-({\mit\Omega}_i/\omega) ({\rm i} E_x/E_y)},$">|; 

$key = q/displaystyle=frac{1}{2,xi,(1+xi)^{1slash2}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img949.png"
 ALT="$\displaystyle = \frac{1}{2 \xi (1+\xi)^{1/2}}.$">|; 

$key = q/displaystyle=frac{1}{2,xi,(1+xi)^{3slash2}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img947.png"
 ALT="$\displaystyle = \frac{1}{2 \xi (1+\xi)^{3/2}},$">|; 

$key = q/displaystyle=frac{1}{2},{rme}^{-s^2slash2},I_n(s^2slash2),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img2410.png"
 ALT="$\displaystyle =\frac{1}{2}  {\rm e}^{-s^2/2} I_n(s^2/2),$">|; 

$key = q/displaystyle=frac{1}{2}left[1-left(ln|hat{z}|+2,gamma-1right)hat{z}-{rmi},{rmarg}(a),hat{z},right]+{calO}left(hat{z}^{2}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img2011.png"
 ALT="$\displaystyle = \frac{1}{2}\left[
1 -\left( \ln\vert\hat{z}\vert + 2 \gamma-1\...
... - {\rm i} {\rm arg}(a) 
\hat{z} \right]
+ {\cal O}\left(\hat{z}^{2}\right),$">|; 

$key = q/displaystyle=frac{1}{4},{rme}^{-s^2slash2}left[2,n^2,I_n(s^2slash2)slashs^2+s^2,I_n(s^2slash2)-s^2,I_n'(s^2slash2)right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img2412.png"
 ALT="$\displaystyle =\frac{1}{4}  {\rm e}^{-s^2/2}\left[2 n^2 I_n(s^2/2)/s^2 + s^2 I_n(s^2/2)
-s^2 I_n'(s^2/2)\right],$">|; 

$key = q/displaystyle=frac{1}{T},{bfV},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img875.png"
 ALT="$\displaystyle = \frac{1}{T} {\bf V},$">|; 

$key = q/displaystyle=frac{1}{r},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3162.png"
 ALT="$\displaystyle = \frac{1}{r},$">|; 

$key = q/displaystyle=frac{2,gamma_{ss'}}{m_{s'}},frac{partialH_{s'}}{partial{bfv}_s},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img806.png"
 ALT="$\displaystyle =\frac{2 \gamma_{ss'}}{m_{s'}} \frac{\partial H_{s'}}{\partial {\bf v}_s},$">|; 

$key = q/displaystyle=frac{2,r,V_{S,1}^{2}}{({mitGamma}+1)-({mitGamma}-1),r},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img3188.png"
 ALT="$\displaystyle = \frac{2 r V_{S 1}^{2}}{({\mit\Gamma}+1)-({\mit\Gamma}-1) r},$">|; 

$key = q/displaystyle=frac{2^{3slash2}}{sqrt{pi}},frac{S^{1slash2}}{P^{1slash4}},hat{mitPsi}^{3slash4}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.58ex; vertical-align: -2.30ex; " SRC="|."$dir".q|img3758.png"
 ALT="$\displaystyle = \frac{2^{3/2}}{\sqrt{\pi}} \frac{S^{1/2}}{P^{1/4}} \hat{\mit\Psi}^{3/4}.$">|; 

$key = q/displaystyle=frac{3,m_e}{m_i}frac{n,(T_e-T_i)}{tau_e},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.96ex; " SRC="|."$dir".q|img1160.png"
 ALT="$\displaystyle = \frac{3 m_e}{m_i} \frac{n (T_e-T_i)}{\tau_e},$">|; 

$key = q/displaystyle=frac{3,n,T_i}{10,{mitOmega}_i^{2},tau_i}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.35ex; vertical-align: -2.43ex; " SRC="|."$dir".q|img1281.png"
 ALT="$\displaystyle = \frac{3  n T_i}{10 {\mit\Omega}_i^{2} \tau_i}.$">|; 

$key = q/displaystyle=frac{5,n,T_e}{2,m_e,|{mitOmega}_e|},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.98ex; " SRC="|."$dir".q|img1246.png"
 ALT="$\displaystyle = \frac{5 n T_e}{2 m_e \vert{\mit\Omega}_e\vert},$">|; 

$key = q/displaystyle=frac{5,n,T_i}{2,m_i,{mitOmega}_i}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.96ex; " SRC="|."$dir".q|img1248.png"
 ALT="$\displaystyle =\frac{5 n T_i}{2 m_i {\mit\Omega}_i}.$">|; 

$key = q/displaystyle=frac{5pi^{1slash2}}{16}left(1+frac{1}{44}+cdotsright)nu,l^{2}=A_t,nu,l^{2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1127.png"
 ALT="$\displaystyle = \frac{5\pi^{1/2}}{16}\left(
1+ \frac{1}{44}+\cdots\right)\nu l^{2} = A_t \nu l^{2}.$">|; 

$key = q/displaystyle=frac{75pi^{1slash2}}{64}left(1+frac{3}{202}+cdotsright)nu,l^{2}=A_v,nu,l^{2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1125.png"
 ALT="$\displaystyle = \frac{75\pi^{1/2}}{64}\left(1+ \frac{3}{202}
+\cdots\right)\nu l^{2} = A_v \nu l^{2},$">|; 

$key = q/displaystyle=frac{B_0}{mu_0,a},cosh^{-2}left(frac{x}{a}right),{bfe}_z,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img3278.png"
 ALT="$\displaystyle =\frac{B_0}{\mu_0 a} \cosh^{-2}\left(\frac{x}{a}\right) {\bf e}_z,$">|; 

$key = q/displaystyle=frac{R,L}{S},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1759.png"
 ALT="$\displaystyle = \frac{R L}{S},$">|; 

$key = q/displaystyle=frac{bar{rho}_e}{L},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.35ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img1322.png"
 ALT="$\displaystyle =\frac{\bar{\rho}_e}{L},$">|; 

$key = q/displaystyle=frac{bar{rho}_e}{bar{l}_e},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -2.14ex; " SRC="|."$dir".q|img1324.png"
 ALT="$\displaystyle = \frac{\bar{\rho}_e}{\bar{l}_e},$">|; 

$key = q/displaystyle=frac{bar{rho}_i}{L},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.35ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img1387.png"
 ALT="$\displaystyle = \frac{\bar{\rho}_i}{L},$">|; 

$key = q/displaystyle=frac{bar{rho}_i}{bar{l}_i},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -2.14ex; " SRC="|."$dir".q|img1389.png"
 ALT="$\displaystyle = \frac{\bar{\rho}_i}{\bar{l}_i},$">|; 

$key = q/displaystyle=frac{c^2,k_x}{omega},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img2145.png"
 ALT="$\displaystyle = \frac{c^2 k_x}{\omega},$">|; 

$key = q/displaystyle=frac{c^2,k_z}{omega},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img2147.png"
 ALT="$\displaystyle = \frac{c^2 k_z}{\omega},$">|; 

$key = q/displaystyle=frac{c^2}{omega},{bfk},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img2140.png"
 ALT="$\displaystyle = \frac{c^2}{\omega} {\bf k},$">|; 

$key = q/displaystyle=frac{d^2hat{psi}}{dhat{x}^2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3338.png"
 ALT="$\displaystyle = \frac{d^2\hat{\psi}}{d\hat{x}^2},$">|; 

$key = q/displaystyle=frac{delta_{alphabeta}}{3}intH(v),v^{2},d^3{bfv},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img940.png"
 ALT="$\displaystyle = \frac{\delta_{\alpha\beta}}{3}\int H(v) v^{2} d^3{\bf v},$">|; 

$key = q/displaystyle=frac{e,B_0}{m_i},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.85ex; vertical-align: -1.96ex; " SRC="|."$dir".q|img1697.png"
 ALT="$\displaystyle = \frac{e B_0}{m_i},$">|; 

$key = q/displaystyle=frac{e}{epsilon,m},({bfE}+{bfv}times{bfB}),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img278.png"
 ALT="$\displaystyle = \frac{e}{\epsilon m}  ({\bf E} + {\bf v}\times
{\bf B}),$">|; 

$key = q/displaystyle=frac{e}{m},({bfv}times{bfB}_0).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img2358.png"
 ALT="$\displaystyle = \frac{e}{m} ({\bf v}\times{\bf B}_0).$">|; 

$key = q/displaystyle=frac{gamma_{ss'}}{m_s},frac{partial^2G_{s'}}{partial{bfv}_spartial{bfv}_s}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img807.png"
 ALT="$\displaystyle = \frac{\gamma_{ss'}}{m_s} \frac{\partial^2 G_{s'}}{\partial {\bf v}_s\partial{\bf v}_s}.$">|; 

$key = q/displaystyle=frac{gamma_{ss'}}{m_s}int{bfw}_{ss'},f_{s'},d^3{bfv}_{s'},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img805.png"
 ALT="$\displaystyle =\frac{\gamma_{ss'}}{m_s}\int {\bf w}_{ss'} f_{s'} d^3{\bf v}_{s'},$">|; 

$key = q/displaystyle=frac{gamma_{ss'}}{m_s}int{bfw}_{ss'},f_{s'},d^3{bfv}_{s'}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img790.png"
 ALT="$\displaystyle =\frac{\gamma_{ss'}}{m_s}\int {\bf w}_{ss'} f_{s'} d^3{\bf v}_{s'}.$">|; 

$key = q/displaystyle=frac{gamma_{ss'}}{m_{s'}}int{bfw}_{ss'}cdotfrac{partialf_{s'}}{partial{bfv}_{s'}},d^3{bfv}_{s'},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img788.png"
 ALT="$\displaystyle =\frac{\gamma_{ss'}}{m_{s'}}\int {\bf w}_{ss'}\cdot\frac{\partial f_{s'}}{\partial {\bf v}_{s'}} d^3{\bf v}_{s'},$">|; 

$key = q/displaystyle=frac{hat{W}}{skew{3}hat{mitPsi}}int_{-1}^inftyhat{J}({mitOmega}),langlecosxirangle,d{mitOmega}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.05ex; " SRC="|."$dir".q|img3525.png"
 ALT="$\displaystyle = \frac{\hat{W}}{\skew{3}\hat{\mit\Psi}}\int_{-1}^\infty
\hat{J}({\mit\Omega}) \langle\cos\xi\rangle d{\mit\Omega}.$">|; 

$key = q/displaystyle=frac{hat{psi}}{F},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3328.png"
 ALT="$\displaystyle = \frac{\hat{\psi}}{F},$">|; 

$key = q/displaystyle=frac{k_perp,v_perp}{{mitOmega}_s}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img2404.png"
 ALT="$\displaystyle = \frac{k_\perp v_\perp}{{\mit\Omega}_s}.$">|; 

$key = q/displaystyle=frac{lambda_e,bar{v}_e,t}{L},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.46ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img1336.png"
 ALT="$\displaystyle = \frac{\lambda_e \bar{v}_e t}{L},$">|; 

$key = q/displaystyle=frac{lambda_i,bar{v}_i,t}{L},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.46ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img1392.png"
 ALT="$\displaystyle = \frac{\lambda_i \bar{v}_i t}{L},$">|; 

$key = q/displaystyle=frac{mbox{boldmathpi}_e}{lambda_e,delta_e,zeta_e^{-1},m_e,bar{n},bar{v}_e^{2}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -2.18ex; " SRC="|."$dir".q|img1348.png"
 ALT="$\displaystyle = \frac{\mbox{\boldmath$\pi$}_e}{\lambda_e \delta_e \zeta_e^{-1} m_e \bar{n} \bar{v}_e^{2}},$">|; 

$key = q/displaystyle=frac{mbox{boldmathpi}_i}{lambda_i,delta_i,zeta_i^{-1},m_i,bar{n},bar{v}_i^{2}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.85ex; vertical-align: -2.43ex; " SRC="|."$dir".q|img1400.png"
 ALT="$\displaystyle = \frac{\mbox{\boldmath$\pi$}_i}{\lambda_i \delta_i \zeta_i^{-1} m_i \bar{n} \bar{v}_i^{2}},$">|; 

$key = q/displaystyle=frac{mu_0,a^2}{eta},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.35ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img2993.png"
 ALT="$\displaystyle =\frac{\mu_0 a^2}{\eta},$">|; 

$key = q/displaystyle=frac{n,T_i}{2,{mitOmega}_i}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.85ex; vertical-align: -1.96ex; " SRC="|."$dir".q|img1287.png"
 ALT="$\displaystyle = \frac{n T_i}{2 {\mit\Omega}_i}.$">|; 

$key = q/displaystyle=frac{n,e}{sigma_parallel},{bfj}-0.71,n,nablaT_e,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -2.19ex; " SRC="|."$dir".q|img1158.png"
 ALT="$\displaystyle = \frac{n e}{\sigma_\parallel} {\bf j} - 0.71 n \nabla T_e,$">|; 

$key = q/displaystyle=frac{n_s}{pi^{3slash2},v_{t,s}^{3}}expleft(-frac{|{bfv}-{bfV}_s|^{2}}{v_{t,s}^{2}}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.58ex; vertical-align: -2.31ex; " SRC="|."$dir".q|img886.png"
 ALT="$\displaystyle = \frac{n_s}{\pi^{3/2} v_{t s}^{3}}\exp\left(-\frac{\vert{\bf v} - {\bf V}_s\vert^{2}}{v_{t s}^{2}}\right),$">|; 

$key = q/displaystyle=frac{n_{s'},v_{t,{s'}}^{2}}{2,v^{3}}left{-F_2(zeta),delta_{alphabeta}+[F_2(zeta)+2,F_1(zeta)],frac{v_alpha,v_beta}{v^{2}}right},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img913.png"
 ALT="$\displaystyle = \frac{n_{s'} v_{t {s'}}^{2}}{2 v^{3}}\left\{-F_2(\zeta) \de...
...pha\beta}+ [F_2(\zeta)+2 F_1(\zeta)] \frac{v_\alpha v_\beta}{v^{2}}\right\},$">|; 

$key = q/displaystyle=frac{n_{s'}}{pi^{3slash2},v_{t,{s'}}^{3}}expleft(-frac{v^2}{v_{t,{s'}}^{2}}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.69ex; vertical-align: -2.44ex; " SRC="|."$dir".q|img888.png"
 ALT="$\displaystyle = \frac{n_{s'}}{\pi^{3/2} v_{t {s'}}^{3}}\exp\left(-\frac{v^2}{v_{t {s'}}^{2}}\right),$">|; 

$key = q/displaystyle=frac{n}{bar{n}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img1328.png"
 ALT="$\displaystyle = \frac{n}{\bar{n}},$">|; 

$key = q/displaystyle=frac{p_e}{m_e,bar{n},bar{v}_e^{2}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -2.18ex; " SRC="|."$dir".q|img1346.png"
 ALT="$\displaystyle = \frac{p_e}{m_e \bar{n} \bar{v}_e^{2}},$">|; 

$key = q/displaystyle=frac{p_i}{m_i,bar{n},bar{v}_i^{2}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.85ex; vertical-align: -2.43ex; " SRC="|."$dir".q|img1398.png"
 ALT="$\displaystyle =\frac{ p_i}{m_i \bar{n} \bar{v}_i^{2}},$">|; 

$key = q/displaystyle=frac{partial^2skew{3}hat{phi}}{partialhat{x}^2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3488.png"
 ALT="$\displaystyle =\frac{\partial^2 \skew{3}\hat{\phi}}{\partial \hat{x}^2}$">|; 

$key = q/displaystyle=frac{partial^2u_{ss'}}{partialu_{ss',alpha},partialu_{ss',beta}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.52ex; vertical-align: -2.26ex; " SRC="|."$dir".q|img801.png"
 ALT="$\displaystyle = \frac{\partial^2 u_{ss'}}{\partial u_{ss' \alpha} \partial u_{ss' \beta}},$">|; 

$key = q/displaystyle=frac{partialf_0}{partialv_parallel}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.19ex; vertical-align: -2.19ex; " SRC="|."$dir".q|img2384.png"
 ALT="$\displaystyle = \frac{\partial f_0}{\partial v_\parallel}.$">|; 

$key = q/displaystyle=frac{partialf_s}{partial{bfv}_s},frac{f_{s'}}{m_s}-frac{f_s}{m_{s'}},frac{partialf_{s'}}{partial{bfv}_{s'}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img1000.png"
 ALT="$\displaystyle = \frac{\partial f_s}{\partial{\bf v}_s} \frac{f_{s'}}{m_s} -\frac{f_s}{m_{s'}} \frac{\partial f_{s'}}{\partial {\bf v}_{s'}}.$">|; 

$key = q/displaystyle=frac{partialw_{ss',betabeta}}{partialu_{ss',alpha}}=2,frac{partial}{partialu_{ss',alpha}}left(frac{1}{u_{ss'}}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img803.png"
 ALT="$\displaystyle = \frac{\partial w_{ss' \beta\beta}}{\partial u_{ss' \alpha}} = 2 \frac{\partial}{\partial u_{ss'
 \alpha}}\left(\frac{1}{u_{ss'}}\right).$">|; 

$key = q/displaystyle=frac{partial{calM}slashpartial{bfr}}{partial{calM}slashpartialomega},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img2128.png"
 ALT="$\displaystyle = \frac{\partial{\cal M}/\partial{\bf r} }
{\partial{\cal M}/\partial\omega},$">|; 

$key = q/displaystyle=frac{partial{mitOmega}}{partialt}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2126.png"
 ALT="$\displaystyle = \frac{\partial{\mit\Omega}}{\partial t}.$">|; 

$key = q/displaystyle=frac{partial{mitOmega}}{partial{bfk}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2122.png"
 ALT="$\displaystyle = \frac{\partial{\mit\Omega}}{\partial {\bf k}},$">|; 

$key = q/displaystyle=frac{pi}{2}-frac{xi}{2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.46ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3598.png"
 ALT="$\displaystyle = \frac{\pi}{2}-\frac{\xi}{2}.$">|; 

$key = q/displaystyle=frac{pi}{2}-{rmsgn}(xi),cos^{-1}[cos(xislash2)slashk],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.01ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3596.png"
 ALT="$\displaystyle = \frac{\pi}{2}-{\rm sgn}(\xi) \cos^{-1}[\cos(\xi/2)/k],$">|; 

$key = q/displaystyle=frac{r}{a},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img2991.png"
 ALT="$\displaystyle = \frac{r}{a},$">|; 

$key = q/displaystyle=frac{u_{ss',alpha}}{u_{ss'}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.41ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img797.png"
 ALT="$\displaystyle = \frac{u_{ss' \alpha}}{u_{ss'}},$">|; 

$key = q/displaystyle=frac{u_{ss'}^{2},{bfI}-{bfu}_{ss'}{bfu}_{ss'}}{u_{ss'}^{3}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.44ex; " SRC="|."$dir".q|img996.png"
 ALT="$\displaystyle = \frac{u_{ss'}^{2} {\bf I} - {\bf u}_{ss'}{\bf u}_{ss'}}{u_{ss'}^{3}},$">|; 

$key = q/displaystyle=frac{v_e}{bar{v}_e},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.41ex; vertical-align: -1.96ex; " SRC="|."$dir".q|img1330.png"
 ALT="$\displaystyle = \frac{v_e}{\bar{v}_e},$">|; 

$key = q/displaystyle=frac{v_i}{bar{v}_i},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.41ex; vertical-align: -1.96ex; " SRC="|."$dir".q|img1391.png"
 ALT="$\displaystyle = \frac{v_i}{\bar{v}_i},$">|; 

$key = q/displaystyle=frac{v_perp}{{mitOmega}},left(cosleft[{mitOmega},(t-t')+theta,right]-costhetaright),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.01ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img2374.png"
 ALT="$\displaystyle = \frac{v_\perp}{{\mit\Omega}} \left(\cos\left[{\mit\Omega} (t-t')
+\theta \right] -\cos\theta\right),$">|; 

$key = q/displaystyle=frac{v_{1}^{2}-cos^2theta_1,V_{A,1}^{2}}{v_{1}^{2}-r,cos^2theta_1,V_{A,1}^{2}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.80ex; vertical-align: -2.44ex; " SRC="|."$dir".q|img3164.png"
 ALT="$\displaystyle =
\frac{v_{1}^{2} -\cos^2\theta_1  V_{A 1}^{2}}{v_{1}^{2}-r \cos^2\theta_1 V_{A 1}^{2}},$">|; 

$key = q/displaystyle=frac{w_T}{(1+lambda_e^{2}),delta_e,m_e,bar{n},bar{v}_e^{3}slashL}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -2.18ex; " SRC="|."$dir".q|img1362.png"
 ALT="$\displaystyle = \frac{w_T}{(1+\lambda_e^{2}) \delta_e  m_e \bar{n} \bar{v}_e^{3}/L}.$">|; 

$key = q/displaystyle=frac{w_U}{(1+lambda_e^{2})^2,delta_e,zeta_e,m_e,bar{n},bar{v}_e^{3}slashL},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -2.18ex; " SRC="|."$dir".q|img1360.png"
 ALT="$\displaystyle = \frac{w_U}{(1+\lambda_e^{2})^2 \delta_e \zeta_e  m_e \bar{n} \bar{v}_e^{3}/L},$">|; 

$key = q/displaystyle=frac{w_i}{delta_e^{-1},zeta_e,mu^2,m_e,bar{n},bar{v}_e^{3}slashL},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -2.18ex; " SRC="|."$dir".q|img1358.png"
 ALT="$\displaystyle = \frac{w_i}{\delta_e^{-1} \zeta_e \mu^2  m_e \bar{n} \bar{v}_e^{3}/L},$">|; 

$key = q/displaystyle=frac{w_i}{delta_i^{-1},zeta_i,mu,m_i,bar{n},bar{v}_i^{3}slashL}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -2.45ex; " SRC="|."$dir".q|img1405.png"
 ALT="$\displaystyle = \frac{w_i}{\delta_i^{-1} \zeta_i \mu  m_i \bar{n} \bar{v}_i^{3}/L}.$">|; 

$key = q/displaystyle=frac{{bfB}}{bar{B}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.74ex; " SRC="|."$dir".q|img1340.png"
 ALT="$\displaystyle = \frac{{\bf B}}{\bar{B}},$">|; 

$key = q/displaystyle=frac{{bfE}}{lambda_e,bar{v}_e,bar{B}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -2.09ex; " SRC="|."$dir".q|img1342.png"
 ALT="$\displaystyle = \frac{{\bf E}}{ \lambda_e \bar{v}_e \bar{B}},$">|; 

$key = q/displaystyle=frac{{bfE}}{lambda_i,bar{v}_i,bar{B}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -2.09ex; " SRC="|."$dir".q|img1395.png"
 ALT="$\displaystyle = \frac{{\bf E}}{ \lambda_i \bar{v}_i \bar{B}},$">|; 

$key = q/displaystyle=frac{{bfF}_T}{m_e,bar{n},bar{v}_e^{2}slashL},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.13ex; vertical-align: -2.18ex; " SRC="|."$dir".q|img1356.png"
 ALT="$\displaystyle = \frac{{\bf F}_T}{m_e \bar{n} \bar{v}_e^{2}/L},$">|; 

$key = q/displaystyle=frac{{bfF}_T}{m_i,bar{n},bar{v}_i^{2}slashL},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.35ex; vertical-align: -2.43ex; " SRC="|."$dir".q|img1404.png"
 ALT="$\displaystyle =\frac{ {\bf F}_T}{m_i \bar{n} \bar{v}_i^{2}/L},$">|; 

$key = q/displaystyle=frac{{bfF}_U}{(1+lambda_e^{2}),zeta_e,m_e,bar{n},bar{v}_e^{2}slashL},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.13ex; vertical-align: -2.18ex; " SRC="|."$dir".q|img1354.png"
 ALT="$\displaystyle = \frac{{\bf F}_U}{(1+\lambda_e^{2})  \zeta_e m_e \bar{n} \bar{v}_e^{2}/L},$">|; 

$key = q/displaystyle=frac{{bfF}_U}{(1+lambda_i^{2}),zeta_i,mu,m_i,bar{n},bar{v}_i^{2}slashL},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.35ex; vertical-align: -2.43ex; " SRC="|."$dir".q|img1403.png"
 ALT="$\displaystyle = \frac{{\bf F}_U}{ (1+\lambda_i^{2})  \zeta_i \mu m_i \bar{n} \bar{v}_i^{2}/L},$">|; 

$key = q/displaystyle=frac{{bfU}}{(1+lambda_e^{2}),delta_e,bar{v}_e},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.13ex; vertical-align: -2.18ex; " SRC="|."$dir".q|img1344.png"
 ALT="$\displaystyle =\frac{{\bf U} }{ (1+\lambda_e^{2}) \delta_e \bar{v}_e},$">|; 

$key = q/displaystyle=frac{{bfU}}{(1+lambda_i^{2}),delta_i,bar{v}_i},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.35ex; vertical-align: -2.43ex; " SRC="|."$dir".q|img1396.png"
 ALT="$\displaystyle =\frac{{\bf U} }{ (1+\lambda_i^{2}) \delta_i \bar{v}_i},$">|; 

$key = q/displaystyle=frac{{bfV}_e}{lambda_e,bar{v}_e},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.96ex; " SRC="|."$dir".q|img1338.png"
 ALT="$\displaystyle = \frac{{\bf V}_e}{\lambda_e \bar{v}_e},$">|; 

$key = q/displaystyle=frac{{bfV}_i}{lambda_i,bar{v}_i},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.96ex; " SRC="|."$dir".q|img1394.png"
 ALT="$\displaystyle = \frac{{\bf V}_i}{\lambda_i \bar{v}_i},$">|; 

$key = q/displaystyle=frac{{bfe}_1+{rmi},{bfe}_2}{sqrt{2}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.30ex; vertical-align: -2.30ex; " SRC="|."$dir".q|img1704.png"
 ALT="$\displaystyle = \frac{ {\bf e}_1 +{\rm i} {\bf e}_2}{\sqrt{2}},$">|; 

$key = q/displaystyle=frac{{bfe}_1-{rmi},{bfe}_2}{sqrt{2}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.30ex; vertical-align: -2.30ex; " SRC="|."$dir".q|img1706.png"
 ALT="$\displaystyle = \frac{ {\bf e}_1 - {\rm i} {\bf e}_2}{\sqrt{2}}.$">|; 

$key = q/displaystyle=frac{{bfj}cdot{bfF}_T}{n,e}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img1303.png"
 ALT="$\displaystyle = \frac{{\bf j}\cdot{\bf F}_T}{n e}.$">|; 

$key = q/displaystyle=frac{{bfj}cdot{bfF}_U}{n,e},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img1301.png"
 ALT="$\displaystyle = \frac{{\bf j}\cdot{\bf F}_U}{n e},$">|; 

$key = q/displaystyle=frac{{bfq}_{Te}}{delta_e,zeta_e^{-1},m_e,bar{n},bar{v}_e^{3}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -2.18ex; " SRC="|."$dir".q|img1350.png"
 ALT="$\displaystyle = \frac{{\bf q}_{Te} }{ \delta_e \zeta_e^{-1} m_e \bar{n} \bar{v}_e^{3}},$">|; 

$key = q/displaystyle=frac{{bfq}_{Ue}}{(1+lambda_e^{2}),delta_e,m_e,bar{n},bar{v}_e^{3}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -2.18ex; " SRC="|."$dir".q|img1352.png"
 ALT="$\displaystyle = \frac{{\bf q}_{Ue} }{ (1+\lambda_e^{2}) \delta_e m_e \bar{n} \bar{v}_e^{3}},$">|; 

$key = q/displaystyle=frac{{bfq}_{i}}{delta_i,zeta_i^{-1},m_i,bar{n},bar{v}_i^{3}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -2.45ex; " SRC="|."$dir".q|img1402.png"
 ALT="$\displaystyle = \frac{{\bf q}_{i} }{ \delta_i \zeta_i^{-1} m_i \bar{n} \bar{v}_i^{3}},$">|; 

$key = q/displaystyle=frac{{bfr}}{L},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img1332.png"
 ALT="$\displaystyle = \frac{{\bf r}}{ L},$">|; 

$key = q/displaystyle=frac{{mitOmega}}{2pi},{mitPhi}_2-R,I,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img2908.png"
 ALT="$\displaystyle = \frac{{\mit\Omega}}{2\pi} {\mit\Phi}_2 - R I,$">|; 

$key = q/displaystyle=hat{z}+{calO}left(hat{z}^{2}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.23ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img2005.png"
 ALT="$\displaystyle = \hat{z} + {\cal O}\left(\hat{z}^{2}\right),$">|; 

$key = q/displaystyle=int_0^varphifrac{du}{sqrt{1-k^2sin^2u}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.80ex; vertical-align: -2.70ex; " SRC="|."$dir".q|img3571.png"
 ALT="$\displaystyle = \int_0^\varphi \frac{du}{\sqrt{1-k^2\sin^2 u}},$">|; 

$key = q/displaystyle=int_0^varphisqrt{1-k^2sin^2u},,du;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.13ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img3573.png"
 ALT="$\displaystyle = \int_0^\varphi \sqrt{1-k^2\sin^2 u}  du$">|; 

$key = q/displaystyle=int_{-infty}^{infty}bar{psi}(p),{rme}^{,{rmi},S^{1slash3},hat{x},p},dp,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img3382.png"
 ALT="$\displaystyle = \int_{-\infty}^{\infty} \bar{\psi}(p) 
{\rm e}^{ {\rm i} S^{1/3} \hat{x} p} dp,$">|; 

$key = q/displaystyle=int_{-infty}^{infty}skew{3}bar{phi}(p),{rme}^{,{rmi},S^{1slash3},hat{x},p},dp,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img3381.png"
 ALT="$\displaystyle = \int_{-\infty}^{\infty}
\skew{3}\bar{\phi}(p)  {\rm e}^{ {\rm i} S^{1/3}  \hat{x} p} 
dp,$">|; 

$key = q/displaystyle=intf,d^3{bfv},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img984.png"
 ALT="$\displaystyle = \int f d^3{\bf v},$">|; 

$key = q/displaystyle=intf_s,d^3{bfv}_s,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img880.png"
 ALT="$\displaystyle = \int f_s d^3{\bf v}_s,$">|; 

$key = q/displaystyle=intfrac{1}{2},m,v^2,f,d^3{bfv}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img988.png"
 ALT="$\displaystyle = \int \frac{1}{2} m v^2 f d^3{\bf v}.$">|; 

$key = q/displaystyle=intfrac{1}{2},m_s,v_s^{2},f_s,d^3{bfv}_s.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img884.png"
 ALT="$\displaystyle = \int \frac{1}{2} m_s v_s^{2} f_s d^3{\bf v}_s.$">|; 

$key = q/displaystyle=intu_{ss'},f_{s'},d^3{bfv}_{s'},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img792.png"
 ALT="$\displaystyle = \int u_{ss'} f_{s'} d^3{\bf v}_{s'},$">|; 

$key = q/displaystyle=intu_{ss'}^{-1},f_{s'},d^3{bfv}_{s'}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img794.png"
 ALT="$\displaystyle = \int u_{ss'}^{-1} f_{s'} d^3{\bf v}_{s'}.$">|; 

$key = q/displaystyle=int{bfv},f,d^3{bfv},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img986.png"
 ALT="$\displaystyle = \int {\bf v} f d^3{\bf v},$">|; 

$key = q/displaystyle=int{bfv}_s,f_s,d^3{bfv}_s,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img882.png"
 ALT="$\displaystyle = \int {\bf v}_s f_s d^3{\bf v}_s,$">|; 

$key = q/displaystyle=k^2,a^2+gamma,tau_R+{rmi},(m,{mitOmega}-k,U),tau_R,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2995.png"
 ALT="$\displaystyle = k^2  a^2 + \gamma \tau_R + {\rm i} (m {\mit\Omega} - k U) \tau_R,$">|; 

$key = q/displaystyle=k^2,a^2+gamma,tau_R.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2997.png"
 ALT="$\displaystyle = k^2  a^2 + \gamma \tau_R.$">|; 

$key = q/displaystyle=k_{ss'},frac{{bfr}_{ss'}}{|{bfr}_{ss'}|^{3}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.98ex; " SRC="|."$dir".q|img665.png"
 ALT="$\displaystyle = k_{ss'} \frac{{\bf r}_{ss'}}{\vert{\bf r}_{ss'}\vert^{3}},$">|; 

$key = q/displaystyle=left(1-2,zeta^{2}right){rmerf}(zeta)-zeta,frac{d,{rmerf}}{dzeta}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img917.png"
 ALT="$\displaystyle = \left(1-2 \zeta^{2}\right){\rm erf}(\zeta)-\zeta \frac{d {\rm erf}}{d\zeta}.$">|; 

$key = q/displaystyle=left(frac{2,{calE}}{m}right)^{1slash2}frac{cosvartheta_m}{cosvartheta},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img531.png"
 ALT="$\displaystyle = \left(\frac{2 {\cal E}}{m}\right)^{1/2}\frac{\cos\vartheta_m}{\cos\vartheta},$">|; 

$key = q/displaystyle=left(frac{d^2}{dhat{x}^2}-hat{k}^2right)hat{psi},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3316.png"
 ALT="$\displaystyle = \left(\frac{d^2}{d\hat{x}^2}-\hat{k}^2\right)\hat{\psi},$">|; 

$key = q/displaystyle=left(frac{e_s,e_{s'}}{4pi,epsilon_0}right)^22pi,ln{mitLambda}_c,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img994.png"
 ALT="$\displaystyle = \left(\frac{e_s e_{s'}}{4\pi \epsilon_0}\right)^2 2\pi \ln{\mit\Lambda}_c,$">|; 

$key = q/displaystyle=left[frac{Gamma(1slash4)}{pi,Gamma(3slash4)}right]^{4slash5}(k,a)^{-2slash5},{calS}^{-3slash5},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.91ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3680.png"
 ALT="$\displaystyle = \left[\frac{\Gamma(1/4)}{\pi \Gamma(3/4)}\right]^{4/5}(k a)^{-2/5} {\cal S}^{-3/5},$">|; 

$key = q/displaystyle=lnleft(frac{m_i}{2pi,m_e}right)^{1slash2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1612.png"
 ALT="$\displaystyle = \ln\left(\frac{m_i}{2\pi m_e}\right)^{1/2},$">|; 

$key = q/displaystyle=lnleft[n_s,left(frac{m_s}{2pi,T}right)^{3slash2}right]-frac{m_s,V^{2}}{2,T},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img873.png"
 ALT="$\displaystyle = \ln\left[n_s \left(\frac{m_s}{2\pi T}\right)^{3/2}\right] - \frac{m_s V^{2}}{2 T},$">|; 

$key = q/displaystyle=m,n,{mitchi}_v,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1119.png"
 ALT="$\displaystyle =m  n  {\mit\chi}_v,$">|; 

$key = q/displaystyle=mu_0,{bfj},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2683.png"
 ALT="$\displaystyle = \mu_0 {\bf j},$">|; 

$key = q/displaystyle=mu_0,{bfj}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3249.png"
 ALT="$\displaystyle = \mu_0 {\bf j}.$">|; 

$key = q/displaystyle=n,eleft(frac{{bfj}_parallel}{sigma_parallel}+frac{{bfj}_perp}{sigma_perp}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1293.png"
 ALT="$\displaystyle = n e\left(\frac{{\bf j}_\parallel}{\sigma_\parallel}
+\frac{{\bf j}_\perp}{\sigma_\perp}\right),$">|; 

$key = q/displaystyle=n,{mitchi}_t,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1121.png"
 ALT="$\displaystyle = n {\mit\chi}_t,$">|; 

$key = q/displaystyle=n_sleft[1-frac{2,e}{m_i,V_s^{,2}},({mitPhi}-{mitPhi}_s)right]^{-1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1571.png"
 ALT="$\displaystyle = n_s\left[1- \frac{2 e}{m_i V_s^{ 2}} ({\mit\Phi}-{\mit\Phi}_s)\right]^{-1/2}$">|; 

$key = q/displaystyle=nabla^2phi,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3269.png"
 ALT="$\displaystyle =\nabla^2\phi,$">|; 

$key = q/displaystyle=nabla^2phi.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3738.png"
 ALT="$\displaystyle =\nabla^2\phi.$">|; 

$key = q/displaystyle=nabla^2psi,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3268.png"
 ALT="$\displaystyle =\nabla^2\psi,$">|; 

$key = q/displaystyle=nablaphitimes{bfe}_z+V_z,{bfe}_z,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3225.png"
 ALT="$\displaystyle =\nabla\phi\times {\bf e}_z+ V_z {\bf e}_z,$">|; 

$key = q/displaystyle=nablaphitimes{bfe}_z,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3252.png"
 ALT="$\displaystyle =\nabla\phi\times {\bf e}_z,$">|; 

$key = q/displaystyle=nablapsitimes{bfe}_z+B_z,{bfe}_z,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3224.png"
 ALT="$\displaystyle = \nabla\psi\times{\bf e}_z + B_z {\bf e}_z,$">|; 

$key = q/displaystyle=nablapsitimes{bfe}_z,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3253.png"
 ALT="$\displaystyle = \nabla\psi\times{\bf e}_z,$">|; 

$key = q/displaystyle=nablatimesleft(frac{phi}{varpi},{bfe}_thetaright)equivfrac{nablaphitimes{bfe}_theta}{varpi},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img2942.png"
 ALT="$\displaystyle = \nabla\times\left(\frac{\phi}{\varpi} {\bf e}_\theta\right)
\equiv \frac{\nabla\phi\times{\bf e}_\theta}{\varpi},$">|; 

$key = q/displaystyle=nablatimesleft(frac{psi}{varpi},{bfe}_thetaright)equivfrac{nablapsitimes{bfe}_theta}{varpi},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img2940.png"
 ALT="$\displaystyle = \nabla\times\left(\frac{\psi}{\varpi} {\bf e}_\theta\right)
\equiv \frac{\nabla\psi\times{\bf e}_\theta}{\varpi},$">|; 

$key = q/displaystyle=omega,{bfB},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img1674.png"
 ALT="$\displaystyle = \omega {\bf B},$">|; 

$key = q/displaystyle=p_0,n_0^{-{mitGamma}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.57ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img1901.png"
 ALT="$\displaystyle =p_0 n_0^{-{\mit\Gamma}},$">|; 

$key = q/displaystyle=phi_1(x),{rme}^{,{rmi},k,y+gamma,t},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3295.png"
 ALT="$\displaystyle = \phi_1(x) {\rm e}^{ {\rm i} k y+\gamma t},$">|; 

$key = q/displaystyle=pi^{1slash2},{rme}^{-zeta^{2}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.57ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img2621.png"
 ALT="$\displaystyle = \pi^{1/2} {\rm e}^{-\zeta^{2}},$">|; 

$key = q/displaystyle=pmcsqrt{n^2-S^2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.16ex; " SRC="|."$dir".q|img2154.png"
 ALT="$\displaystyle = \pm c\sqrt{n^2-S^2}.$">|; 

$key = q/displaystyle=pmleft(frac{2,{calE}}{m}right)^{1slash2}left(1-frac{cos^2vartheta_m}{cos^2vartheta}right)^{1slash2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.91ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img533.png"
 ALT="$\displaystyle =\pm \left(\frac{2 {\cal E}}{m}\right)^{1/2}\left(1-\frac{\cos^2\vartheta_m}{\cos^2\vartheta}\right)^{1/2},$">|; 

$key = q/displaystyle=pm{rmi},{bfe}_pm,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img1709.png"
 ALT="$\displaystyle = \pm {\rm i} {\bf e}_\pm,$">|; 

$key = q/displaystyle=r,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img3095.png"
 ALT="$\displaystyle = r,$">|; 

$key = q/displaystyle=r,V_{A,1}^{2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.66ex; " SRC="|."$dir".q|img3189.png"
 ALT="$\displaystyle = r V_{A 1}^{2},$">|; 

$key = q/displaystyle=r,V_{A,1}^{2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.66ex; " SRC="|."$dir".q|img3190.png"
 ALT="$\displaystyle = r V_{A 1}^{2}.$">|; 

$key = q/displaystyle=r,frac{d{mitOmega}}{dr},B_r-{rmi},(m,{mitOmega}-k,U),B_theta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2984.png"
 ALT="$\displaystyle = r \frac{d{\mit\Omega}}{dr} B_r
-{\rm i} (m {\mit\Omega}-k  U) B_\theta$">|; 

$key = q/displaystyle=r^{-1},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img3097.png"
 ALT="$\displaystyle = r^{-1},$">|; 

$key = q/displaystyle=rho,(-cosgamma,{bfe}_1+singamma,{bfe}_2),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img311.png"
 ALT="$\displaystyle = \rho (-\cos\gamma {\bf e}_1+\sin\gamma {\bf e}_2),$">|; 

$key = q/displaystyle=rho,[phi,U]+mu_0^{-1},[J,psi]+mu,nabla^2U,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.57ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img3737.png"
 ALT="$\displaystyle = \rho [\phi,U] + \mu_0^{-1} [J,\psi]+\mu \nabla^2 U,$">|; 

$key = q/displaystyle=rho,[phi,U]+mu_0^{-1},[J,psi],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.57ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img3266.png"
 ALT="$\displaystyle = \rho [\phi,U] + \mu_0^{-1} [J,\psi],$">|; 

$key = q/displaystyle=rho_0,frac{{bfk}cdot{bfV}}{omega},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img2715.png"
 ALT="$\displaystyle = \rho_0 \frac{{\bf k}\cdot{\bf V}}{\omega},$">|; 

$key = q/displaystyle=rleft(frac{2,V_{S,1}^{2}+[{mitGamma}+(2-{mitGamma}),r],V_{A,1}^{2}}{[{mitGamma}+1]-[{mitGamma}-1],r}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.69ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3199.png"
 ALT="$\displaystyle = r \left(\frac{2 V_{S 1}^{2} + [{\mit\Gamma}+(2-{\mit\Gamma}) r] V_{A 1}^{2}}
{[{\mit\Gamma}+1]-[{\mit\Gamma}-1] r}\right)
,$">|; 

$key = q/displaystyle=rleft(frac{v_{1}^{2}-cos^2theta_1,V_{A,1}^{2}}{v_{1}^{2}-r,cos^2theta_1,V_{A,1}^{2}}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.80ex; vertical-align: -2.44ex; " SRC="|."$dir".q|img3160.png"
 ALT="$\displaystyle =
r\left(\frac{v_{1}^{2} - \cos^2\theta_1 V_{A 1}^{2}}{v_{1}^{2}-r \cos^2\theta_1 V_{A 1}^{2}}\right),$">|; 

$key = q/displaystyle=sqrt{frac{m_e}{m_i}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.23ex; " SRC="|."$dir".q|img1326.png"
 ALT="$\displaystyle = \sqrt{\frac{m_e}{m_i}}.$">|; 

$key = q/displaystyle=sqrt{frac{n_e,e^2}{epsilon_0,m_e}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.75ex; vertical-align: -2.57ex; " SRC="|."$dir".q|img1691.png"
 ALT="$\displaystyle = \sqrt{\frac{n_e e^2}{\epsilon_0 m_e}},$">|; 

$key = q/displaystyle=sqrt{frac{n_e,e^2}{epsilon_0,m_i}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.75ex; vertical-align: -2.57ex; " SRC="|."$dir".q|img1693.png"
 ALT="$\displaystyle = \sqrt{\frac{n_e e^2}{\epsilon_0 m_i}},$">|; 

$key = q/displaystyle=sum_se_s!int!{calF}_s({bfr},{bfv},t),d^3{bfv},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.58ex; vertical-align: -2.62ex; " SRC="|."$dir".q|img572.png"
 ALT="$\displaystyle = \sum_s e_s\! \int\! {\cal F}_s({\bf r}, {\bf v}, t) d^3{\bf v},$">|; 

$key = q/displaystyle=sum_se_s!int{bfv},{calF}_s({bfr},{bfv},t),d^3{bfv}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.58ex; vertical-align: -2.62ex; " SRC="|."$dir".q|img574.png"
 ALT="$\displaystyle = \sum_s e_s \!\int {\bf v} {\cal F}_s({\bf r}, {\bf v}, t) d^3
{\bf v}.$">|; 

$key = q/displaystyle=sum_se_s,n_s,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -2.62ex; " SRC="|."$dir".q|img1020.png"
 ALT="$\displaystyle = \sum_s e_s  n_s,$">|; 

$key = q/displaystyle=sum_se_s,n_s,{bfV}_s.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -2.62ex; " SRC="|."$dir".q|img1021.png"
 ALT="$\displaystyle = \sum_s e_s  n_s {\bf V}_s.$">|; 

$key = q/displaystyle=sum_{n=0,4};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img1265.png"
 ALT="$\displaystyle = \sum_{n=0,4}$">|; 

$key = q/displaystyle=tau_b(0)left[frac{k(0)}{k(t)}right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img547.png"
 ALT="$\displaystyle =\tau_b(0)\left[\frac{k(0)}{k(t)}\right],$">|; 

$key = q/displaystyle=u,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img2815.png"
 ALT="$\displaystyle = u,$">|; 

$key = q/displaystyle=v_parallel,(t'-t).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img2376.png"
 ALT="$\displaystyle = v_\parallel (t'-t).$">|; 

$key = q/displaystyle=w_e,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1148.png"
 ALT="$\displaystyle = w_e,$">|; 

$key = q/displaystyle=w_i,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1155.png"
 ALT="$\displaystyle = w_i,$">|; 

$key = q/displaystyle=w_i.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1381.png"
 ALT="$\displaystyle =w_i.$">|; 

$key = q/displaystyle=w_s.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1077.png"
 ALT="$\displaystyle = w_s.$">|; 

$key = q/displaystyle=x_m(0)left[frac{k(0)}{k(t)}right]^{1slash2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img545.png"
 ALT="$\displaystyle = x_m(0)\left[\frac{k(0)}{k(t)}\right]^{1/2},$">|; 

$key = q/displaystyle=y,psi(y),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1991.png"
 ALT="$\displaystyle = y \psi(y),$">|; 

$key = q/displaystyle=y,psi(y).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1984.png"
 ALT="$\displaystyle = y \psi(y).$">|; 

$key = q/displaystyle={bf0},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img680.png"
 ALT="$\displaystyle ={\bf0},$">|; 

$key = q/displaystyle={bfB}_p+{bfB}_t,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2935.png"
 ALT="$\displaystyle = {\bf B}_p + {\bf B}_t,$">|; 

$key = q/displaystyle={bfF},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img1145.png"
 ALT="$\displaystyle = {\bf F},$">|; 

$key = q/displaystyle={bfF}_0({bfZ},t)+epsilon,{bfF}_1({bfZ},t)+epsilon^2,{bfF}_2({bfZ},t)+cdots,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img259.png"
 ALT="$\displaystyle ={\bf F}_0({\bf Z}, t) + \epsilon 
{\bf F}_1({\bf Z}, t) + \epsilon^2 {\bf F}_2({\bf Z}, t) +
\cdots,$">|; 

$key = q/displaystyle={bfF}_U+{bfF}_T,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1312.png"
 ALT="$\displaystyle = {\bf F}_U +{\bf F}_T,$">|; 

$key = q/displaystyle={bfF}_s,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1075.png"
 ALT="$\displaystyle = {\bf F}_s,$">|; 

$key = q/displaystyle={bfR}(t)+epsilon,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img280.png"
 ALT="$\displaystyle = {\bf R}(t) + \epsilon $">|; 

$key = q/displaystyle={bfR}_{ss'}+frac{mu_{ss'}}{m_s},{bfr}_{ss'},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.41ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img674.png"
 ALT="$\displaystyle = {\bf R} _{ss'}+ \frac{\mu_{ss'}}{m_s} {\bf r}_{ss'},$">|; 

$key = q/displaystyle={bfR}_{ss'}-frac{mu_{ss'}}{m_{s'}},{bfr}_{ss'},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.41ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img676.png"
 ALT="$\displaystyle = {\bf R}_{ss'}-\frac{\mu_{ss'}}{m_{s'}} {\bf r}_{ss'},$">|; 

$key = q/displaystyle={bfU}(t)+{bfu}({bfR},{bfU},t,gamma),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img283.png"
 ALT="$\displaystyle = {\bf U}(t) + {\bf u} ({\bf R}, {\bf U}, t, \gamma),$">|; 

$key = q/displaystyle={bfU}_{ss'}+frac{mu_{ss'}}{m_s},{bfu}_{ss'},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.41ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img596.png"
 ALT="$\displaystyle = {\bf U}_{ss'} + \frac{\mu_{ss'}}{m_s} {\bf u}_{ss'},$">|; 

$key = q/displaystyle={bfU}_{ss'}-frac{mu_{ss'}}{m_{s'}},{bfu}_{ss'}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.41ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img598.png"
 ALT="$\displaystyle = {\bf U}_{ss'} - \frac{\mu_{ss'}}{m_{s'}} {\bf u}_{ss'}.$">|; 

$key = q/displaystyle={bfV}_p+{bfV}_t.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2937.png"
 ALT="$\displaystyle = {\bf V}_p + {\bf V}_t.$">|; 

$key = q/displaystyle={bfb},langle;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img323.png"
 ALT="$\displaystyle = {\bf b} \langle$">|; 

$key = q/displaystyle={bfb}cdot(m_s,{bfv}_s+m_{s'},{bfv}_{s'}-m_s,{bfv}_s'-m_{s'},{bfv}_{s'}');MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img868.png"
 ALT="$\displaystyle = {\bf b}\cdot(m_s {\bf v}_s+m_{s'} {\bf v}_{s'}-m_s {\bf v}_s'-m_{s'} {\bf v}_{s'}')$">|; 

$key = q/displaystyle={bfe}_pm.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img1711.png"
 ALT="$\displaystyle = {\bf e}_\pm.$">|; 

$key = q/displaystyle={bfj}times{bfB}-nablap,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1547.png"
 ALT="$\displaystyle = {\bf j}\times{\bf B} - \nabla p,$">|; 

$key = q/displaystyle={bfj}times{bfB}_0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.54ex; " SRC="|."$dir".q|img1685.png"
 ALT="$\displaystyle = {\bf j}\times{\bf B}_0,$">|; 

$key = q/displaystyle={bfp}_s+m_s,n_s,{bfV}_s{bfV}_s,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1035.png"
 ALT="$\displaystyle ={\bf p}_s + m_s  n_s {\bf V}_s{\bf V}_s,$">|; 

$key = q/displaystyle={bfq}_s+{bfp}_scdot{bfV}_s+frac{3}{2},p_s,{bfV}_s+frac{1}{2},m_s,n_s,V_s^{2},{bfV}_s.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img1037.png"
 ALT="$\displaystyle = {\bf q}_s + {\bf p}_s\cdot{\bf V}_s + \frac{3}{2} p_s {\bf V}_s
+\frac{1}{2} m_s  n_s V_s^{2}  {\bf V}_s.$">|; 

$key = q/displaystyle={bfu}_0({bfR},{bfU},t,gamma)+epsilon,{bfu}_1({bfR},{bfU},t,gamma)+cdots.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img291.png"
 ALT="$\displaystyle = {\bf u}_0({\bf R}, {\bf U}, t, \gamma) +
\epsilon {\bf u}_1({\bf R}, {\bf U}, t, \gamma) + \cdots.$">|; 

$key = q/displaystyle={bfv},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img276.png"
 ALT="$\displaystyle = {\bf v},$">|; 

$key = q/displaystyle={bfv}_s+frac{mu_{ss'}}{m_s},{bfg}_{ss'},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.41ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img736.png"
 ALT="$\displaystyle = {\bf v}_s + \frac{\mu_{ss'}}{m_s} {\bf g}_{ss'},$">|; 

$key = q/displaystyle={bfv}_{s'}-frac{mu_{ss'}}{m_{s'}},{bfg}_{ss'}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.41ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img738.png"
 ALT="$\displaystyle = {\bf v}_{s'} -\frac{\mu_{ss'}}{m_{s'}} {\bf g}_{ss'}.$">|; 

$key = q/displaystyle={calE}_{0,perp}+left[frac{k(t)}{k(0)}right]{calE}_{0,parallel}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img549.png"
 ALT="$\displaystyle = {\cal E}_{0 \perp} + \left[\frac{k(t)}{k(0)}\right]{\cal E}_{0 \parallel}.$">|; 

$key = q/displaystyle={mitGamma},p_0,frac{{bfk}cdot{bfV}}{omega},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img2717.png"
 ALT="$\displaystyle ={\mit\Gamma} p_0 \frac{{\bf k}\cdot{\bf V}}{\omega},$">|; 

$key = q/displaystyle={rmerf}(zeta)-zeta,frac{d,{rmerf}}{dzeta},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img915.png"
 ALT="$\displaystyle = {\rm erf}(\zeta)-\zeta \frac{d {\rm erf}}{d\zeta},$">|; 

$key = q/displaystyle={rme}^{+z}left[1-frac{4,m^2-1}{8,z}+{calO}left(frac{1}{z^2}right)right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3024.png"
 ALT="$\displaystyle = {\rm e}^{+z}\left[1-\frac{4 m^2-1}{8 z} +{\cal O}\left(\frac{1}{z^2}\right)\right],$">|; 

$key = q/displaystyle={rme}^{-skew{3}hat{mitPhi}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1618.png"
 ALT="$\displaystyle = {\rm e}^{-\skew{3}\hat{\mit\Phi}}.$">|; 

$key = q/displaystyle={rme}^{-z}left[1+frac{4,m^2-1}{8,z}+{calO}left(frac{1}{z^2}right)right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3022.png"
 ALT="$\displaystyle = {\rm e}^{-z}\left[1+\frac{4 m^2-1}{8 z} +{\cal O}\left(\frac{1}{z^2}\right)\right],$">|; 

$key = q/displaystyle={rmi},k,B_0,F,phi_1+frac{eta}{mu_0}left(frac{d^2}{dx^2}-k^2right)psi_1,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3303.png"
 ALT="$\displaystyle = {\rm i} k B_0 F \phi_1 + \frac{\eta}{\mu_0}\left(\frac{d^2}{dx^2}-k^2\right)\psi_1,$">|; 

$key = q/displaystyle={rmi},k_0,c,{bfB},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2176.png"
 ALT="$\displaystyle ={\rm i} k_0 c {\bf B},$">|; 

$key = q/displaystyle={rmi},mu_0^{-1},k,B_0,Fleft(frac{d^2}{dx^2}-k^2-frac{d^2Fslashdx^2}{F}right)psi_1+muleft(frac{d^2}{dx^2}-k^2right)^2phi_1.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.91ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3739.png"
 ALT="$\displaystyle = {\rm i} \mu_0^{-1} k B_0 F\left(
\frac{d^2}{dx^2}-k^2 - \frac{d^2F/dx^2}{F}\right)\psi_1+\mu\left(\frac{d^2}{dx^2}-k^2\right)^2\phi_1.$">|; 

$key = q/displaystyle={rmi},mu_0^{-1},k,B_0,Fleft(frac{d^2}{dx^2}-k^2-frac{d^2Fslashdx^2}{F}right)psi_1,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3305.png"
 ALT="$\displaystyle = {\rm i} \mu_0^{-1} k B_0 F\left(
\frac{d^2}{dx^2}-k^2 - \frac{d^2F/dx^2}{F}\right)\psi_1,$">|; 

$key = q/displaystyle={skew{3}hat{phi},hat{U}}+S^{2},{hat{J},hat{psi}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3484.png"
 ALT="$\displaystyle = \{\skew{3}\hat{\phi},\hat{U}\}+S^{2} \{\hat{J},\hat{\psi}\},$">|; 

$key = q/displaystyle={skew{3}hat{phi},hat{psi}}+hat{J},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3482.png"
 ALT="$\displaystyle =\{\skew{3}\hat{\phi},\hat{\psi}\}+\hat{J},$">|; 

$key = q/displaystyle=|{bfv}_s-{bfv}_{s'}|,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img998.png"
 ALT="$\displaystyle = \vert{\bf v}_s-{\bf v}_{s'}\vert,$">|; 

$key = q/displaystyleA;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img1744.png"
 ALT="$\displaystyle A$">|; 

$key = q/displaystyleA=-{rmi},{rmsgn}(epsilon),B.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.58ex; " SRC="|."$dir".q|img2021.png"
 ALT="$\displaystyle A = -{\rm i} {\rm sgn}(\epsilon) B.$">|; 

$key = q/displaystyleB(x,t)=B_0,(1+k^2,x^2),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img539.png"
 ALT="$\displaystyle B(x,t) = B_0 (1+k^2 x^2),
$">|; 

$key = q/displaystyleB,frac{dmu}{dt}=m,frac{d}{dt}left(U_{0,parallel},{bfv}_Ecdot{bfb}right)=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img382.png"
 ALT="$\displaystyle B \frac{d\mu}{dt} = m \frac{d}{dt}\left(U_{0 \parallel} {\bf v}_E\cdot{\bf b}\right) = 0,$">|; 

$key = q/displaystyleB;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img1746.png"
 ALT="$\displaystyle B$">|; 

$key = q/displaystyleB=frac{B_E}{L^3}frac{(1+3,sin^2vartheta)^{1slash2}}{cos^6vartheta},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img444.png"
 ALT="$\displaystyle B = \frac{B_E}{L^3} \frac{(1+3 \sin^2\vartheta)^{1/2}}{\cos^6\vartheta},$">|; 

$key = q/displaystyleB_phi(r,theta,phi);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2830.png"
 ALT="$\displaystyle B_\phi(r,\theta,\phi)$">|; 

$key = q/displaystyleB_pm(y)=C_pm,frac{I_{mpm1}(q,y)}{I_{mpm1}(q)};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -2.08ex; " SRC="|."$dir".q|img3005.png"
 ALT="$\displaystyle B_\pm(y) = C_\pm \frac{I_{m\pm 1}(q y)}{I_{m\pm 1}(q)}$">|; 

$key = q/displaystyleB_pm(y)=D_pm,frac{K_{mpm1}(s,y)}{K_{mpm1}(s)};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img3006.png"
 ALT="$\displaystyle B_\pm(y) = D_\pm   \frac{K_{m\pm 1}(s y)}{K_{m\pm 1}(s)}$">|; 

$key = q/displaystyleB_pm;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img2989.png"
 ALT="$\displaystyle B_\pm$">|; 

$key = q/displaystyleB_r(r,theta,phi);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2827.png"
 ALT="$\displaystyle B_r(r,\theta,\phi)$">|; 

$key = q/displaystyleB_t=varpi,chi.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2971.png"
 ALT="$\displaystyle B_t = \varpi \chi.$">|; 

$key = q/displaystyleB_theta(r,theta,phi);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2829.png"
 ALT="$\displaystyle B_\theta(r,\theta,\phi)$">|; 

$key = q/displaystyleB_x(z,t)equivB_x(z),exp(-{rmi},omega,t).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.58ex; " SRC="|."$dir".q|img1912.png"
 ALT="$\displaystyle B_x(z,t) \equiv B_x(z) \exp(-{\rm i} \omega t).$">|; 

$key = q/displaystyleB_z=B_0left(1+frac{z^2}{L^2}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img536.png"
 ALT="$\displaystyle B_z = B_0\left(1+\frac{z^2}{L^2}\right),
$">|; 

$key = q/displaystyleB_{rmmirror}=frac{mu_{rmtrap}}{mu},B_{rmmax}<B_{rmmax}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img428.png"
 ALT="$\displaystyle B_{\rm mirror} = \frac{\mu_{\rm trap}}{\mu} B_{\rm max} &lt; B_{\rm max}.$">|; 

$key = q/displaystyleC;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img1748.png"
 ALT="$\displaystyle C$">|; 

$key = q/displaystyleC=-nu,(f-f_0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1635.png"
 ALT="$\displaystyle C = -\nu (f-f_0)
$">|; 

$key = q/displaystyleC=frac{epsilon_0,A}{d}frac{(dslash!sqrt{2},lambda_D)}{tanh(dslash!sqrt{2},lambda_D)}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.91ex; vertical-align: -2.47ex; " SRC="|."$dir".q|img181.png"
 ALT="$\displaystyle C = \frac{\epsilon_0 A}{d}\frac{(d/\!\sqrt{2} \lambda_D)}{\tanh(d/\!\sqrt{2} \lambda_D)}.
$">|; 

$key = q/displaystyleC_e=-nu_e,(f_e-f_0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1651.png"
 ALT="$\displaystyle C_e = -\nu_e (f_e-f_0)
$">|; 

$key = q/displaystyleC_pm=D_pm.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3012.png"
 ALT="$\displaystyle C_\pm = D_\pm.$">|; 

$key = q/displaystyleC_s(f)=sum_{s'}C_{ss'}(f_s,f_{s'}),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -2.62ex; " SRC="|."$dir".q|img1038.png"
 ALT="$\displaystyle C_s(f) =\sum_{s'} C_{ss'}(f_s, f_{s'}),$">|; 

$key = q/displaystyleC_{ss'}(f_s,f_{s'})=frac{gamma_{ss'}}{m_s},frac{partial}{partial{bfv}_s}cdotint{bfw}_{ss'}cdot{bfJ}_{ss'},d^3{bfv}_{s'},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img992.png"
 ALT="$\displaystyle C_{ss'}(f_s,f_{s'}) = \frac{\gamma_{ss'}}{m_s} \frac{\partial}{\partial{\bf v}_s}\cdot\int {\bf w}_{ss'}\cdot {\bf J}_{ss'} d^3{\bf v}_{s'},
$">|; 

$key = q/displaystyleC_{ss'},d^3{bfv}_s=C_{s's},d^3{bfv}_{s'}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img656.png"
 ALT="$\displaystyle C_{ss'} d^3{\bf v}_s=C_{s's} d^3{\bf v}_{s'}.$">|; 

$key = q/displaystyleC_{ss'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img748.png"
 ALT="$\displaystyle C_{ss'}$">|; 

$key = q/displaystyleC_{ss'}=-frac{1}{m_s},frac{partial}{partial{bfv}_s}cdot{bfA}_{ss'},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img785.png"
 ALT="$\displaystyle C_{ss'} = -\frac{1}{m_s} \frac{\partial}{\partial {\bf v}_s}\cdot {\bf A}_{ss'},$">|; 

$key = q/displaystyleC_{ss'}=frac{gamma_{ss'}}{m_s},frac{partial}{partial{bfv}_s}cdotint{bfw}_{ss'}cdot{bfJ}_{ss'},d^3{bfv}_{s'},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img783.png"
 ALT="$\displaystyle C_{ss'} = \frac{\gamma_{ss'}}{m_s} \frac{\partial}{\partial {\bf v}_s}\cdot\int {\bf w}_{ss'}\cdot{\bf J}_{ss'} d^3{\bf v}_{s'},$">|; 

$key = q/displaystyleC_{ss'}=int!!int!!intu_{ss'},frac{dsigma}{d{mitOmega}},(f_s',f_{s'}'-f_s,f_{s'}),d^3{bfv}_{s'},d{mitOmega},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img731.png"
 ALT="$\displaystyle C_{ss'}= \int\!\!\int\!\!\int u_{ss'} \frac{d\sigma}{d{\mit\Omega}} (f_s' f_{s'}'-f_s f_{s'}) 
d^3{\bf v}_{s'} d{\mit\Omega},$">|; 

$key = q/displaystyleD;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img1801.png"
 ALT="$\displaystyle D$">|; 

$key = q/displaystyleD=frac{R-L}{2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.46ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img1737.png"
 ALT="$\displaystyle D = \frac{R-L}{2},$">|; 

$key = q/displaystyleE(varphi,k);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3572.png"
 ALT="$\displaystyle E(\varphi,k)$">|; 

$key = q/displaystyleE_0=frac{m_i,g}{2,e}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img188.png"
 ALT="$\displaystyle E_0 = \frac{m_i g}{2 e}.
$">|; 

$key = q/displaystyleE_1simeqfrac{E_0}{epsilon},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img513.png"
 ALT="$\displaystyle E_1 \simeq \frac{E_0}{\epsilon},
$">|; 

$key = q/displaystyleE_parallelequiv{bfE}cdot{bfb}simepsilon,E.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img298.png"
 ALT="$\displaystyle E_\parallel \equiv {\bf E}\cdot {\bf b} \sim \epsilon E.$">|; 

$key = q/displaystyleE_parallelsimeq0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img1518.png"
 ALT="$\displaystyle E_\parallel \simeq 0.$">|; 

$key = q/displaystyleE_t+({bfV}_ptimes{bfB}_p)cdot{bfe}_theta=eta,j_t.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2954.png"
 ALT="$\displaystyle E_t + ({\bf V}_p\times{\bf B}_p)\cdot {\bf e}_\theta=\eta  j_t.$">|; 

$key = q/displaystyleE_t=-frac{1}{varpi}frac{partialpsi}{partialt}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2955.png"
 ALT="$\displaystyle E_t =-\frac{1}{\varpi}\frac{\partial\psi}{\partial t}.$">|; 

$key = q/displaystyleE_x(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2197.png"
 ALT="$\displaystyle E_x(z)$">|; 

$key = q/displaystyleE_x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1761.png"
 ALT="$\displaystyle E_x$">|; 

$key = q/displaystyleE_y(hat{z});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2027.png"
 ALT="$\displaystyle E_y(\hat{z})$">|; 

$key = q/displaystyleE_y(hat{z})=Asqrt{hat{z}},J_1!left(2sqrt{hat{z}}right)+Bsqrt{hat{z}},Y_1!left(2sqrt{hat{z}}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.23ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img1989.png"
 ALT="$\displaystyle E_y(\hat{z}) = A\sqrt{\hat{z}} J_1\!\left(2\sqrt{\hat{z}}\right) + B\sqrt{\hat{z}} Y_1\!\left(2\sqrt{\hat{z}}\right),$">|; 

$key = q/displaystyleE_y(hat{z})=C,{rmAi}(-hat{z})simeqfrac{C}{sqrt{pi}},hat{z}^{-1slash4},sinleft(frac{2}{3},hat{z}^{3slash2}+frac{pi}{4}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.52ex; vertical-align: -2.30ex; " SRC="|."$dir".q|img1964.png"
 ALT="$\displaystyle E_y(\hat{z}) = C {\rm Ai}(-\hat{z}) \simeq \frac{C}{\sqrt{\pi}}  \hat{z}^{-1/4} \sin
\left(\frac{2}{3} \hat{z}^{3/2}+\frac{\pi}{4}\right),$">|; 

$key = q/displaystyleE_y(hat{z})=Csqrt{a,hat{z}},I_1!left(2sqrt{a,hat{z}}right)+Dsqrt{a,hat{z}},K_1!left(2sqrt{a,hat{z}}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.23ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img1997.png"
 ALT="$\displaystyle E_y(\hat{z}) = C\sqrt{a \hat{z}} I_1\!\left(2\sqrt{a \hat{z}}\right) + D\sqrt{a \hat{z}} K_1\!\left(2\sqrt{a \hat{z}}\right),$">|; 

$key = q/displaystyleE_y(t)=int_{-infty}^{infty}F(omega),{rme}^{-{rmi},omega,t},domega,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img2058.png"
 ALT="$\displaystyle E_y(t) = \int_{-\infty}^{\infty} F(\omega) {\rm e}^{-{\rm i}   \omega  t} d\omega,$">|; 

$key = q/displaystyleE_y(y);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1983.png"
 ALT="$\displaystyle E_y(y)$">|; 

$key = q/displaystyleE_y(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1940.png"
 ALT="$\displaystyle E_y(z)$">|; 

$key = q/displaystyleE_y(z)=A,{rme}^{,{rmi},phi(z)},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.68ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1919.png"
 ALT="$\displaystyle E_y(z) = A {\rm e}^{ {\rm i} \phi(z)},$">|; 

$key = q/displaystyleE_y(z)=E,n^{-1slash2},expleft(-{rmi},k_0!int_0^z!n,dz'right)+F,n^{-1slash2},expleft(+{rmi},k_0!int_0^z!n,dz'right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2031.png"
 ALT="$\displaystyle E_y(z) = E  n^{-1/2} \exp\left(- {\rm i}  k_0 \!\int_0^z \!n dz'\right)
+ F n^{-1/2} \exp\left(+{\rm i}  k_0 \!\int_0^z \!n dz'\right).$">|; 

$key = q/displaystyleE_y(z)=n^{-1slash2},expleft(-{rmi},k_0!int_0^z!n,dz'right)+R,n^{-1slash2},expleft(+{rmi},k_0!int_0^z!n,dz'right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1961.png"
 ALT="$\displaystyle E_y(z) = n^{-1/2} \exp\left(- {\rm i}  k_0 \!\int_0^z \!n dz'\right)
+ R n^{-1/2} \exp\left(+{\rm i}  k_0 \!\int_0^z \!n dz'\right).$">|; 

$key = q/displaystyleE_y(z)simeqn^{-1slash2},expleft(pm{rmi},k_0!int^z!n,dz'right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1935.png"
 ALT="$\displaystyle E_y(z) \simeq n^{-1/2} \exp\left(\pm {\rm i}  k_0\! \int^z \!n dz'\right).$">|; 

$key = q/displaystyleE_y(z,t)=int_{-infty}^{infty}frac{F(omega)}{n^{1slash2}(omega,z)},,{rme}^{,{rmi},phi(omega,z,t)},domega,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.05ex; " SRC="|."$dir".q|img2066.png"
 ALT="$\displaystyle E_y(z,t) = \int_{-\infty}^{\infty} \frac{F(\omega)}{n^{1/2}(\omega, z)}  
{\rm e}^{ {\rm i}  \phi(\omega, z,t)} d\omega,$">|; 

$key = q/displaystyleE_y(z,t)equivE_y(z),exp(-{rmi},omega,t),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1911.png"
 ALT="$\displaystyle E_y(z,t) \equiv E_y(z) \exp(-{\rm i} \omega t),$">|; 

$key = q/displaystyleE_y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1763.png"
 ALT="$\displaystyle E_y$">|; 

$key = q/displaystyleE_z(z)=E_0left[1-expleft(frac{sqrt{2},z}{lambda_D}right)right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.69ex; vertical-align: -2.26ex; " SRC="|."$dir".q|img187.png"
 ALT="$\displaystyle E_z(z) = E_0\left[1-\exp\left(\frac{\sqrt{2} z}{\lambda_D}\right)\right],
$">|; 

$key = q/displaystyleE_zsimfrac{eta,B_ast}{mu_0,delta_ast}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img3633.png"
 ALT="$\displaystyle E_z \sim \frac{\eta B_\ast}{\mu_0 \delta_\ast}.$">|; 

$key = q/displaystyleE_{ss'}=frac{1}{2},mu_{ss'},h^{2}left[left(frac{dz}{dtheta}right)^2+z^{2}right]+k_{ss'},z.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.26ex; " SRC="|."$dir".q|img696.png"
 ALT="$\displaystyle E_{ss'} = \frac{1}{2} \mu_{ss'} h^{2}\left[\left(\frac{dz}{d\theta}\right)^2 + z^{2}\right] + k_{ss'} z.$">|; 

$key = q/displaystyleE_{ss'}=frac{1}{2},mu_{ss'},|dot{bfr}_{ss'}|^{2}+frac{k_{ss'}}{|{bfr}_{ss'}|};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.98ex; " SRC="|."$dir".q|img684.png"
 ALT="$\displaystyle E_{ss'} = \frac{1}{2} \mu_{ss'} \vert\dot{\bf r}_{ss'}\vert^{2} + \frac{k_{ss'}}{\vert{\bf r}_{ss'}\vert}$">|; 

$key = q/displaystyleE_{ss'}=frac{1}{2},mu_{ss'}left(skew{3}dot{r}^{2}+r^{2},skew{3}dot{theta}^{2}right)+frac{k_{ss'}}{r}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img691.png"
 ALT="$\displaystyle E_{ss'}= \frac{1}{2} \mu_{ss'}\left(\skew{3}\dot{r}^{2} + r^{2} \skew{3}\dot{\theta}^{2}\right) + \frac{k_{ss'}}{r}.$">|; 

$key = q/displaystyleE_{y,s}simeqsqrt{frac{2pi,{rmi}}{phi_s''}},frac{F(omega_s)}{n^{1slash2}(omega_s,z)},{rme}^{,{rmi},phi_s}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.75ex; vertical-align: -2.74ex; " SRC="|."$dir".q|img2078.png"
 ALT="$\displaystyle E_{y s}\simeq \sqrt{\frac{2\pi {\rm i}}{\phi_s''}}
  \frac{F(\omega_s)}{n^{1/2}(\omega_s, z)}  {\rm e}^{ {\rm i} \phi_s}.$">|; 

$key = q/displaystyleF(hat{x})=left{{array}{lcl}F'(0),hat{x}&mbox{hspace{0.5cm}}&|hat{x}|<1[0.5ex]F'(0),{rmsgn}(hat{x})&&|hat{x}|geq1{array}right..;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.27ex; " SRC="|."$dir".q|img3726.png"
 ALT="$\displaystyle F(\hat{x}) = \left\{\begin{array}{lcl}
F'(0) \hat{x}&amp;\mbox{\hspa...
... [0.5ex]
F'(0) {\rm sgn}(\hat{x})&amp;&amp;\vert\hat{x}\vert\geq 1\end{array}\right..
$">|; 

$key = q/displaystyleF^{2}=(B^{2}-4,A,C)=(R,L-P,S)^2,sin^4theta+4,P^{2},D^{2},cos^2theta.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1752.png"
 ALT="$\displaystyle F^{2} = (B^{2}-4 A C) = (R L - P S)^2 \sin^4\theta + 4 P^{2}  D^{2} \cos^2\theta.$">|; 

$key = q/displaystyleF^{2}=(R,L-P,S)^2,sin^4theta+4,P^{2},D^{2},cos^2theta.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1876.png"
 ALT="$\displaystyle F^{2} = (R L-P S)^2 \sin^4\theta + 4 P^{2} D^{2} \cos^2\theta.
$">|; 

$key = q/displaystyleF_0(u)=frac{n}{(2pi,T_eslashm_e)^{1slash2}},expleft(-frac{m_e,u^2}{2,T_e}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2284.png"
 ALT="$\displaystyle F_0(u) = \frac{n}{(2\pi T_e/m_e)^{1/2}} \exp\left(-\frac{m_e u^2}{2 T_e}\right).$">|; 

$key = q/displaystyleF_0(u)=n_e,frac{v_e}{2pi}left[frac{1}{v_e^{2}+(u-V)^{2}}+frac{1}{v_e^{2}+(u+V)^{2}}right].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2546.png"
 ALT="$\displaystyle F_0(u) = n_e \frac{v_e}{2\pi}\left[\frac{1}{v_e^{2}+(u-V)^{2}} + \frac{1}{v_e^{2}+(u+V)^{2}}\right].$">|; 

$key = q/displaystyleF_1(u,t)=frac{1}{2pi,{rmi}}int_Cbar{F}_1(u,p),{rme}^{p,t},dp,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img2263.png"
 ALT="$\displaystyle F_1(u,t) = \frac{1}{2\pi {\rm i}}\int_C \bar{F}_1(u,p) {\rm e}^{p t} dp,$">|; 

$key = q/displaystyleF_1(zeta);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img914.png"
 ALT="$\displaystyle F_1(\zeta)$">|; 

$key = q/displaystyleF_2(zeta);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img916.png"
 ALT="$\displaystyle F_2(\zeta)$">|; 

$key = q/displaystyleF_{0,e}(u_e)=frac{n}{(2pi,T_eslashm_e)^{1slash2}}expleft[-frac{m_e,(u_e-U_e)^{2}}{2,T_e}right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2573.png"
 ALT="$\displaystyle F_{0 e}(u_e) = \frac{n}{(2\pi T_e/m_e)^{1/2}}\exp\left[-\frac{m_e (u_e-U_e)^{2}}{2 T_e}\right],$">|; 

$key = q/displaystyleF_{0,e}(u_e)=n,frac{v_e}{pi},frac{1}{v_e^{2}+(u_e-U_e)^2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.13ex; vertical-align: -2.18ex; " SRC="|."$dir".q|img2557.png"
 ALT="$\displaystyle F_{0 e}(u_e) = n \frac{v_e}{\pi} \frac{1}{v_e^{2} + (u_e-U_e)^2},$">|; 

$key = q/displaystyleF_{0,i}(u_i)=frac{n}{(2pi,T_islashm_i)^{1slash2}}expleft(-frac{m_i,u_i^{2}}{2,T_i}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.63ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2574.png"
 ALT="$\displaystyle F_{0 i}(u_i) = \frac{n}{(2\pi T_i/m_i)^{1/2}}\exp\left(-\frac{m_i u_i^{2}}{2 T_i}\right),$">|; 

$key = q/displaystyleF_{0,i}(u_i)=n,frac{v_i}{pi},frac{1}{v_i^{2}+u_i^{2}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.35ex; vertical-align: -2.43ex; " SRC="|."$dir".q|img2558.png"
 ALT="$\displaystyle F_{0 i}(u_i) = n \frac{v_i}{\pi} \frac{1}{v_i^{2} + u_i^{2}}.$">|; 

$key = q/displaystyleF_{ss',alpha};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img935.png"
 ALT="$\displaystyle F_{ss' \alpha}$">|; 

$key = q/displaystyleG=intg,d^3{bfr}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img1064.png"
 ALT="$\displaystyle G = \int g d^3{\bf r}.$">|; 

$key = q/displaystyleG_+,G_-=frac{{rmi}}{2},{mitOmega},tau_R,(G_+-G_-),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3017.png"
 ALT="$\displaystyle G_+ G_- = \frac{{\rm i}}{2} {\mit\Omega} \tau_R (G_+-G_-),$">|; 

$key = q/displaystyleG_pm=q+s+left(frac{m^2}{2}pmm+frac{3}{8}right),left(frac{1}{q}+frac{1}{s}right)+{calO}left(frac{1}{q^{2}}+frac{1}{s^{2}}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3026.png"
 ALT="$\displaystyle G_\pm = q + s + \left(\frac{m^2}{2}\pm m + \frac{3}{8}\right) \l...
...q} + \frac{1}{s}\right) + {\cal O}\left(\frac{1}{q^{2}}+\frac{1}{s^{2}}\right).$">|; 

$key = q/displaystyleG_pm=q,frac{I_{mpm1}'(q)}{I_{mpm1}(q)}-s,frac{K_{mpm1}'(s)}{K_{mpm1}(s)}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -2.08ex; " SRC="|."$dir".q|img3018.png"
 ALT="$\displaystyle G_\pm = q \frac{I_{m\pm 1}'(q)}{I_{m\pm 1}(q)} - s \frac{K_{m\pm 1}'(s)}
{K_{m\pm 1}(s)}.$">|; 

$key = q/displaystyleG_{s'}(zeta)=frac{n_{s'},v_{t,{s'}}}{2,zeta}left[zeta,frac{d,{rmerf}}{dzeta}+left(1+2,zeta^{2}right){rmerf}(zeta)right].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img909.png"
 ALT="$\displaystyle G_{s'}(\zeta) = \frac{n_{s'} v_{t {s'}}}{2 \zeta}\left[\zeta \frac{d {\rm erf}}{d\zeta}+\left(1+2 \zeta^{2}\right){\rm erf}(\zeta)\right].$">|; 

$key = q/displaystyleG_{s'}({bfv}_s);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img791.png"
 ALT="$\displaystyle G_{s'}({\bf v}_s)$">|; 

$key = q/displaystyleH=sum_sintf_s,lnf_s,d^3{bfv}_s.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.58ex; vertical-align: -2.62ex; " SRC="|."$dir".q|img850.png"
 ALT="$\displaystyle H = \sum_s\int f_s \ln f_s d^3{\bf v}_s.$">|; 

$key = q/displaystyleH_{s'}(zeta)=frac{n_{s'}}{v_{t,{s'}}},frac{{rmerf}(zeta)}{zeta},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img905.png"
 ALT="$\displaystyle H_{s'}(\zeta) = \frac{n_{s'}}{v_{t {s'}}} \frac{{\rm erf}(\zeta)}{\zeta},$">|; 

$key = q/displaystyleH_{s'}({bfv}_s);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img793.png"
 ALT="$\displaystyle H_{s'}({\bf v}_s)$">|; 

$key = q/displaystyleI=2pi,frac{m}{e},mu+{calO}(epsilon).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img407.png"
 ALT="$\displaystyle I = 2\pi  \frac{m}{e} \mu + {\cal O}(\epsilon).$">|; 

$key = q/displaystyleI=2pi,m,frac{u_perp^{2}}{{mitOmega}}+2pi,frac{e}{{mitOmega}},langle{bfu}cdot(;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.85ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img403.png"
 ALT="$\displaystyle I = 2\pi m \frac{u_\perp^{2}}{{\mit\Omega}} + 2\pi \frac{e}{{\mit\Omega}} 
\langle {\bf u}\cdot($">|; 

$key = q/displaystyleI=A,e,n_s,left(frac{T_e}{m_i}right)^{1slash2}left[left(frac{m_i}{2pi,m_e}right)^{1slash2}expleft(frac{e,V}{T_e}right)-1right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.26ex; " SRC="|."$dir".q|img1620.png"
 ALT="$\displaystyle I = A e n_s \left(\frac{T_e}{m_i}\right)^{1/2}\left[\left(\frac{m_i}{2\pi m_e}\right)^{1/2}\exp\left(\frac{e V}{T_e}\right)-1\right],$">|; 

$key = q/displaystyleI_1,frac{dhat{W}}{dhat{t}}={mitDelta}',;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.13ex; vertical-align: -1.71ex; " SRC="|."$dir".q|img3530.png"
 ALT="$\displaystyle I_1 \frac{d\hat{W}}{d\hat{t}} = {\mit\Delta}',$">|; 

$key = q/displaystyleI_1,frac{dhat{W}}{dhat{t}}simeq{mitDelta}'(0)-alpha,hat{W}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.13ex; vertical-align: -1.71ex; " SRC="|."$dir".q|img3604.png"
 ALT="$\displaystyle I_1 \frac{d\hat{W}}{d\hat{t}} \simeq {\mit\Delta}'(0)-\alpha \hat{W}.$">|; 

$key = q/displaystyleI_1,tau_R,frac{d(Wslasha)}{dt}={mitDelta}',;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3535.png"
 ALT="$\displaystyle I_1 \tau_R \frac{d(W/a)}{dt} = {\mit\Delta}',$">|; 

$key = q/displaystyleI_1=2int_0^inftyfrac{langlecosxirangle^2}{langle1rangle},d{mitOmega}=0.8227.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.35ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img3531.png"
 ALT="$\displaystyle I_1 =2\int_0^\infty \frac{\langle \cos\xi\rangle^2}{\langle 1\rangle} d{\mit\Omega} = 0.8227.$">|; 

$key = q/displaystyleI_m,frac{dhat{W}}{dhat{t}}={mitDelta}'_m,frac{skew{3}hat{mitPsi}_m}{skew{3}hat{mitPsi}_1},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.69ex; vertical-align: -2.28ex; " SRC="|."$dir".q|img3551.png"
 ALT="$\displaystyle I_m \frac{d\hat{W}}{d\hat{t}} = {\mit\Delta}'_m \frac{\skew{3}\hat{\mit\Psi}_m}{\skew{3}\hat{\mit\Psi}_1},$">|; 

$key = q/displaystyleI_m=2int_{-1}^inftyfrac{langlecos(m,xi)rangle,langlecosxirangle}{langle1rangle},d{mitOmega}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.05ex; " SRC="|."$dir".q|img3552.png"
 ALT="$\displaystyle I_m = 2\int_{-1}^\infty \frac{\langle\cos(m \xi)\rangle \langle \cos\xi\rangle}{\langle 1\rangle} d{\mit\Omega}.$">|; 

$key = q/displaystyleI_m=int_0^inftyK_m(k),dk,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.13ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img3574.png"
 ALT="$\displaystyle I_m = \int_0^\infty K_m(k) dk,$">|; 

$key = q/displaystyleI_n(lambda_s)rightarrowleft(frac{lambda_s}{2}right)^{|n|};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img2429.png"
 ALT="$\displaystyle I_n(\lambda_s) \rightarrow \left(\frac{\lambda_s}{2}\right)^{\vert n\vert}$">|; 

$key = q/displaystyleI_n=intfrac{f}{n}left(frac{v}{v_t}right)^n,d^3{bfv}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.52ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1629.png"
 ALT="$\displaystyle I_n = \int \frac{f}{n}\left(\frac{v}{v_t}\right)^n d^3{\bf v}.
$">|; 

$key = q/displaystyleI_s=A,e,n_s,left(frac{T_e}{m_i}right)^{1slash2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1621.png"
 ALT="$\displaystyle I_s = A e n_s \left(\frac{T_e}{m_i}\right)^{1/2}.$">|; 

$key = q/displaystyleJ(x,y,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3292.png"
 ALT="$\displaystyle J(x,y,t)$">|; 

$key = q/displaystyleJ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3267.png"
 ALT="$\displaystyle J$">|; 

$key = q/displaystyleJ=mointv_parallel,ds+e,ointA_parallel,ds=mointv_parallel,ds+e,{mitPsi}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img492.png"
 ALT="$\displaystyle J = m\oint v_\parallel ds + e \oint A_\parallel  ds
= m\oint v_\parallel ds + e {\mit\Psi}.$">|; 

$key = q/displaystyleJ=mointv_parallel,ds.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img494.png"
 ALT="$\displaystyle J = m\oint v_\parallel ds.$">|; 

$key = q/displaystyleJ_0(x)=-frac{B_0}{a},cosh^{-2}left(frac{x}{a}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img3274.png"
 ALT="$\displaystyle J_0(x) = -\frac{B_0}{a} \cosh^{-2}\left(\frac{x}{a}\right).$">|; 

$key = q/displaystyleK(p)=frac{p^2}{Q+p^2},frac{dskew{3}bar{phi}}{dp}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.35ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img3431.png"
 ALT="$\displaystyle K(p) = \frac{p^2}{Q+p^2} \frac{d\skew{3}\bar{\phi}}{dp}.$">|; 

$key = q/displaystyleK(varphi,k);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3570.png"
 ALT="$\displaystyle K(\varphi,k)$">|; 

$key = q/displaystyleK(z)={rme}^{-zslash2},L(z).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3438.png"
 ALT="$\displaystyle K(z)= {\rm e}^{-z/2} L(z).$">|; 

$key = q/displaystyleK=frac{m_i,V_s^{,2}}{2,T_e},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.30ex; vertical-align: -1.96ex; " SRC="|."$dir".q|img1579.png"
 ALT="$\displaystyle K =\frac{m_i V_s^{ 2}}{2 T_e},$">|; 

$key = q/displaystyleK=frac{m}{2}(U_{0,parallel}^{2}+{bfv}_E^{2}+u_perp^{2});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.01ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img377.png"
 ALT="$\displaystyle K = \frac{m}{2} (U_{0 \parallel}^{2} + {\bf v}_E^{2} + u_\perp^{2})$">|; 

$key = q/displaystyleK_m(k)=8,k,frac{langlecos(m,xi)rangle,langlecosxirangle}{langle1rangle}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.98ex; " SRC="|."$dir".q|img3575.png"
 ALT="$\displaystyle K_m(k) = 8 k  \frac{\langle\cos(m \xi)\rangle \langle \cos\xi\rangle}{\langle 1\rangle}.$">|; 

$key = q/displaystyleK_{11};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img2432.png"
 ALT="$\displaystyle K_{11}$">|; 

$key = q/displaystyleK_{12};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img2434.png"
 ALT="$\displaystyle K_{12}$">|; 

$key = q/displaystyleK_{33};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2436.png"
 ALT="$\displaystyle K_{33}$">|; 

$key = q/displaystyleK_{ss'}=frac{1}{2},m_s,v_s^{2}+frac{1}{2},m_{s'},v_{s'}^{2}=frac{1}{2},(m_s+m_{s'}),U_{ss'}^{2}+frac{1}{2},mu_{ss'},u_{ss'}^{2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img600.png"
 ALT="$\displaystyle K_{ss'} = \frac{1}{2} m_s v_s^{2} + \frac{1}{2} m_{s'} v_{s'}...
...= \frac{1}{2} (m_s+m_{s'}) U_{ss'}^{2} + \frac{1}{2} \mu_{ss'} u_{ss'}^{2}.$">|; 

$key = q/displaystyleKsimeqeointA_phi,ds=e,{mitPsi},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img502.png"
 ALT="$\displaystyle K \simeq e\oint A_\phi ds = e {\mit\Psi},$">|; 

$key = q/displaystyleKsimeqointp_phi,ds,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img498.png"
 ALT="$\displaystyle K \simeq \oint p_\phi ds,$">|; 

$key = q/displaystyleL(z)=U!left[frac{1}{4},(Q^{3slash2}-1),-frac{1}{2},zright],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3441.png"
 ALT="$\displaystyle L(z) =U\!\left[\frac{1}{4} (Q^{3/2}-1),-\frac{1}{2},z\right],$">|; 

$key = q/displaystyleL,frac{dI}{dt}+R,I=frac{M}{2pi},{mitOmega},I,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2895.png"
 ALT="$\displaystyle L \frac{dI}{dt} + R I = \frac{M}{2\pi} {\mit\Omega} I,$">|; 

$key = q/displaystyleL,v_0simdelta_ast,v_ast,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3634.png"
 ALT="$\displaystyle L v_0 \sim \delta_\ast v_\ast,$">|; 

$key = q/displaystyleL;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img1719.png"
 ALT="$\displaystyle L$">|; 

$key = q/displaystyleL=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1774.png"
 ALT="$\displaystyle L=0.$">|; 

$key = q/displaystyleL={mitOmega},r_A^{2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.64ex; " SRC="|."$dir".q|img2868.png"
 ALT="$\displaystyle L = {\mit\Omega} r_A^{2}.$">|; 

$key = q/displaystyleLrightarrowinfty.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1778.png"
 ALT="$\displaystyle L\rightarrow \infty.$">|; 

$key = q/displaystyleM_1^{2}>1+frac{2}{{mitGamma},beta_1}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img3149.png"
 ALT="$\displaystyle M_1^{2} &gt; 1 + \frac{2}{{\mit\Gamma} \beta_1}.$">|; 

$key = q/displaystyleM_2=left[frac{2+({mitGamma}-1),M_1^{2}}{2,{mitGamma},M_1^{2}-({mitGamma}-1)}right]^{1slash2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.25ex; vertical-align: -2.44ex; " SRC="|."$dir".q|img3233.png"
 ALT="$\displaystyle M_2 = \left[\frac{2+({\mit\Gamma}-1) M_1^{2}}{2 {\mit\Gamma} M_1^{2} - ({\mit\Gamma}-1)}\right]^{1/2}.
$">|; 

$key = q/displaystyleM_2^{2}<1+frac{2}{{mitGamma},beta_2}:;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img3235.png"
 ALT="$\displaystyle M_2^{2} &lt; 1+ \frac{2}{{\mit\Gamma} \beta_2}:
$">|; 

$key = q/displaystyleM_A=sqrt{frac{u_r^{2}}{B_r^{2}slashmu_0,rho}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.75ex; vertical-align: -2.64ex; " SRC="|."$dir".q|img2865.png"
 ALT="$\displaystyle M_A = \sqrt{\frac{u_r^{2}}{B_r^{2}/\mu_0 \rho}}$">|; 

$key = q/displaystyleM_A^{2}=frac{u_r,r^{2}}{u_{r,A},r_A^{2}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.63ex; vertical-align: -2.41ex; " SRC="|."$dir".q|img2872.png"
 ALT="$\displaystyle M_A^{2} = \frac{u_r r^{2}}{u_{r A} r_A^{2}},$">|; 

$key = q/displaystyleM_{11};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img2443.png"
 ALT="$\displaystyle M_{11}$">|; 

$key = q/displaystyleM_{12};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img2445.png"
 ALT="$\displaystyle M_{12}$">|; 

$key = q/displaystyleM_{22};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img2459.png"
 ALT="$\displaystyle M_{22}$">|; 

$key = q/displaystyleM_{33};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2447.png"
 ALT="$\displaystyle M_{33}$">|; 

$key = q/displaystyleN_psimL,k_psimepsilon^{1slash4},{calS}^{3slash8}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.62ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3716.png"
 ALT="$\displaystyle N_p \sim L k_p \sim \epsilon^{1/4} {\cal S}^{3/8}.$">|; 

$key = q/displaystyleP;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img1721.png"
 ALT="$\displaystyle P$">|; 

$key = q/displaystyleP=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img1772.png"
 ALT="$\displaystyle P=0,$">|; 

$key = q/displaystyleP=frac{mu_0,mu}{eta,rho},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img3750.png"
 ALT="$\displaystyle P = \frac{\mu_0 \mu}{\eta \rho},
$">|; 

$key = q/displaystyleP=frac{tau_R}{tau_M};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.35ex; vertical-align: -1.95ex; " SRC="|."$dir".q|img3742.png"
 ALT="$\displaystyle P = \frac{\tau_R}{\tau_M}
$">|; 

$key = q/displaystyleP_z=-frac{(E_y,B_x^{,ast}+E_y^{,ast},B_x)}{4,mu_0}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img2037.png"
 ALT="$\displaystyle P_z = - \frac{(E_y B_x^{ \ast} + E_y^{ \ast} B_x)}{4  \mu_0}.$">|; 

$key = q/displaystyleP_z=-frac{{rmi}}{4,mu_0,omega}left(frac{dE_y}{dz},E_y^{,ast}-frac{dE_y^{,ast}}{dz},E_yright).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.58ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2039.png"
 ALT="$\displaystyle P_z = -\frac{{\rm i}}{4 \mu_0 \omega} \left(\frac{d E_y}{dz}  E_y^{ \ast}
- \frac{d E_y^{ \ast}}{dz}  E_y\right).$">|; 

$key = q/displaystylePsimeq1-frac{{{mitPi}}_e^{2}}{omega^2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img1782.png"
 ALT="$\displaystyle P \simeq 1 - \frac{{{\mit\Pi}}_e^{2}}{\omega^2}.$">|; 

$key = q/displaystylePsimeq1-frac{{{mitPi}}_e^{2}}{omega^2}=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img1826.png"
 ALT="$\displaystyle P \simeq 1 - \frac{{{\mit\Pi}}_e^{2}}{\omega^2} = 0,$">|; 

$key = q/displaystyleQ(r)=-qleft[1-left(1+frac{sqrt{2},r}{lambda_D}right)expleft(-frac{sqrt{2},r}{lambda_D}right)right].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.69ex; vertical-align: -2.26ex; " SRC="|."$dir".q|img174.png"
 ALT="$\displaystyle Q(r) = -q\left[1-\left(1+\frac{\sqrt{2} r}{\lambda_D}\right)\exp\left(-\frac{\sqrt{2} r}{\lambda_D}\right)\right].
$">|; 

$key = q/displaystyleQ,K(p)=-a_{-1}+frac{a_{-1},Q^{2},p^2}{2}+frac{a_0,Q^2,p^3}{3}+{calO}(p^4).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3433.png"
 ALT="$\displaystyle Q K(p) =-a_{-1} + \frac{a_{-1} Q^{2} p^2}{2}+\frac{a_0 Q^2 p^3}{3}+ {\cal O}(p^4).$">|; 

$key = q/displaystyleQ,K(z)=-a_{-1}+frac{a_{-1},Q^{3slash2},z}{2}+frac{a_0,Q^{5slash4},z^{3slash2}}{3}+{calO}(z^2),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3436.png"
 ALT="$\displaystyle Q K(z) = -a_{-1} + \frac{a_{-1} Q^{3/2} z}{2} +\frac{a_0 Q^{5/4} z^{3/2}}{3} + {\cal O}(z^2),$">|; 

$key = q/displaystyleQ,L(z)=-a_{-1}+frac{a_{-1},(Q^{3slash2}-1),z}{2}+frac{a_0,Q^{5slash4},z^{3slash2}}{3}+{calO}(z^2),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3440.png"
 ALT="$\displaystyle Q L(z)= -a_{-1}+ \frac{a_{-1} (Q^{3/2}-1) z}{2} + \frac{a_0 Q^{5/4} z^{3/2}}{3} +{\cal O}(z^2),$">|; 

$key = q/displaystyleQ=S^{1slash3},hat{gamma}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3386.png"
 ALT="$\displaystyle Q = S^{1/3} \hat{\gamma}.$">|; 

$key = q/displaystyleQ^{1slash2}llpllQ^{-1slash4},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3402.png"
 ALT="$\displaystyle Q^{1/2} \ll p \ll Q^{-1/4},$">|; 

$key = q/displaystyleQll1.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3396.png"
 ALT="$\displaystyle Q\ll 1.$">|; 

$key = q/displaystyleR;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img1717.png"
 ALT="$\displaystyle R$">|; 

$key = q/displaystyleR=-{rmi}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1966.png"
 ALT="$\displaystyle R = -{\rm i}.$">|; 

$key = q/displaystyleR=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img1773.png"
 ALT="$\displaystyle R=0,$">|; 

$key = q/displaystyleR=1+{mitGamma},M_1^{2},(1-r^{-1})+beta_1^{-1},(1-r^{2}),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.66ex; " SRC="|."$dir".q|img3137.png"
 ALT="$\displaystyle R = 1+ {\mit\Gamma} M_1^{2} (1-r^{-1}) + \beta_1^{-1} (1-r^{2}),$">|; 

$key = q/displaystyleR=L=S;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img1878.png"
 ALT="$\displaystyle R=L=S$">|; 

$key = q/displaystyleRrightarrowinfty,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img1777.png"
 ALT="$\displaystyle R\rightarrow \infty,$">|; 

$key = q/displaystyleRsimeq1-frac{{mitPi}_e^{2}}{omega,(omega+{rmi},nu_e-|{mitOmega}_e|)}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.30ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img2050.png"
 ALT="$\displaystyle R \simeq 1- \frac{{\mit\Pi}_e^{2}}{\omega (\omega+{\rm i} \nu_e
-\vert{\mit\Omega}_e\vert)}.$">|; 

$key = q/displaystyleS,hat{gamma},(hat{psi}-hat{x},skew{3}hat{phi});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3337.png"
 ALT="$\displaystyle S \hat{\gamma} (\hat{\psi}-\hat{x} \skew{3}\hat{\phi})$">|; 

$key = q/displaystyleS,hat{gamma}left(hat{psi}-F,skew{3}hat{phi}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.23ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img3315.png"
 ALT="$\displaystyle S \hat{\gamma}\left(\hat{\psi}-F \skew{3}\hat{\phi}\right)$">|; 

$key = q/displaystyleS;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img1799.png"
 ALT="$\displaystyle S$">|; 

$key = q/displaystyleS=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img1779.png"
 ALT="$\displaystyle S = 0.$">|; 

$key = q/displaystyleS=1-frac{{{mitPi}}_e^{2}}{omega^2-{{mitOmega}}_e^{2}}-frac{{{mitPi}}_i^{2}}{omega^2-{{mitOmega}}_i^{2}}=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.43ex; " SRC="|."$dir".q|img1860.png"
 ALT="$\displaystyle S = 1- \frac{{{\mit\Pi}}_e^{2}}{\omega^2-{{\mit\Omega}}_e^{2}}
- \frac{{{\mit\Pi}}_i^{2}}{\omega^2-{{\mit\Omega}}_i^{2}}=0.$">|; 

$key = q/displaystyleS=frac{R+L}{2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.46ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img1736.png"
 ALT="$\displaystyle S =\frac{R+L}{2},$">|; 

$key = q/displaystyleS=frac{mu_0,V,L}{eta}simeqfrac{|nablatimes({bfV}times{bfB})|}{|(etaslashmu_0),nabla^{2}{bfB}|},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img3239.png"
 ALT="$\displaystyle S = \frac{\mu_0 V L}{\eta} \simeq \frac{\vert\nabla\times({\bf V}\times {\bf B})\vert}
{\vert(\eta/\mu_0) \nabla^{2}{\bf B}\vert},$">|; 

$key = q/displaystyleS=frac{tau_R,({mitOmega}^{2},a^2+U^{2})^{1slash2}}{a};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img3042.png"
 ALT="$\displaystyle S = \frac{\tau_R ({\mit\Omega}^{2} a^2+U^{2})^{1/2}}{a}$">|; 

$key = q/displaystyleS=frac{tau_R}{tau_H},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.35ex; vertical-align: -1.95ex; " SRC="|."$dir".q|img3038.png"
 ALT="$\displaystyle S = \frac{\tau_R}{\tau_H},$">|; 

$key = q/displaystyleS=frac{tau_R}{tau_H}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.35ex; vertical-align: -1.95ex; " SRC="|."$dir".q|img3309.png"
 ALT="$\displaystyle S= \frac{\tau_R}{\tau_H}.$">|; 

$key = q/displaystyleS=lnleft(frac{p}{rho^{{mitGamma}}}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3116.png"
 ALT="$\displaystyle S = \ln\left(\frac{p}{\rho^{{\mit\Gamma}}}\right).$">|; 

$key = q/displaystyleS^2-D^{2}=R,L.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img1874.png"
 ALT="$\displaystyle S^2-D^{2} = R L.
$">|; 

$key = q/displaystyleS^2-D^{2}equivR,L,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img1742.png"
 ALT="$\displaystyle S^2 - D^{2} \equiv R L,$">|; 

$key = q/displaystyleS_c=17.7.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img3043.png"
 ALT="$\displaystyle S_c = 17.7.$">|; 

$key = q/displaystyleT(r)=T(a)left(frac{a}{r}right)^{2slash7}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.74ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img2765.png"
 ALT="$\displaystyle T(r) = T(a)\left(\frac{a}{r}\right)^{2/7}.$">|; 

$key = q/displaystyleT<T_0equivfrac{G,M_odot,m_p}{4,a},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.74ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img2779.png"
 ALT="$\displaystyle T &lt; T_0 \equiv \frac{G M_\odot m_p}{4 a},$">|; 

$key = q/displaystyleT_e<10,{rmeV}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img845.png"
 ALT="$\displaystyle T_e&lt;10 {\rm eV}.$">|; 

$key = q/displaystyleT_sequivfrac{1}{3},m_s,langlev_s^{2}rangle;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img31.png"
 ALT="$\displaystyle T_s \equiv \frac{1}{3}  m_s  \langle v_s^{2}\rangle$">|; 

$key = q/displaystyleT_sequivfrac{p_s}{n_s}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.41ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img1033.png"
 ALT="$\displaystyle T_s \equiv \frac{p_s}{n_s}.$">|; 

$key = q/displaystyleT_{alphabeta}=frac{B_alpha,B_beta-delta_{alphabeta},B^{2}slash2}{mu_0}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img2686.png"
 ALT="$\displaystyle T_{\alpha\beta} = \frac{B_\alpha B_\beta- \delta_{\alpha\beta}  B^{2}/2}{\mu_0}.$">|; 

$key = q/displaystyleU(x,y,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3296.png"
 ALT="$\displaystyle U(x,y,t)$">|; 

$key = q/displaystyleU;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img2400.png"
 ALT="$\displaystyle U$">|; 

$key = q/displaystyleU=frac{1}{2},rho,V^{2}+frac{p}{{mitGamma}-1}+frac{B^{2}}{2,mu_0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.35ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img3054.png"
 ALT="$\displaystyle U = \frac{1}{2} \rho V^{2} + \frac{p}{{\mit \Gamma}-1} + \frac{B^{2}}{2 \mu_0}$">|; 

$key = q/displaystyleU_parallel=pmleft[(2slashm),({calE}-mu,B-e,{mitPhi})-{bfv}_E^{2}right]^{1slash2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.68ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img415.png"
 ALT="$\displaystyle U_\parallel = \pm \left[(2/m) ({\cal E} -\mu B-e {\mit\Phi})-{\bf v}_E^{2}\right]^{1/2}.$">|; 

$key = q/displaystyleU_{e,c}=c_sleft[1+left(frac{m_i}{m_e}right)^{1slash2},left(frac{T_e}{T_i}right)^{3slash2}expleft(-frac{T_e}{2,T_i}right)right].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.26ex; " SRC="|."$dir".q|img2589.png"
 ALT="$\displaystyle U_{e c}= c_s\left[1+\left(\frac{m_i}{m_e}\right)^{1/2} \left(\frac{T_e}{T_i}\right)^{3/2}
\exp\left(-\frac{T_e}{2 T_i}\right)\right].$">|; 

$key = q/displaystyleU_{e,c}=left(frac{T_i}{m_e}right)^{1slash2}=left(frac{T_i}{T_e}right)^{1slash2}v_e.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2572.png"
 ALT="$\displaystyle U_{e c} = \left(\frac{T_i}{m_e}\right)^{1/2} = \left(\frac{T_i}{T_e}\right)^{1/2} v_e.$">|; 

$key = q/displaystyleUsimdelta,V.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img2680.png"
 ALT="$\displaystyle U \sim \delta  V.$">|; 

$key = q/displaystyleV_1^{2}>V_{S,1}^{2}+V_{A,1}^{2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.57ex; vertical-align: -0.69ex; " SRC="|."$dir".q|img3150.png"
 ALT="$\displaystyle V_1^{2} &gt; V_{S 1}^{2} + V_{A 1}^{2},$">|; 

$key = q/displaystyleV_2<V_{+,2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3236.png"
 ALT="$\displaystyle V_2 &lt; V_{+ 2},
$">|; 

$key = q/displaystyleV_A=sqrt{frac{B_0^{2}}{mu_0,rho_0}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.75ex; vertical-align: -2.43ex; " SRC="|."$dir".q|img2722.png"
 ALT="$\displaystyle V_A = \sqrt{\frac{B_0^{2}}{\mu_0 \rho_0}}$">|; 

$key = q/displaystyleV_A=sqrt{frac{B_0^{2}}{mu_0,rho}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.75ex; vertical-align: -2.43ex; " SRC="|."$dir".q|img1812.png"
 ALT="$\displaystyle V_A = \sqrt{\frac{B_0^{2}}{\mu_0 \rho}}$">|; 

$key = q/displaystyleV_S=sqrt{frac{{mitGamma},p_0}{rho_0}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.75ex; vertical-align: -2.71ex; " SRC="|."$dir".q|img2723.png"
 ALT="$\displaystyle V_S = \sqrt{\frac{{\mit\Gamma} p_0}{\rho_0}}$">|; 

$key = q/displaystyleV_esimV_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1427.png"
 ALT="$\displaystyle V_e \sim V_i$">|; 

$key = q/displaystyleV_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1568.png"
 ALT="$\displaystyle V_i$">|; 

$key = q/displaystyleV_pm=left{frac{1}{2}left[V_A^{2}+V_S^{2}pmsqrt{(V_A^{2}+V_S^{2})^{2}-4,V_A^{2},V_S^{2},cos^2theta},right]right}^{1slash2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2731.png"
 ALT="$\displaystyle V_\pm = \left\{\frac{1}{2}\left[V_A^{2} + V_S^{2} \pm \sqrt{
(V_A^{2} + V_S^{2})^{2} - 4  V_A^{2} V_S^{2} \cos^2\theta}
 \right]\right\}^{1/2}.$">|; 

$key = q/displaystyleV_s=left(frac{T_e}{m_i}right)^{1slash2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1590.png"
 ALT="$\displaystyle V_s = \left(\frac{T_e}{m_i}\right)^{1/2}.$">|; 

$key = q/displaystyleV_x=frac{E_y}{B_0},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img1822.png"
 ALT="$\displaystyle V_x = \frac{E_y}{B_0},$">|; 

$key = q/displaystyleV_y=-frac{E_x}{B_0},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.85ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img1820.png"
 ALT="$\displaystyle V_y = - \frac{E_x}{B_0},$">|; 

$key = q/displaystyleV_{+,1}>costheta_1,V_{A,1}>V_{-,1}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3176.png"
 ALT="$\displaystyle V_{+ 1}&gt; \cos\theta_1 V_{A 1}&gt; V_{- 1}.$">|; 

$key = q/displaystyleV_{e,s}=frac{j_e}{e,n_s}=left(frac{T_e}{2pi,m_e}right)^{1slash2}expleft[frac{e,({mitPhi}_w-{mitPhi}_s)}{T_e}right];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1599.png"
 ALT="$\displaystyle V_{e s} = \frac{j_e}{e n_s}= \left(\frac{T_e}{2\pi m_e}\right)^{1/2} \exp\left[\frac{e ({\mit\Phi}_w-{\mit\Phi}_s)}{T_e}\right]$">|; 

$key = q/displaystyleV_{x,1},B_{y,1}-V_{y,1},B_{x,1}=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3155.png"
 ALT="$\displaystyle V_{x 1} B_{y 1} - V_{y 1} B_{x 1} = 0.$">|; 

$key = q/displaystyleV_{x,2},B_{y,2}-V_{y,2},B_{x,2}=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3156.png"
 ALT="$\displaystyle V_{x 2} B_{y 2} - V_{y 2} B_{x 2} = 0,$">|; 

$key = q/displaystyleVggv_t.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1434.png"
 ALT="$\displaystyle V\gg v_t.$">|; 

$key = q/displaystyleVsimdelta,v_tsimv_d,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1454.png"
 ALT="$\displaystyle V \sim \delta v_t \sim v_d,$">|; 

$key = q/displaystyleVsimv_t.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1444.png"
 ALT="$\displaystyle V \sim v_t.$">|; 

$key = q/displaystyleW;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img2402.png"
 ALT="$\displaystyle W$">|; 

$key = q/displaystyleW=-frac{{rmi}}{4,mu_0,omega}left(frac{d^2E_y}{dz^{2}},E_y^{,ast}-frac{d^2E_y^{,ast}}{dz^{2}},E_yright).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.26ex; " SRC="|."$dir".q|img2043.png"
 ALT="$\displaystyle W = -\frac{{\rm i}}{4 \mu_0 \omega}\left(\frac{d^2 E_y}{dz^{2}} E_y^{ \ast}
- \frac{d^2 E_y^{ \ast}}{dz^{2}} E_y\right).$">|; 

$key = q/displaystyleW=left(frac{k_0^{2},b}{2,mu_0,omega}right)left(frac{epsilon}{z^{2}+epsilon^{2}}right)|E_y|^{2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.69ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2044.png"
 ALT="$\displaystyle W = \left(\frac{k_0^{2} b}{2 \mu_0 \omega}\right)\left( \frac{\epsilon}{z^{2} + \epsilon^{2}}\right)\vert E_y\vert^{2}.$">|; 

$key = q/displaystyleW_{s's}=-W_{ss'}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img932.png"
 ALT="$\displaystyle W_{s's} = - W_{ss'}.$">|; 

$key = q/displaystyleW_{ss'}({bfr},t)=intfrac{1}{2},m_s,v_s^{2},C_{ss'},d^3{bfv}_s,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img929.png"
 ALT="$\displaystyle W_{ss'}({\bf r},t) = \int\frac{1}{2} m_s v_s^{2} C_{ss'} d^3{\bf v}_s,$">|; 

$key = q/displaystyleW_{ss'}({bfr},t)=intfrac{1}{2},m_{s'},v_{s'}^{2},C_{ss'},d^3{bfv}_{s'},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img930.png"
 ALT="$\displaystyle W_{ss'}({\bf r},t) = \int\frac{1}{2} m_{s'} v_{s'}^{2} C_{ss'} d^3{\bf v}_{s'},$">|; 

$key = q/displaystyleW_{ss'}+W_{s's}=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1048.png"
 ALT="$\displaystyle W_{ss'} + W_{s's} =0.$">|; 

$key = q/displaystyleW_{ss'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img958.png"
 ALT="$\displaystyle W_{ss'}$">|; 

$key = q/displaystyleW_{ss'}=-frac{3,mu_{ss'},n_s}{tau_{ss'},m_{s'}},(T_s-T_{s'}).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img968.png"
 ALT="$\displaystyle W_{ss'} = -\frac{3 \mu_{ss'} n_s}{\tau_{ss'} m_{s'}} (T_s-T_{s'}).$">|; 

$key = q/displaystyleW_{ss'}=-frac{8,gamma_{ss'},n_s,n_{s'}}{pi^{1slash2},m_s,m_{s'},(v_{t,s}^{2}+v_{t,{s'}}^{2})^{3slash2}},(T_s-T_{s'}).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.35ex; vertical-align: -2.42ex; " SRC="|."$dir".q|img963.png"
 ALT="$\displaystyle W_{ss'} = -\frac{8 \gamma_{ss'} n_s n_{s'}}{\pi^{1/2} m_s m_{s'} (v_{t s}^{2}+v_{t {s'}}^{2})^{3/2}} (T_s-T_{s'}).$">|; 

$key = q/displaystyleW_{ss'}=w_{ss'}+{bfV}_scdot{bfF}_{ss'}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1051.png"
 ALT="$\displaystyle W_{ss'} = w_{ss'} + {\bf V}_s\cdot{\bf F}_{ss'}.$">|; 

$key = q/displaystyleW_{ss'}equivintfrac{1}{2},m_s,v^2,C_{ss'},d^3{bfv};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img1047.png"
 ALT="$\displaystyle W_{ss'} \equiv \int \frac{1}{2} m_s v^2 C_{ss'} d^3{\bf v}$">|; 

$key = q/displaystyleZ'(xi_n);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2427.png"
 ALT="$\displaystyle Z'(\xi_n)$">|; 

$key = q/displaystyleZ'(zeta)=-pi^{-1slash2}int_{-infty}^{infty}frac{2,t}{t-zeta},{rme}^{-t^{2}},dt=-2,(1+zeta,Z).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.13ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img2324.png"
 ALT="$\displaystyle Z'(\zeta) =-\pi^{-1/2}\int_{-\infty}^{\infty} \frac{2 t}{t-\zeta} 
{\rm e}^{-t^{2}} dt = -2 (1+\zeta Z).$">|; 

$key = q/displaystyleZ'(zeta)=pi^{-1slash2}int_{-infty}^{infty}frac{{rme}^{-t^{2}}}{(t-zeta)^2},dt,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.63ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img2323.png"
 ALT="$\displaystyle Z'(\zeta) = \pi^{-1/2}\int_{-\infty}^{\infty} \frac{{\rm e}^{-t^{2}}}{(t-\zeta)^2} 
dt,$">|; 

$key = q/displaystyleZ'(zeta_e)simeq-{rmi},2!sqrt{pi},zeta_e,{rme}^{-zeta_e^{2}}-2,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.73ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2581.png"
 ALT="$\displaystyle Z'(\zeta_e) \simeq - {\rm i} 2\!\sqrt{\pi} \zeta_e {\rm e}^{-\zeta_e^{2}} - 2,$">|; 

$key = q/displaystyleZ'(zeta_e)simeq-{rmi},2!sqrt{pi},zeta_e,{rme}^{-zeta_e^{2}}-2.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.73ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2664.png"
 ALT="$\displaystyle Z'(\zeta_e) \simeq - {\rm i} 2\!\sqrt{\pi} \zeta_e {\rm e}^{-\zeta_e^{2}} - 2.
$">|; 

$key = q/displaystyleZ'(zeta_i)simeq-{rmi},2!sqrt{pi},zeta_i,{rme}^{-zeta_i^{2}}+frac{1}{zeta_i^{2}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.35ex; vertical-align: -2.43ex; " SRC="|."$dir".q|img2582.png"
 ALT="$\displaystyle Z'(\zeta_i)\simeq - {\rm i} 2\!\sqrt{\pi} \zeta_i {\rm e}^{-\zeta_i^{2}} + \frac{1}{\zeta_i^{2}},$">|; 

$key = q/displaystyleZ(0)=pi^{-1slash2},P!int_{-infty}^{infty}frac{{rme}^{-t^{2}}}{t},dt+{rmi},pi^{1slash2}={rmi},pi^{1slash2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.52ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img2325.png"
 ALT="$\displaystyle Z(0) = \pi^{-1/2} P\!\int_{-\infty}^{\infty} \frac{{\rm e}^{-t^{2}}}{t} dt
+ {\rm i} \pi^{1/2} = {\rm i} \pi^{1/2}.$">|; 

$key = q/displaystyleZ(xi_n);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2425.png"
 ALT="$\displaystyle Z(\xi_n)$">|; 

$key = q/displaystyleZ(zeta)=pi^{-1slash2}int_{-infty}^{infty}frac{{rme}^{-t^{2}}}{t-zeta},dt,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.63ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img2319.png"
 ALT="$\displaystyle Z(\zeta) = \pi^{-1/2}\int_{-\infty}^{\infty} \frac{{\rm e}^{-t^{2}}}{t-\zeta} dt,$">|; 

$key = q/displaystyleZ(zeta)={rme}^{-zeta^{2}}left({rmi},pi^{1slash2}-2!int_0^zeta{rme}^{x^2},dxright).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.63ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2327.png"
 ALT="$\displaystyle Z(\zeta) = {\rm e}^{-\zeta^{2}}\left({\rm i} \pi^{1/2}
-2\!\int_0^\zeta {\rm e}^{x^2} dx\right).$">|; 

$key = q/displaystyleZ_i'(zeta);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.65ex; " SRC="|."$dir".q|img2622.png"
 ALT="$\displaystyle Z_i'(\zeta)$">|; 

$key = q/displaystyleZ_i(zeta);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2620.png"
 ALT="$\displaystyle Z_i(\zeta)$">|; 

$key = q/displaystyle[1+{rmi},k^{2}slash(mu_0,sigma,omega)],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3206.png"
 ALT="$\displaystyle [1+{\rm i} k^{2}/(\mu_0 \sigma \omega)],$">|; 

$key = q/displaystyle[1+{rmi},mu,k^{2}slash(rho_0,omega)].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3207.png"
 ALT="$\displaystyle [1+{\rm i} \mu k^{2}/(\rho_0 \omega)].$">|; 

$key = q/displaystyle[B_x]^2_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.66ex; " SRC="|."$dir".q|img3073.png"
 ALT="$\displaystyle [B_x]^2_1$">|; 

$key = q/displaystyle[S]^2_1=lnR-{mitGamma},lnr.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.66ex; " SRC="|."$dir".q|img3117.png"
 ALT="$\displaystyle [S]^2_1 =\ln R - {\mit\Gamma} \ln r.$">|; 

$key = q/displaystyle[V_x,B_y-V_y,B_x]^2_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.62ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3074.png"
 ALT="$\displaystyle [V_x B_y-V_y B_x]^2_1$">|; 

$key = q/displaystyle[phi,psi]=B_0,k,hat{x},frac{partialphi}{partialxi}+B_0,k,frac{partialphi}{partialhat{x}},skew{3}hat{mitPsi},sinxi.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img3468.png"
 ALT="$\displaystyle [\phi,\psi] = B_0 k \hat{x} \frac{\partial\phi}{\partial\xi} + B_0 k \frac{\partial\phi}{\partial \hat{x}} \skew{3}\hat{\mit\Psi} \sin\xi.$">|; 

$key = q/displaystyle[rho,V_x,V_y-B_x,B_yslashmu_0]^2_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.62ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3077.png"
 ALT="$\displaystyle [\rho V_x V_y - B_x B_y/\mu_0]^2_1$">|; 

$key = q/displaystyle[rho,V_x]_1^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.66ex; " SRC="|."$dir".q|img3075.png"
 ALT="$\displaystyle [\rho V_x]_1^2$">|; 

$key = q/displaystyle[rho,V_x^{2}+p+B_y^{2}slash2,mu_0]_1^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.79ex; vertical-align: -0.95ex; " SRC="|."$dir".q|img3076.png"
 ALT="$\displaystyle [\rho V_x^{2}+p + B_y^{2}/2 \mu_0]_1^2$">|; 

$key = q/displaystyle_0({bfR},{bfU},t,gamma)+epsilon,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img288.png"
 ALT="$\displaystyle _0({\bf R}, {\bf U}, t, \gamma) +
\epsilon $">|; 

$key = q/displaystyle_0({bfZ},t,tau)+epsilon,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img255.png"
 ALT="$\displaystyle _0({\bf Z}, t, \tau) + \epsilon $">|; 

$key = q/displaystyle_0({bfZ},t,tau)=int_0^tauleft[{bff}({bfZ},t,tau')-langle{bff}rangle({bfZ},t)right]dtau'.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.13ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img262.png"
 ALT="$\displaystyle _0 ({\bf Z}, t,\tau) = \int_0^\tau\left[
{\bf f}({\bf Z},t,\tau') - \langle{\bf f}\rangle({\bf Z},t)\right]d\tau'.$">|; 

$key = q/displaystyle_0({bfZ},t,tau)cdotnabla{bff}({bfZ},t,tau)rangleequivlangle;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img265.png"
 ALT="$\displaystyle _0({\bf Z},t,\tau)\cdot\nabla{\bf f}({\bf Z},t,\tau)\rangle\equiv \langle$">|; 

$key = q/displaystyle_0=-3,eta_0,left({bfb}{bfb}-frac{1}{3},{bfI}right)left({bfb}{bfb}-frac{1}{3},{bfI}right):nabla{bfV},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1267.png"
 ALT="$\displaystyle _0 = - 3 \eta_0 \left({\bf b}{\bf b} - \frac{1}{3} {\bf I}\right)
\left({\bf b}{\bf b} - \frac{1}{3} {\bf I}\right): \nabla {\bf V},$">|; 

$key = q/displaystyle_0cdotnabla{bff}rangle({bfZ},t)+{calO}(epsilon^2).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img268.png"
 ALT="$\displaystyle _0\cdot
\nabla {\bf f}\rangle({\bf Z},t) + {\cal O}(\epsilon^2).$">|; 

$key = q/displaystyle_0cdotnabla{bff}rangle({bfZ},t).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img266.png"
 ALT="$\displaystyle _0\cdot\nabla{\bf f}\rangle({\bf Z},t).$">|; 

$key = q/displaystyle_1({bfR},{bfU},t,gamma)+cdots,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img289.png"
 ALT="$\displaystyle _1({\bf R}, {\bf U}, t, \gamma) + \cdots,$">|; 

$key = q/displaystyle_1({bfZ},t,tau)+epsilon^2,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img256.png"
 ALT="$\displaystyle _1({\bf Z}, t, \tau) + \epsilon^2 $">|; 

$key = q/displaystyle_1=-eta_1left[{bfI}_perpcdot{bfW}cdot{bfI}_perp+frac{1}{2},{bfI}_perp,({bfb}cdot{bfW}cdot{bfb})right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1268.png"
 ALT="$\displaystyle _1 =- \eta_1\left[{\bf I}_\perp \cdot{\bf W}\cdot{\bf I}_\perp
+ \frac{1}{2} {\bf I}_\perp ({\bf b}\cdot{\bf W}\cdot{\bf b})\right],$">|; 

$key = q/displaystyle_2({bfZ},t,tau)+cdots,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img257.png"
 ALT="$\displaystyle _2({\bf Z}, t, \tau) +
\cdots,$">|; 

$key = q/displaystyle_2=-4,eta_1,left({bfI}_perpcdot{bfW}cdot{bfb}{bfb}+{bfb}{bfb}cdot{bfW}cdot{bfI}_perpright).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1269.png"
 ALT="$\displaystyle _2 = -4 \eta_1 \left({\bf I}_\perp\cdot
{\bf W}\cdot{\bf b}{\bf b}
+ {\bf b}{\bf b}\cdot{\bf W} \cdot{\bf I}_\perp\right).$">|; 

$key = q/displaystyle_3=frac{eta_3}{2},left({bfb}times{bfW}cdot{bfI}_perp-{bfI}_perpcdot{bfW}times{bfb}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.01ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img1270.png"
 ALT="$\displaystyle _3 = \frac{\eta_3}{2} \left( {\bf b}\times
{\bf W}\cdot{\bf I}_\perp - {\bf I}_\perp\cdot{\bf W}\times{\bf b}
\right),$">|; 

$key = q/displaystyle_4=2,eta_3,left({bfb}times{bfW}cdot{bfb}{bfb}-{bfb}{bfb}cdot{bfW}times{bfb}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1271.png"
 ALT="$\displaystyle _4 = 2 \eta_3 \left({\bf b} \times{\bf W} \cdot {\bf b}{\bf b}
- {\bf b}{\bf b} \cdot{\bf W} \times{\bf b}\right).$">|; 

$key = q/displaystyle_e+e,n,({bfE}+{bfV}_etimes{bfB});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1144.png"
 ALT="$\displaystyle _e + e  n 
({\bf E} + {\bf V}_e\times {\bf B})$">|; 

$key = q/displaystyle_e:nabla{bfV}_e+nablacdot{bfq}_e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1147.png"
 ALT="$\displaystyle _e:\nabla{\bf V}_e+ \nabla\cdot{\bf q}_e$">|; 

$key = q/displaystyle_e:nabla{bfV}_e+nablacdot{bfq}_{Te}+nablacdot{bfq}_{Ue};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1313.png"
 ALT="$\displaystyle _e:\nabla{\bf V}_e+ \nabla\cdot{\bf q}_{Te}
+ \nabla\cdot{\bf q}_{Ue}$">|; 

$key = q/displaystyle_e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 0.72ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1457.png"
 ALT="$\displaystyle _e$">|; 

$key = q/displaystyle_i-e,n,({bfE}+{bfV}_itimes{bfB});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1151.png"
 ALT="$\displaystyle _i - e  n 
({\bf E} + {\bf V}_i\times {\bf B})$">|; 

$key = q/displaystyle_i-en,({bfE}+{bfV}_itimes{bfB});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1379.png"
 ALT="$\displaystyle _i - e n 
({\bf E} + {\bf V}_i\times {\bf B})$">|; 

$key = q/displaystyle_i:nabla{bfV}_i+nablacdot{bfq}_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1154.png"
 ALT="$\displaystyle _i:\nabla{\bf V}_i+ \nabla\cdot{\bf q}_i$">|; 

$key = q/displaystyle_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1463.png"
 ALT="$\displaystyle _i$">|; 

$key = q/displaystyle_n,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 0.72ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1266.png"
 ALT="$\displaystyle _n,$">|; 

$key = q/displaystyle_s,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 0.72ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1084.png"
 ALT="$\displaystyle _s,$">|; 

$key = q/displaystyle_s-e_s,n_s,({bfE}+{bfV}_stimes{bfB});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1086.png"
 ALT="$\displaystyle _s - e_s  n_s 
({\bf E} + {\bf V}_s\times {\bf B})$">|; 

$key = q/displaystyle_s:nabla{bfV}_s+nablacdot{bfq}_s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1088.png"
 ALT="$\displaystyle _s:\nabla{\bf V}_s + \nabla \cdot{\bf q}_s$">|; 

$key = q/displaystylea,{mitOmega},B_r=frac{eta}{mu_0}left[frac{dB_theta}{dr}right]_{r=a_-}^{r=a_+}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.58ex; vertical-align: -2.32ex; " SRC="|."$dir".q|img3014.png"
 ALT="$\displaystyle a {\mit\Omega} B_r = \frac{\eta}{\mu_0}
\left[\frac{d B_\theta}{dr}\right]_{r=a_-}^{r=a_+}.$">|; 

$key = q/displaystylea=expleft[-{rmi},pi,{rmsgn}(epsilon)right].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.60ex; " SRC="|."$dir".q|img1992.png"
 ALT="$\displaystyle a = \exp\left[-{\rm i} \pi {\rm sgn}(\epsilon)\right].$">|; 

$key = q/displaystylea_s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img872.png"
 ALT="$\displaystyle a_s$">|; 

$key = q/displaystylealpha=frac{4}{pi},(2-hat{k}^2),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img3602.png"
 ALT="$\displaystyle \alpha = \frac{4}{\pi} (2-\hat{k}^2),$">|; 

$key = q/displaystylealpha=tan^{-1}(v_perpslashv_parallel),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.51ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img452.png"
 ALT="$\displaystyle \alpha = \tan^{-1}(v_\perp/v_\parallel),$">|; 

$key = q/displaystyleb=frac{h}{u_infty}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.85ex; vertical-align: -1.88ex; " SRC="|."$dir".q|img698.png"
 ALT="$\displaystyle b = \frac{h}{u_\infty}.$">|; 

$key = q/displaystyleb=frac{{mitPi}_e^{2}}{omega,|{mitOmega}_e|'},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.30ex; vertical-align: -1.98ex; " SRC="|."$dir".q|img2055.png"
 ALT="$\displaystyle b = \frac{{\mit\Pi}_e^{2}}{\omega \vert{\mit\Omega}_e\vert'},$">|; 

$key = q/displaystyleb^{2}left(frac{dz}{dtheta}right)^2=1-b^{2},z^{2}-left(frac{k_{ss'}}{E_{ss'}}right)z.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img699.png"
 ALT="$\displaystyle b^{2}\left(\frac{dz}{d\theta}\right)^2 = 1-b^{2} z^{2}- \left(\frac{k_{ss'}}{E_{ss'}}\right)z.$">|; 

$key = q/displaystyleb_{rmmax}=lambda_D,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img825.png"
 ALT="$\displaystyle b_{\rm max} = \lambda_D,$">|; 

$key = q/displaystyleb_{rmmin}simeqfrac{e_s,e_{s'}}{2pi,epsilon_0,mu_{ss'},u_{ss'}^{2}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.85ex; vertical-align: -2.42ex; " SRC="|."$dir".q|img821.png"
 ALT="$\displaystyle b_{\rm min} \simeq \frac{e_s e_{s'}}{2\pi \epsilon_0 \mu_{ss'} u_{ss'}^{2}}.$">|; 

$key = q/displaystyleb_{rmmin}simeqfrac{e_s,e_{s'}}{4pi,epsilon_0,T}=r_c,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.41ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img823.png"
 ALT="$\displaystyle b_{\rm min} \simeq \frac{e_s e_{s'}}{4\pi \epsilon_0 T}= r_c,$">|; 

$key = q/displaystylebar{E}(p)=-frac{(eslashepsilon_0)}{{rmi},k,epsilon(k,p)}int_{-infty}^inftyfrac{F_1(u,t=0)}{p+{rmi},k,u},du,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.13ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img2256.png"
 ALT="$\displaystyle \bar{E}(p) = -\frac{(e/\epsilon_0)}{{\rm i} k \epsilon(k,p)}
\int_{-\infty}^\infty \frac{F_1(u,t=0)}{p+{\rm i} k u} du,$">|; 

$key = q/displaystylebar{F}_1(u,p)=int_0^inftyF_1(u,t),{rme}^{-p,t},dt.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.13ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img2249.png"
 ALT="$\displaystyle \bar{F}_1(u,p) = \int_0^\infty F_1(u,t) {\rm e}^{-p t} dt.$">|; 

$key = q/displaystylebar{F}_1=frac{e}{m_e},bar{E},frac{partialF_0slashpartialu}{p+{rmi},k,u}+frac{F_1(u,t=0)}{p+{rmi},k,u},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img2261.png"
 ALT="$\displaystyle \bar{F}_1 = \frac{e}{m_e} \bar{E}  \frac{\partial F_0/\partial u}
{p+ {\rm i} k u} + \frac{F_1(u,t=0)}{p+ {\rm i} k u},$">|; 

$key = q/displaystylebeta=frac{2,mu_0,p}{B^{2}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img1541.png"
 ALT="$\displaystyle \beta = \frac{2 \mu_0 p}{B^{2}}$">|; 

$key = q/displaystylebeta=sum_sbeta_s.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -2.62ex; " SRC="|."$dir".q|img147.png"
 ALT="$\displaystyle \beta = \sum_s \beta_s.$">|; 

$key = q/displaystylebeta_s=frac{2,mu_0,p_s}{B^{2}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img146.png"
 ALT="$\displaystyle \beta_s = \frac{2 \mu_0 p_s}{B^{2}}.$">|; 

$key = q/displaystylebetall1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1545.png"
 ALT="$\displaystyle \beta\ll 1$">|; 

$key = q/displaystylebetasimleft(frac{V_S}{V_A}right)^2,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1542.png"
 ALT="$\displaystyle \beta \sim \left(\frac{V_S}{V_A}\right)^2,$">|; 

$key = q/displaystylec,B_x(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1942.png"
 ALT="$\displaystyle c B_x(z)$">|; 

$key = q/displaystylec,B_y(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2195.png"
 ALT="$\displaystyle c B_y(z)$">|; 

$key = q/displaystylec;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img876.png"
 ALT="$\displaystyle c$">|; 

$key = q/displaystylecdot(;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img324.png"
 ALT="$\displaystyle \cdot ($">|; 

$key = q/displaystylecdotfrac{partial{bfB}}{partialt}=e,{bfU}cdot{bfE}+mu,frac{partialB}{partialt}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img376.png"
 ALT="$\displaystyle \cdot
\frac{\partial {\bf B}}{\partial t} = e {\bf U}\cdot{\bf E} + \mu 
\frac{\partial B}{\partial t}.$">|; 

$key = q/displaystylecdotfrac{partial{bfB}}{partialt}=mu,frac{partialB}{partialt},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img374.png"
 ALT="$\displaystyle \cdot
\frac{\partial {\bf B}}{\partial t}= \mu \frac{\partial B}{\partial t},$">|; 

$key = q/displaystylecdotnabla),{bfA}({bfR})+{calO}(rho^2).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img400.png"
 ALT="$\displaystyle \cdot\nabla) {\bf A}({\bf R})
+ {\cal O}(\rho^2).$">|; 

$key = q/displaystylecdotnabla),{bfA}rangle+{calO}(epsilon).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img404.png"
 ALT="$\displaystyle \cdot
\nabla) {\bf A}\rangle + {\cal O}(\epsilon).$">|; 

$key = q/displaystylecdotnabla),{bfA}rangle=-2pi,e,frac{u_perp^{2}}{2,{mitOmega}^{2}},{bfb}cdotnablatimes{bfA}=-pi,m,frac{u_perp^{2}}{{mitOmega}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.85ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img406.png"
 ALT="$\displaystyle \cdot
\nabla) {\bf A}\rangle = -2\pi e \frac{u_\perp^{2}}{2 {...
...,
{\bf b}\cdot \nabla\times{\bf A} = -\pi m \frac{u_\perp^{2}}{{\mit\Omega}}.$">|; 

$key = q/displaystylecdotnabla),{bfA}rangle=-mu,B.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img510.png"
 ALT="$\displaystyle \cdot\nabla) {\bf A}\rangle = - \mu B.
$">|; 

$key = q/displaystylecdotnabla),{bfB}rangle-langle;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img325.png"
 ALT="$\displaystyle \cdot\nabla) {\bf B} \rangle
- \langle$">|; 

$key = q/displaystylecdotnabla),{bfB}rangle;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img322.png"
 ALT="$\displaystyle \cdot\nabla) {\bf B} \rangle$">|; 

$key = q/displaystylecdotnabla),{bfB}rangle=-mu,nablaB.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img507.png"
 ALT="$\displaystyle \cdot\nabla) {\bf B}\rangle =- \mu \nabla B.
$">|; 

$key = q/displaystylecdotnabla),{bfB}rangle=frac{m,u_perp^{2}}{2,B},nablaB.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.85ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img333.png"
 ALT="$\displaystyle \cdot\nabla ) {\bf B}\rangle =
\frac{m u_\perp^{2}}{2 B}  \nabla B.$">|; 

$key = q/displaystylecdotnabla),{bfE}rangle.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img368.png"
 ALT="$\displaystyle \cdot\nabla) {\bf E}\rangle.$">|; 

$key = q/displaystylecdotnabla),{bfE}rangle=-mu,{bfb}cdotnablatimes{bfE}=;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img373.png"
 ALT="$\displaystyle \cdot\nabla)
 {\bf E}\rangle = - \mu {\bf b}\cdot\nabla\times{\bf E} =$">|; 

$key = q/displaystylecdotnabla),{bfE}rangle=mu,frac{partialB}{partialt}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img509.png"
 ALT="$\displaystyle \cdot\nabla) {\bf E}\rangle = \mu \frac{\partial B}{\partial t}.
$">|; 

$key = q/displaystylecdotnablaB)rangle.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img328.png"
 ALT="$\displaystyle \cdot\nabla B)\rangle.$">|; 

$key = q/displaystylecdotnablaB-m,{bfb}cdotfrac{d{bfv}_E}{dt}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img345.png"
 ALT="$\displaystyle \cdot\nabla B
- m {\bf b}\cdot\frac{d{\bf v}_E}{dt}.$">|; 

$key = q/displaystylecdot{bfE},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img1678.png"
 ALT="$\displaystyle \cdot{\bf E},$">|; 

$key = q/displaystylechi=2,sin^{-1}left(frac{alpha}{sqrt{4+alpha^{2}}}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.52ex; vertical-align: -2.30ex; " SRC="|."$dir".q|img716.png"
 ALT="$\displaystyle \chi = 2 \sin^{-1}\left(\frac{\alpha}{\sqrt{4+\alpha^{2}}}\right),$">|; 

$key = q/displaystylechi=pi-2,{mitTheta}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img703.png"
 ALT="$\displaystyle \chi = \pi-2 {\mit\Theta}.$">|; 

$key = q/displaystylechi={mitOmega},(t-t')+theta.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2393.png"
 ALT="$\displaystyle \chi = {\mit\Omega} (t-t') + \theta.$">|; 

$key = q/displaystylechisimeqfrac{e_s,e_{s'}}{2pi,epsilon_0,mu_{ss'},u_{ss'}^{2},b},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.85ex; vertical-align: -2.42ex; " SRC="|."$dir".q|img770.png"
 ALT="$\displaystyle \chi\simeq \frac{e_s e_{s'}}{2\pi \epsilon_0 \mu_{ss'} u_{ss'}^{2} b},$">|; 

$key = q/displaystylecos^2vartheta_E=L^{-1}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img465.png"
 ALT="$\displaystyle \cos^2\vartheta_E = L^{-1}.$">|; 

$key = q/displaystylecotleft(frac{chi}{2}right)=frac{2,E_{ss'},b}{k_{ss'}}=frac{4pi,epsilon_0,mu_{ss'},u_{ss'}^{2},b}{e_s,e_{s'}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img717.png"
 ALT="$\displaystyle \cot\left(\frac{\chi}{2}\right) = \frac{2 E_{ss'} b}{k_{ss'}}= \frac{4\pi \epsilon_0 \mu_{ss'} u_{ss'}^{2} b}{e_s e_{s'}}.$">|; 

$key = q/displaystyled^3{bfv}_s,d^3{bfv}_{s'}=d^3{bfU}_{ss'},d^3{bfu}_{ss'}=d^3{bfU}_{ss'},d^3{bfu}_{ss'}'=d^3{bfv}_s',d^3{bfv}_{s'}'.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.51ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img609.png"
 ALT="$\displaystyle d^3{\bf v}_s d^3{\bf v}_{s'} = d^3{\bf U}_{ss'} d^3{\bf u}_{ss'} =d^3 {\bf U}_{ss'} d^3{\bf u}_{ss'}'= d^3{\bf v}_s' d^3{\bf v}_{s'}'.$">|; 

$key = q/displaystyledelta^{-1},v_tggVggdelta,v_t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2675.png"
 ALT="$\displaystyle \delta^{-1} v_t \gg V \gg \delta v_t$">|; 

$key = q/displaystyledelta_e,delta_illzeta_e,zeta_i,mull1,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1421.png"
 ALT="$\displaystyle \delta_e, \delta_i \ll \zeta_e, \zeta_i, \mu \ll 1,$">|; 

$key = q/displaystyledelta_e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1321.png"
 ALT="$\displaystyle \delta_e$">|; 

$key = q/displaystyledelta_esimdelta_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1425.png"
 ALT="$\displaystyle \delta_e \sim \delta_i$">|; 

$key = q/displaystyledelta_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1386.png"
 ALT="$\displaystyle \delta_i$">|; 

$key = q/displaystyledelta_iequivfrac{rho_i}{L}ll1.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.01ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img139.png"
 ALT="$\displaystyle \delta_i \equiv \frac{\rho_i}{L} \ll 1.$">|; 

$key = q/displaystyledelta_p<frac{1}{3},delta_{rmSP};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3723.png"
 ALT="$\displaystyle \delta_p &lt; \frac{1}{3} \delta_{\rm SP}$">|; 

$key = q/displaystyledelta_psimfrac{1}{Q^{1slash4}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img3418.png"
 ALT="$\displaystyle \delta_p \sim \frac{1}{Q^{1/4}}.$">|; 

$key = q/displaystyledeltaequivfrac{rho}{L}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.01ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img138.png"
 ALT="$\displaystyle \delta \equiv \frac{\rho}{L}.$">|; 

$key = q/displaystyledeltaomegasimeq-{rmi}sqrt{frac{pi}{8}}frac{{mitPi}_e}{(k,lambda_D)^3}expleft[-frac{1}{2,(k,lambda_D)^2}right].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.58ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2301.png"
 ALT="$\displaystyle \delta\omega \simeq - {\rm i}\sqrt{\frac{\pi}{8}} \frac{{\mit\Pi}_e}
{(k \lambda_D)^3} \exp\left[-\frac{1}{2 (k \lambda_D)^2}\right].$">|; 

$key = q/displaystyledeltaomegasimeqfrac{{rmi},pi}{2}frac{e^2,omega_0}{epsilon_0,m_e,k^2}left(frac{partialF_0}{partialu}right)_{u=omegaslashk},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.80ex; vertical-align: -2.52ex; " SRC="|."$dir".q|img2300.png"
 ALT="$\displaystyle \delta\omega \simeq \frac{{\rm i} \pi}{2} \frac{e^2 \omega_0}{\epsilon_0 m_e k^2}
\left(\frac{\partial
F_0}{\partial u}\right)_{u=\omega/k},$">|; 

$key = q/displaystyledeltarho(r)=-frac{2,q}{4pi,r,lambda_D^{2}}expleft(-frac{sqrt{2},r}{lambda_D}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.41ex; " SRC="|."$dir".q|img172.png"
 ALT="$\displaystyle \delta\rho(r) = - \frac{2 q}{4\pi r \lambda_D^{2}}\exp\left(-\frac{\sqrt{2} r}{\lambda_D}\right),
$">|; 

$key = q/displaystyledeltarho=deltarho_{rmext}+e,(deltan_i-deltan_e)simeqdeltarho_{rmext}-2,e^2,n_0,delta{mitPhi}slashT.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img65.png"
 ALT="$\displaystyle \delta\rho = \delta\rho_{\rm ext} + e (\delta n_i - \delta n_e)
\simeq \delta\rho_{\rm ext} -2  e^2  n_0  \delta{\mit\Phi}/T.$">|; 

$key = q/displaystyledeltasim|epsilon|=frac{nu_e}{|{mitOmega_e}|'}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.46ex; vertical-align: -1.98ex; " SRC="|."$dir".q|img2057.png"
 ALT="$\displaystyle \delta \sim \vert\epsilon\vert = \frac{\nu_e}{\vert{\mit\Omega_e}\vert'}.$">|; 

$key = q/displaystyledelta{mitPhi}(r)=frac{q}{4pi,epsilon_0,r},expleft(-frac{sqrt{2},r}{lambda_D}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.69ex; vertical-align: -2.26ex; " SRC="|."$dir".q|img70.png"
 ALT="$\displaystyle \delta{\mit\Phi}(r) = \frac{q}{4\pi \epsilon_0 r} \exp\left(-\frac{\sqrt{2} r}{\lambda_D}\right).$">|; 

$key = q/displaystyled{bfr}=frac{partialmbox{boldmathrho}}{partialgamma},dgamma=frac{{bfu}}{{mitOmega}},,dgamma.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img401.png"
 ALT="$\displaystyle d{\bf r} = \frac{\partial\mbox{\boldmath$\rho$}}{\partial \gamma} d\gamma =
\frac{{\bf u}}{{\mit\Omega}}  d\gamma.$">|; 

$key = q/displaystylee,({mitPhi}_w-{mitPhi}_s)=-T_e,lnleft(frac{m_i}{2pi,m_e}right)^{1slash2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1604.png"
 ALT="$\displaystyle e ({\mit\Phi}_w-{\mit\Phi}_s)= -T_e \ln\left(\frac{m_i}{2\pi m_e}\right)^{1/2}.$">|; 

$key = q/displaystylee,langle{bfu}cdot(;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img508.png"
 ALT="$\displaystyle e \langle {\bf u}\cdot($">|; 

$key = q/displaystylee,langle{bfu}times(;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img506.png"
 ALT="$\displaystyle e \langle {\bf u}\times ($">|; 

$key = q/displaystylee,{bfU}_1cdot{bfE}=m,{bfv}_Ecdotleft[frac{d}{dt},(U_{0,parallel},{bfb}+{bfv}_E)+frac{mu}{m},nablaBright].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img381.png"
 ALT="$\displaystyle e {\bf U}_1\cdot{\bf E} = m {\bf v}_E\cdot\left[\frac{d}{dt} (U_{0 \parallel} {\bf b} + {\bf v}_E) + \frac{\mu}{m} \nabla B\right].$">|; 

$key = q/displaystylee,{mitOmega},langle(;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img371.png"
 ALT="$\displaystyle e {\mit\Omega}  \langle ($">|; 

$key = q/displaystyleepsilon(k,omega);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2591.png"
 ALT="$\displaystyle \epsilon(k,\omega)$">|; 

$key = q/displaystyleepsilon(k,omega)=1+frac{e^2}{epsilon_0,m_e,k}int_{-infty}^{infty}frac{partialF_0slashpartialu}{omega-k,u},du=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -2.05ex; " SRC="|."$dir".q|img2283.png"
 ALT="$\displaystyle \epsilon(k,\omega) = 1 + \frac{e^2}{\epsilon_0 m_e k}
\int_{-\infty}^{\infty} \frac{\partial F_0/\partial u}{\omega-
k u} du=0,$">|; 

$key = q/displaystyleepsilon(k,omega)=epsilon_r(k,omega)+{rmi},epsilon_i(k,omega)=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2593.png"
 ALT="$\displaystyle \epsilon(k,\omega)= \epsilon_r(k,\omega)+{\rm i} \epsilon_i(k,\omega) = 0,$">|; 

$key = q/displaystyleepsilon(k,p)=1+frac{e^2}{epsilon_0,m_e,k}int_{-infty}^{infty}frac{partialF_0slashpartialu}{{rmi},p-k,u},du.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.35ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img2257.png"
 ALT="$\displaystyle \epsilon(k,p) = 1 + \frac{e^2}{\epsilon_0 m_e k}
\int_{-\infty}^{\infty} \frac{\partial F_0/\partial u}{{\rm i} p-
k u} du.$">|; 

$key = q/displaystyleepsilon(x,y)=left(frac{pi}{2}right)^{1slash2}frac{x^{1slash2}}{y^{3}},expleft(-frac{x}{2,y^{2}}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2654.png"
 ALT="$\displaystyle \epsilon(x,y) = \left(\frac{\pi}{2}\right)^{1/2}\frac{x^{1/2}}{y^{3}} \exp\left(-\frac{x}{2 y^{2}}\right).
$">|; 

$key = q/displaystyleepsilon=-frac{nu_e}{|{mitOmega_e}|'}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.46ex; vertical-align: -1.98ex; " SRC="|."$dir".q|img2056.png"
 ALT="$\displaystyle \epsilon = -\frac{\nu_e}{\vert{\mit\Omega_e}\vert'}.$">|; 

$key = q/displaystyleepsilon=1+frac{c^2}{V_A^{2}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.63ex; vertical-align: -2.41ex; " SRC="|."$dir".q|img514.png"
 ALT="$\displaystyle \epsilon = 1 +\frac{c^2}{V_A^{2}},
$">|; 

$key = q/displaystyleepsilon=1-frac{{mitPi}^{2}}{omega^2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img177.png"
 ALT="$\displaystyle \epsilon = 1 - \frac{{\mit\Pi}^{2}}{\omega^2},
$">|; 

$key = q/displaystyleepsilon=frac{l}{L}ll1.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img1107.png"
 ALT="$\displaystyle \epsilon = \frac{l}{L} \ll 1.$">|; 

$key = q/displaystyleepsilon_0,frac{d^2{mitPhi}}{dx^2}=e,(n_e-n_i).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1575.png"
 ALT="$\displaystyle \epsilon_0 \frac{d^2{\mit\Phi}}{dx^2} = e (n_e-n_i).$">|; 

$key = q/displaystyleepsilon_0,nablacdot{bfE};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1902.png"
 ALT="$\displaystyle \epsilon_0 \nabla\cdot {\bf E}$">|; 

$key = q/displaystyleepsilon_i(k,omega);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2595.png"
 ALT="$\displaystyle \epsilon_i(k,\omega)$">|; 

$key = q/displaystyleepsilon_r(k,omega);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2611.png"
 ALT="$\displaystyle \epsilon_r(k,\omega)$">|; 

$key = q/displaystyleepsilon_r(k,omega)simeq1-frac{{mitPi}_e^{2}}{omega^{2}},frac{k_parallel^{2}}{k^{2}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.35ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img2627.png"
 ALT="$\displaystyle \epsilon_r(k,\omega) \simeq 1- \frac{{\mit\Pi}_e^{2}}{\omega^{2}} \frac{k_\parallel^{2}}{k^{2}}.$">|; 

$key = q/displaystyleepsilon_r(k,omega_r)=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2606.png"
 ALT="$\displaystyle \epsilon_r(k,\omega_r) =0,$">|; 

$key = q/displaystyleepsilon_r(k,omega_r)simeq1-frac{{mitPi}_e^{2}}{omega_r^{2}},frac{k_parallel^{2}}{k^{2}}=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.80ex; vertical-align: -2.17ex; " SRC="|."$dir".q|img2630.png"
 ALT="$\displaystyle \epsilon_r(k,\omega_r) \simeq 1- \frac{{\mit\Pi}_e^{2}}{\omega_r^{2}} \frac{k_\parallel^{2}}{k^{2}}=0,$">|; 

$key = q/displaystyleequiv-frac{partialphi}{partialt}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2102.png"
 ALT="$\displaystyle \equiv - \frac{\partial\phi}{\partial t}.$">|; 

$key = q/displaystyleequivnablaphi,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2100.png"
 ALT="$\displaystyle \equiv \nabla\phi,$">|; 

$key = q/displaystyleeta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1118.png"
 ALT="$\displaystyle \eta$">|; 

$key = q/displaystyleeta=frac{1}{2},m,n,nu,l^{2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img1642.png"
 ALT="$\displaystyle \eta = \frac{1}{2} m n \nu l^{2}.
$">|; 

$key = q/displaystyleeta_0^e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.69ex; " SRC="|."$dir".q|img1216.png"
 ALT="$\displaystyle \eta_0^e$">|; 

$key = q/displaystyleeta_0^i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.57ex; vertical-align: -0.69ex; " SRC="|."$dir".q|img1218.png"
 ALT="$\displaystyle \eta_0^i$">|; 

$key = q/displaystyleeta_1^e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img1278.png"
 ALT="$\displaystyle \eta_1^e$">|; 

$key = q/displaystyleeta_1^i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.51ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img1280.png"
 ALT="$\displaystyle \eta_1^i$">|; 

$key = q/displaystyleeta_3^e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.69ex; " SRC="|."$dir".q|img1284.png"
 ALT="$\displaystyle \eta_3^e$">|; 

$key = q/displaystyleeta_3^i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.57ex; vertical-align: -0.69ex; " SRC="|."$dir".q|img1286.png"
 ALT="$\displaystyle \eta_3^i$">|; 

$key = q/displaystyleexpleft[frac{e,({mitPhi}_w-{mitPhi}_s)}{T_e}right]ll1:;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1601.png"
 ALT="$\displaystyle \exp\left[\frac{e ({\mit\Phi}_w-{\mit\Phi}_s)}{T_e}\right]\ll 1:$">|; 

$key = q/displaystylef(U)=frac{e^2}{epsilon_0,m_e}int_{-infty}^inftyfrac{partialF_0slashpartialu}{u-U},du,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -2.05ex; " SRC="|."$dir".q|img2523.png"
 ALT="$\displaystyle f(U)= \frac{e^2}{\epsilon_0 m_e}\int_{-\infty}^\infty \frac{\partial F_0/\partial u}{u-U} du,$">|; 

$key = q/displaystylef({bfr},{bfv},t)=f_0({bfr},{bfv},t)+epsilon,f_1({bfr},{bfv},t)+epsilon^2,f_2({bfr},{bfv},t)+cdots.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1108.png"
 ALT="$\displaystyle f({\bf r}, {\bf v}, t) = f_0({\bf r}, {\bf v}, t) + \epsilon f_1({\bf r}, {\bf v}, t) + \epsilon^2  f_2({\bf r}, {\bf v}, t) + \cdots.$">|; 

$key = q/displaystylef({bfv})=frac{n}{pi^{3slash2},v_t^{3}},expleft(-frac{v^2}{v_t^{2}}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.58ex; vertical-align: -2.29ex; " SRC="|."$dir".q|img1628.png"
 ALT="$\displaystyle f({\bf v}) = \frac{n}{\pi^{3/2} v_t^{3}} \exp\left(-\frac{v^2}{v_t^{2}}\right).
$">|; 

$key = q/displaystylef({bfv})=nleft(frac{m}{2pi,T}right)^{3slash2},expleft[-frac{m,({bfv}-{bfV})^{2}}{2,T}right].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img982.png"
 ALT="$\displaystyle f ({\bf v})= n\left(\frac{m}{2\pi T}\right)^{3/2} \exp\left[-\frac{m ({\bf v}-{\bf V})^{2}}{2 T}\right].
$">|; 

$key = q/displaystylef=f_0-nu^{-1},{bfv}cdotnablaf_0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1639.png"
 ALT="$\displaystyle f =f_0 - \nu^{-1} {\bf v}\cdot\nabla f_0.
$">|; 

$key = q/displaystylef_0({bfr},{bfv},t)=n({bfr})left[frac{m}{2pi,T({bfr})}right]^{3slash2},exp!left[-frac{m,({bfv}-{bfV})^2}{2,T({bfr})}right].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1112.png"
 ALT="$\displaystyle f_0({\bf r}, {\bf v}, t) = n({\bf r})
\left[\frac{m}{2\pi T({\bf...
...ght]^{3/2} \exp\!\left[-\frac{m ({\bf v}-
{\bf V})^2}
{2 T({\bf r})}\right].$">|; 

$key = q/displaystylef_0=frac{n_e}{pi^{3slash2},v_{t,e}^{3}}expleft(-frac{v^2}{v_{t,e}^{2}}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.58ex; vertical-align: -2.29ex; " SRC="|."$dir".q|img1653.png"
 ALT="$\displaystyle f_0 = \frac{n_e}{\pi^{3/2} v_{t e}^{3}}\exp\left(-\frac{v^2}{v_{t e}^{2}}\right).
$">|; 

$key = q/displaystylef_0=frac{n}{pi^{3slash2},v_t^{3}}expleft[-frac{({bfv}-{bfV})^{2}}{v_t^{2}}right].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.58ex; vertical-align: -2.29ex; " SRC="|."$dir".q|img1636.png"
 ALT="$\displaystyle f_0 = \frac{n}{\pi^{3/2} v_t^{3}}\exp\left[-\frac{({\bf v}-{\bf V})^{2}}{v_t^{2}}\right].
$">|; 

$key = q/displaystylef_1({bfr},{bfv},t)=-frac{e}{m}int_{-infty}^tleft[{bfE}({bfr}',t')+{bfv}'times{bfB}({bfr}',t')right]cdotnabla_vf_0({bfv}'),dt',;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.19ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img2362.png"
 ALT="$\displaystyle f_1({\bf r}, {\bf v}, t) =-\frac{e}{m}\int_{-\infty}^t
\left[{\bf...
...+ {\bf v}'\times {\bf B}({\bf r}', t')\right]
\cdot\nabla_v f_0({\bf v}') dt',$">|; 

$key = q/displaystylef_1({bfr},{bfv},t)=f_1({bfv},t),expleft(,{rmi},{bfk}cdot{bfr}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.58ex; " SRC="|."$dir".q|img2238.png"
 ALT="$\displaystyle f_1({\bf r}, {\bf v}, t) = f_1({\bf v},t) \exp\left( {\rm i} {\bf k}\cdot
{\bf r}\right).$">|; 

$key = q/displaystylef_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2385.png"
 ALT="$\displaystyle f_1$">|; 

$key = q/displaystylef_e({bfr},{bfv},t)=f_0({bfv})+f_1({bfr},{bfv},t).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2229.png"
 ALT="$\displaystyle f_e({\bf r}, {\bf v}, t) = f_0({\bf v}) + f_1({\bf r}, {\bf v}, t).$">|; 

$key = q/displaystylef_e=f_0+frac{e}{m_e,nu_e},{bfE}cdotnabla_vf_0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.41ex; vertical-align: -1.96ex; " SRC="|."$dir".q|img1656.png"
 ALT="$\displaystyle f_e =f_0 + \frac{e}{m_e \nu_e} {\bf E}\cdot\nabla_v f_0.
$">|; 

$key = q/displaystylef_s',f_{s'}'-f_s,f_{s'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img745.png"
 ALT="$\displaystyle f_s' f_{s'}' - f_s f_{s'}$">|; 

$key = q/displaystylef_s({bfv});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img885.png"
 ALT="$\displaystyle f_s({\bf v})$">|; 

$key = q/displaystylef_s,f_{s'}=f_s',f_{s'}',;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img862.png"
 ALT="$\displaystyle f_s f_{s'} = f_s' f_{s'}',$">|; 

$key = q/displaystylef_s=n_sleft(frac{m_s}{2pi,T_s}right)^{3slash2},expleft(-frac{m,v_s^{2}}{2,T_s}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img990.png"
 ALT="$\displaystyle f_s= n_s\left(\frac{m_s}{2\pi T_s}\right)^{3/2} \exp\left(-\frac{m v_s^{2}}{2 T_s}\right),
$">|; 

$key = q/displaystylef_s=n_sleft(frac{m_s}{2pi,T}right)^{3slash2},expleft[-frac{m_s,({bfv}_s-{bfV})^{2}}{2,T}right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img878.png"
 ALT="$\displaystyle f_s= n_s\left(\frac{m_s}{2\pi T}\right)^{3/2} \exp\left[-\frac{m_s ({\bf v}_s-{\bf V})^{2}}{2 T}\right],$">|; 

$key = q/displaystylef_{0,s}=frac{n_s}{(2pi,T_sslashm_s)^{3slash2}}expleft[-frac{m_s,(v_perp^{2}+v_parallel^{2})}{2,T_s}right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.19ex; vertical-align: -2.51ex; " SRC="|."$dir".q|img2408.png"
 ALT="$\displaystyle f_{0 s} = \frac{n_s}{(2\pi T_s/m_s)^{3/2}}\exp\left[-\frac{m_s (v_\perp^{2}+v_\parallel^{2})}{2 T_s}\right],$">|; 

$key = q/displaystylef_{1,s};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2502.png"
 ALT="$\displaystyle f_{1 s}$">|; 

$key = q/displaystylef_{s'}({bfv});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img887.png"
 ALT="$\displaystyle f_{s'}({\bf v})$">|; 

$key = q/displaystylefrac{1}{2},m,v_t^{2}=frac{e^2}{4pi,epsilon_0,r_c}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img74.png"
 ALT="$\displaystyle \frac{1}{2}  m v_t^{2} = \frac{e^2}{4\pi \epsilon_0  r_c}.$">|; 

$key = q/displaystylefrac{1}{2},m_i,V_i^{,2}(x)+e,{mitPhi}(x)=frac{1}{2},m_i,V_s^{,2}+e,{mitPhi}_s.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img1563.png"
 ALT="$\displaystyle \frac{1}{2} m_i V_i^{ 2}(x) + e {\mit\Phi}(x) = \frac{1}{2} m_i V_s^{ 2} + e {\mit\Phi}_s.$">|; 

$key = q/displaystylefrac{1}{2}frac{d}{dt}!intpsi^2,dV;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img2959.png"
 ALT="$\displaystyle \frac{1}{2}\frac{d}{dt}\!\int\psi^2 dV$">|; 

$key = q/displaystylefrac{1}{k_0^{2}}left|frac{3}{4}left(frac{1}{n^2}frac{dn}{dz}right)^2-frac{1}{2,n^3}frac{d^2n}{dz^2}right|ll1.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.64ex; vertical-align: -2.77ex; " SRC="|."$dir".q|img1939.png"
 ALT="$\displaystyle \frac{1}{k_0^{2}}\left\vert \frac{3}{4}\left(\frac{1}{n^2}
\frac{dn}{dz}\right)^2 -\frac{1}{2 n^3}\frac{d^2 n}{dz^2}\right\vert \ll 1.$">|; 

$key = q/displaystylefrac{1}{k_0^{2}}left|frac{3}{4}left(frac{1}{q^2},frac{dq}{dz}right)^2-frac{1}{2,q^3},frac{d^2q}{dz^2}right|ll1.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.64ex; vertical-align: -2.77ex; " SRC="|."$dir".q|img2190.png"
 ALT="$\displaystyle \frac{1}{k_0^{2}}\left\vert\frac{3}{4}\left(\frac{1}{q^2} \frac{dq}{dz}\right)^2 - \frac{1}{2 q^3} \frac{d^2q}{dz^2}\right\vert\ll 1.
$">|; 

$key = q/displaystylefrac{1}{omega-k,u}=P,frac{1}{omega-k,u}-{rmi},pi,delta(omega-k,u).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img2288.png"
 ALT="$\displaystyle \frac{1}{\omega-k u} = P \frac{1}{\omega -k u} -{\rm i} \pi \delta(\omega-k u).$">|; 

$key = q/displaystylefrac{1}{omega-k,u}simeqfrac{1}{omega}left(1+frac{k,u}{omega}+frac{k^2,u^2}{omega^2}+frac{k^3,u^3}{omega^3}+cdotsright).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2292.png"
 ALT="$\displaystyle \frac{1}{\omega-k u} \simeq \frac{1}{\omega}\left(1+ \frac{k u}{\omega}
+ \frac{k^2 u^2}{\omega^2} + \frac{k^3  u^3}{\omega^3} + \cdots\right).$">|; 

$key = q/displaystylefrac{1}{r,sintheta}frac{dr}{dphi}simeqfrac{u_r}{u_phi}=-frac{u}{{mitOmega},r,sintheta};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -2.26ex; " SRC="|."$dir".q|img2821.png"
 ALT="$\displaystyle \frac{1}{r \sin\theta}\frac{dr}{d\phi} \simeq \frac{u_r}{u_\phi} = -\frac{u}{
{\mit\Omega} r \sin\theta}$">|; 

$key = q/displaystylefrac{1}{r^{2}}frac{d(r^{2},rho,u)}{dr}=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2775.png"
 ALT="$\displaystyle \frac{1}{r^{2}}\frac{d(r^{2} \rho u)}{dr} = 0.$">|; 

$key = q/displaystylefrac{1}{r^{2}}frac{d}{dr}!left(r^{2},kappa_0,T^{5slash2},frac{dT}{dr}right)=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2764.png"
 ALT="$\displaystyle \frac{1}{r^{2}}\frac{d}{dr}\!\left(r^{2} \kappa_0 T^{5/2} \frac{dT}{dr}\right) =0.$">|; 

$key = q/displaystylefrac{1}{u},frac{du}{dr}left(u^2-frac{2,T}{m_p}right)=frac{4,T}{m_p,r}-frac{G,M_odot}{r^{2}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.26ex; " SRC="|."$dir".q|img2778.png"
 ALT="$\displaystyle \frac{1}{u}  \frac{du}{dr}\left(u^2 - \frac{2 T}{m_p}\right)
= \frac{4 T}{m_p r} - \frac{G M_\odot}{r^{2}}.$">|; 

$key = q/displaystylefrac{1}{{mitOmega}}frac{partialB}{partialt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img271.png"
 ALT="$\displaystyle \frac{1}{{\mit\Omega}}\frac{\partial B}{\partial t}$">|; 

$key = q/displaystylefrac{3}{2},n,T;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img987.png"
 ALT="$\displaystyle \frac{3}{2} n T$">|; 

$key = q/displaystylefrac{3}{2},n_s,T;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img883.png"
 ALT="$\displaystyle \frac{3}{2} n_s T$">|; 

$key = q/displaystylefrac{3}{2},p_s=intfrac{1}{2},m_s,u_s^{2},f_s,d^3{bfv}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img1031.png"
 ALT="$\displaystyle \frac{3}{2} p_s = \int \frac{1}{2} m_s u_s^{2}  f_s d^3{\bf v}.$">|; 

$key = q/displaystylefrac{3}{2}frac{d_ep_e}{dt}+frac{5}{2},p_e,nablacdot{bfV}_e+;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1146.png"
 ALT="$\displaystyle \frac{3}{2}\frac{d_e p_e}{dt} + \frac{5}{2} p_e \nabla\cdot{\bf V}_e
+$">|; 

$key = q/displaystylefrac{3}{2}frac{d_ep_e}{dt}+frac{5}{2},p_e,nablacdot{bfV}_e+[zeta^{-1}],nablacdot{bfq}_{Te}+nablacdot{bfq}_{Ue};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1460.png"
 ALT="$\displaystyle \frac{3}{2}\frac{d_e p_e}{dt} + \frac{5}{2} p_e \nabla\cdot{\bf V}_e
+ [\zeta^{-1}] \nabla\cdot{\bf q}_{Te}
+ \nabla\cdot{\bf q}_{Ue}$">|; 

$key = q/displaystylefrac{3}{2}frac{d_ep_e}{dt}+frac{5}{2},p_e,nablacdot{bfV}_e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1447.png"
 ALT="$\displaystyle \frac{3}{2}\frac{d_e p_e}{dt} + \frac{5}{2} p_e \nabla\cdot{\bf V}_e$">|; 

$key = q/displaystylefrac{3}{2}frac{d_ip_i}{dt}+frac{5}{2},p_i,nablacdot{bfV}_i+;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1153.png"
 ALT="$\displaystyle \frac{3}{2}\frac{d_i p_i}{dt} + \frac{5}{2} p_i \nabla\cdot{\bf V}_i
+$">|; 

$key = q/displaystylefrac{3}{2}frac{d_ip_i}{dt}+frac{5}{2},p_i,nablacdot{bfV}_i+[zeta^{-1}],nablacdot{bfq}_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1466.png"
 ALT="$\displaystyle \frac{3}{2}\frac{d_i p_i}{dt} + \frac{5}{2} p_i \nabla\cdot{\bf V}_i
+ [\zeta^{-1}] \nabla\cdot{\bf q}_i$">|; 

$key = q/displaystylefrac{3}{2}frac{d_ip_i}{dt}+frac{5}{2},p_i,nablacdot{bfV}_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1451.png"
 ALT="$\displaystyle \frac{3}{2}\frac{d_i p_i}{dt} + \frac{5}{2} p_i \nabla\cdot{\bf V}_i$">|; 

$key = q/displaystylefrac{3}{2}frac{d_sp_s}{dt}+frac{3}{2},p_s,nablacdot{bfV}_s+{bfp}_s:nabla{bfV}_s+nablacdot{bfq}_s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1076.png"
 ALT="$\displaystyle \frac{3}{2}\frac{d_s p_s}{dt} + \frac{3}{2} p_s \nabla\cdot{\bf V}_s
+ {\bf p}_s:\nabla{\bf V}_s + \nabla\cdot{\bf q}_s$">|; 

$key = q/displaystylefrac{3}{2}frac{d_sp_s}{dt}+frac{5}{2},p_s,nablacdot{bfV}_s+;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1087.png"
 ALT="$\displaystyle \frac{3}{2}\frac{d_s p_s}{dt} + \frac{5}{2} p_s \nabla\cdot{\bf V}_s
+$">|; 

$key = q/displaystylefrac{3}{2}frac{dp}{dt}+frac{5}{2},p,nablacdot{bfV}+;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1100.png"
 ALT="$\displaystyle \frac{3}{2}\frac{d p}{dt} + \frac{5}{2} p \nabla \cdot {\bf V}
+$">|; 

$key = q/displaystylefrac{3}{2}frac{dp}{dt}+frac{5}{2},p,nablacdot{bfV}simeq0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1494.png"
 ALT="$\displaystyle \frac{3}{2} \frac{dp}{dt} + \frac{5}{2}  p  \nabla\cdot{\bf V} \simeq 0.$">|; 

$key = q/displaystylefrac{3}{2}frac{partialp_e}{partialt}+frac{3}{2},({bfV}_ecdotnabla),p_e+frac{5}{2},p_e,nablacdot{bfV}_e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1485.png"
 ALT="$\displaystyle \frac{3}{2}\frac{\partial p_e}{\partial t} + \frac{3}{2}
 ({\bf V}_e\cdot\nabla)  p_e
+ \frac{5}{2} p_e \nabla\cdot{\bf V}_e$">|; 

$key = q/displaystylefrac{3}{2}frac{partialp_i}{partialt}+frac{3}{2},({bfV}_icdotnabla),p_i+frac{5}{2},p_i,nablacdot{bfV}_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1487.png"
 ALT="$\displaystyle \frac{3}{2}\frac{\partial p_i}{\partial t} + \frac{3}{2}
 ({\bf V}_i\cdot\nabla)  p_i +
\frac{5}{2} p_i \nabla\cdot{\bf V}_i$">|; 

$key = q/displaystylefrac{B_2}{B_1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.95ex; " SRC="|."$dir".q|img3092.png"
 ALT="$\displaystyle \frac{B_2}{B_1}$">|; 

$key = q/displaystylefrac{B_ast^{,2}}{mu_0}simrho,v_ast^{,2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img3635.png"
 ALT="$\displaystyle \frac{B_\ast^{ 2}}{\mu_0} \sim \rho v_\ast^{ 2}.$">|; 

$key = q/displaystylefrac{B_r}{B_phi}=frac{u_r}{u_phi-{mitOmega},r,sintheta}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.13ex; vertical-align: -2.26ex; " SRC="|."$dir".q|img2861.png"
 ALT="$\displaystyle \frac{B_r}{B_\phi} = \frac{u_r}{u_\phi - {\mit\Omega} r \sin\theta}.$">|; 

$key = q/displaystylefrac{B_{x,2}}{B_{x,1}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.85ex; vertical-align: -1.96ex; " SRC="|."$dir".q|img3158.png"
 ALT="$\displaystyle \frac{B_{x 2}}{B_{x 1}}$">|; 

$key = q/displaystylefrac{B_{y,2}}{B_{y,1}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.30ex; vertical-align: -2.26ex; " SRC="|."$dir".q|img3159.png"
 ALT="$\displaystyle \frac{B_{y 2}}{B_{y 1}}$">|; 

$key = q/displaystylefrac{Df_1}{Dt}=-frac{e}{m},({bfE}+{bfv}times{bfB})cdotnabla_vf_0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img2359.png"
 ALT="$\displaystyle \frac{D f_1}{Dt} = -\frac{e}{m} 
({\bf E} + {\bf v}\times{\bf B})\cdot\nabla_v f_0,$">|; 

$key = q/displaystylefrac{E}{B}simdelta,v_tsimv_d.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.46ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img1527.png"
 ALT="$\displaystyle \frac{E}{B} \sim \delta v_t\sim v_d.$">|; 

$key = q/displaystylefrac{E}{B}simv_t,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.46ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img1526.png"
 ALT="$\displaystyle \frac{E}{B} \sim v_t,$">|; 

$key = q/displaystylefrac{I_1,hat{W}}{2},frac{dskew{3}hat{mitPsi}}{dhat{t}}={mitDelta}',skew{3}hat{mitPsi},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.19ex; vertical-align: -1.71ex; " SRC="|."$dir".q|img3613.png"
 ALT="$\displaystyle \frac{I_1 \hat{W}}{2} \frac{d\skew{3}\hat{\mit\Psi}}{d\hat{t}} = {\mit\Delta}'  \skew{3}\hat{\mit\Psi},$">|; 

$key = q/displaystylefrac{T^{3slash2}}{n}llfrac{h^3}{(2,m)^{3slash2}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img152.png"
 ALT="$\displaystyle \frac{T^{3/2}}{n} \ll \frac{h^3}{(2 m)^{3/2}}.$">|; 

$key = q/displaystylefrac{T_2}{T_1}equivfrac{R}{r}rightarrowfrac{2,{mitGamma},({mitGamma}-1),M_1^{2}}{({mitGamma}+1)^{2}}gg1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img3132.png"
 ALT="$\displaystyle \frac{T_2}{T_1} \equiv \frac{R}{r}\rightarrow \frac{2 {\mit\Gamma} ({\mit\Gamma}-1) M_1^{2}}{({\mit\Gamma}+1)^{2}}\gg 1$">|; 

$key = q/displaystylefrac{T_{parallel,i}}{T_{perp,e}}<frac{1}{2,n}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.96ex; " SRC="|."$dir".q|img2649.png"
 ALT="$\displaystyle \frac{T_{\parallel i}}{T_{\perp e}}&lt; \frac{1}{2 n}.$">|; 

$key = q/displaystylefrac{V_2}{V_1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.95ex; " SRC="|."$dir".q|img3096.png"
 ALT="$\displaystyle \frac{V_2}{V_1}$">|; 

$key = q/displaystylefrac{V_i}{V_s};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.85ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img1613.png"
 ALT="$\displaystyle \frac{V_i}{V_s}$">|; 

$key = q/displaystylefrac{V_{x,2}}{V_{x,1}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.85ex; vertical-align: -1.96ex; " SRC="|."$dir".q|img3161.png"
 ALT="$\displaystyle \frac{V_{x 2}}{V_{x 1}}$">|; 

$key = q/displaystylefrac{V_{y,2}}{V_{y,1}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.30ex; vertical-align: -2.26ex; " SRC="|."$dir".q|img3163.png"
 ALT="$\displaystyle \frac{V_{y 2}}{V_{y 1}}$">|; 

$key = q/displaystylefrac{V}{L}simdelta,{mitOmega}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.46ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img1539.png"
 ALT="$\displaystyle \frac{V}{L}\sim \delta {\mit\Omega}.$">|; 

$key = q/displaystylefrac{V}{L}simdelta^{2},{mitOmega}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.46ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img1549.png"
 ALT="$\displaystyle \frac{V}{L} \sim \delta^{2} {\mit\Omega}.$">|; 

$key = q/displaystylefrac{V}{L}sim{mitOmega}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.46ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img1435.png"
 ALT="$\displaystyle \frac{V}{L} \sim {\mit\Omega}.$">|; 

$key = q/displaystylefrac{d(rho,V_x)}{dx};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3069.png"
 ALT="$\displaystyle \frac{d (\rho  V_x)}{dx}$">|; 

$key = q/displaystylefrac{d,(c,B_x)}{dz}+{rmi},k_0,n^2,E_y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.80ex; " SRC="|."$dir".q|img2181.png"
 ALT="$\displaystyle \frac{d (c B_x)}{dz}+{\rm i} k_0 n^2 E_y$">|; 

$key = q/displaystylefrac{d,(c,B_x)}{dz}+{rmi},k_0,q^2,E_y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.80ex; " SRC="|."$dir".q|img2185.png"
 ALT="$\displaystyle \frac{d (c B_x)}{dz}+ {\rm i} k_0 q^2 E_y$">|; 

$key = q/displaystylefrac{d,(c,B_x)}{dz}=-{rmi},k_0,n^2,E_y,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.80ex; " SRC="|."$dir".q|img1916.png"
 ALT="$\displaystyle \frac{d (c B_x)}{dz} = -{\rm i} k_0 n^2 E_y,$">|; 

$key = q/displaystylefrac{dB_{x}}{dx};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3067.png"
 ALT="$\displaystyle \frac{dB_{x}}{dx}$">|; 

$key = q/displaystylefrac{dE_x}{dz}-{rmi},k_0,frac{q^2}{n^2},c,B_y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -1.80ex; " SRC="|."$dir".q|img2193.png"
 ALT="$\displaystyle \frac{dE_x}{dz} -{\rm i} k_0 \frac{q^2}{n^2} c B_y$">|; 

$key = q/displaystylefrac{dE_{ss'}}{dt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img681.png"
 ALT="$\displaystyle \frac{d E_{ss'}}{dt}$">|; 

$key = q/displaystylefrac{dH}{dt}=sum_{s,s'}int(1+lnf_s),C_{ss'}(f_s,f_{s'}),d^3{bfv}_s.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.80ex; vertical-align: -2.80ex; " SRC="|."$dir".q|img851.png"
 ALT="$\displaystyle \frac{dH}{dt} = \sum_{s,s'}\int (1+\ln f_s) C_{ss'}(f_s,f_{s'}) d^3{\bf v}_s.$">|; 

$key = q/displaystylefrac{dH}{dt}leq0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img860.png"
 ALT="$\displaystyle \frac{dH}{dt} \leq 0.$">|; 

$key = q/displaystylefrac{dK}{dt}=-e,{bfU}cdotnabla{mitPhi}=-frac{d(e,{mitPhi})}{dt},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img410.png"
 ALT="$\displaystyle \frac{dK}{dt} = -e {\bf U}\cdot\nabla{\mit\Phi} = - \frac{d(e {\mit\Phi})}{dt},$">|; 

$key = q/displaystylefrac{dK}{dt}=e,{bfU}cdot{bfE}+;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img375.png"
 ALT="$\displaystyle \frac{d K}{dt} = e {\bf U}\cdot{\bf E} +$">|; 

$key = q/displaystylefrac{dP_z}{dz}=W,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.80ex; " SRC="|."$dir".q|img2041.png"
 ALT="$\displaystyle \frac{d P_z}{dz} = W,$">|; 

$key = q/displaystylefrac{dT_{xx}}{dx};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3070.png"
 ALT="$\displaystyle \frac{d T_{xx}}{dx}$">|; 

$key = q/displaystylefrac{dT_{xy}}{dx};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3071.png"
 ALT="$\displaystyle \frac{d T_{xy}}{dx}$">|; 

$key = q/displaystylefrac{d^2(c,B_y)}{dz^2}-frac{1}{n^2},frac{dn^2}{dz},frac{d,(c,B_y)}{dz}+k_0^{2},q^2,c,B_y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.19ex; vertical-align: -1.80ex; " SRC="|."$dir".q|img2194.png"
 ALT="$\displaystyle \frac{d^2(c B_y)}{dz^2}-\frac{1}{n^2} \frac{dn^2}{dz} \frac{d (c B_y)}{dz}+k_0^{2} q^2 c B_y$">|; 

$key = q/displaystylefrac{d^2(zeta,G_{s'})}{dzeta^{2}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.35ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img900.png"
 ALT="$\displaystyle \frac{d^2(\zeta G_{s'})}{d\zeta^{2}}$">|; 

$key = q/displaystylefrac{d^2(zeta,H_{s'})}{dzeta^2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.35ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img898.png"
 ALT="$\displaystyle \frac{d^2(\zeta H_{s'})}{d\zeta^2}$">|; 

$key = q/displaystylefrac{d^2E_y}{dhat{z}^{2}}+frac{E_y}{hat{z}+{rmi},skew{3}hat{epsilon}}=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.19ex; vertical-align: -1.80ex; " SRC="|."$dir".q|img1971.png"
 ALT="$\displaystyle \frac{d^2 E_y}{d\hat{z}^{2}} + \frac{E_y}{\hat{z}+{\rm i} \skew{3}\hat{\epsilon}} = 0,$">|; 

$key = q/displaystylefrac{d^2E_y}{dhat{z}^{2}}+hat{z},E_y=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.19ex; vertical-align: -1.80ex; " SRC="|."$dir".q|img1952.png"
 ALT="$\displaystyle \frac{d^2 E_y}{d\hat{z}^{2}} + \hat{z} E_y = 0,$">|; 

$key = q/displaystylefrac{d^2E_y}{dz^2}+frac{k_0^2,b}{z+{rmi},epsilon}E_y=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -1.80ex; " SRC="|."$dir".q|img2036.png"
 ALT="$\displaystyle \frac{d^2 E_y}{dz^2} + \frac{k_0^2 b}{z+{\rm i} \epsilon} E_y = 0,$">|; 

$key = q/displaystylefrac{d^2E_y}{dz^2}+k_0^{2},n^2,E_y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.19ex; vertical-align: -1.80ex; " SRC="|."$dir".q|img2180.png"
 ALT="$\displaystyle \frac{d^2 E_y}{dz^2} + k_0^{2} n^2 E_y$">|; 

$key = q/displaystylefrac{d^2E_y}{dz^2}+k_0^{2},q^2,E_y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.19ex; vertical-align: -1.80ex; " SRC="|."$dir".q|img2184.png"
 ALT="$\displaystyle \frac{d^2 E_y}{dz^2} + k_0^{2} q^2 E_y$">|; 

$key = q/displaystylefrac{d^2E_y}{dz^{2}}=-k_0^{2},n^2,E_y,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.19ex; vertical-align: -1.80ex; " SRC="|."$dir".q|img1915.png"
 ALT="$\displaystyle \frac{d^2 E_y}{dz^{2}} =-k_0^{2} n^2 E_y,$">|; 

$key = q/displaystylefrac{d^2hat{psi}}{dhat{x}^2}-hat{k}^2,hat{psi}+frac{2}{cosh^2hat{x}},hat{psi}=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -1.92ex; " SRC="|."$dir".q|img3355.png"
 ALT="$\displaystyle \frac{d^2\hat{\psi}}{d\hat{x}^2}-\hat{k}^2 \hat{\psi}+\frac{2}{\cosh^2\hat{x}} \hat{\psi} = 0.$">|; 

$key = q/displaystylefrac{d^2hat{psi}}{dhat{x}^2}-hat{k}^2,hat{psi}-frac{F''}{F},hat{psi};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3329.png"
 ALT="$\displaystyle \frac{d^2\hat{\psi}}{d\hat{x}^2} - \hat{k}^2 \hat{\psi}-\frac{F''}{F} \hat{\psi}$">|; 

$key = q/displaystylefrac{d^2phi}{dz^2}simeqpmk_0,frac{dn}{dz}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -1.80ex; " SRC="|."$dir".q|img1930.png"
 ALT="$\displaystyle \frac{d^2 \phi}{dz^2} \simeq \pm k_0 \frac{dn}{dz}.$">|; 

$key = q/displaystylefrac{d^2psi}{dy^2}+frac{1}{y}frac{dpsi}{dy}+left(1-frac{1}{y^2}right)psi=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1986.png"
 ALT="$\displaystyle \frac{d^2\psi}{dy^2} + \frac{1}{y}\frac{d\psi}{dy} + \left(1-\frac{1}{y^2}\right)
\psi = 0.$">|; 

$key = q/displaystylefrac{d^2psi}{dy^2}+frac{1}{y}frac{dpsi}{dy}-left(1+frac{1}{y^2}right)psi=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1994.png"
 ALT="$\displaystyle \frac{d^2\psi}{dy^2} + \frac{1}{y}\frac{d\psi}{dy} - \left(1+\frac{1}{y^2}\right)
\psi = 0.$">|; 

$key = q/displaystylefrac{d^2skew{3}bar{phi}}{dp^2}-Q,p^{2},skew{3}bar{phi}=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.35ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img3398.png"
 ALT="$\displaystyle \frac{d^2\skew{3}\bar{\phi}}{d p^2} - Q p^{2} \skew{3}\bar{\phi} = 0.$">|; 

$key = q/displaystylefrac{d^2x}{dt^2}=-frac{e}{m_e},k^2,x,{mitPhi}_0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -1.96ex; " SRC="|."$dir".q|img2314.png"
 ALT="$\displaystyle \frac{d^2 x}{dt^2} = - \frac{e}{m_e} k^2 x {\mit\Phi}_0,$">|; 

$key = q/displaystylefrac{d^2x}{dt^2}=frac{e}{m},E_0,{rme}^{,{rmi},(k,x-omega,t)}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2304.png"
 ALT="$\displaystyle \frac{d^2x}{dt^2} = \frac{e}{m} E_0 {\rm e}^{ {\rm i} 
(k x-\omega t)}.$">|; 

$key = q/displaystylefrac{d^2{bfr}}{dt^2}=frac{c^2}{2},nablan^2.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2166.png"
 ALT="$\displaystyle \frac{d^2{\bf r}}{dt^2} = \frac{c^2}{2} \nabla n^2.$">|; 

$key = q/displaystylefrac{d^2}{dzeta^{2}}!left(zeta,G_{s'}right)=2,n_{s'},v_{t,{s'}},{rmerf}(zeta),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.35ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img907.png"
 ALT="$\displaystyle \frac{d^2}{d\zeta^{2}}\!\left(\zeta G_{s'}\right) = 2 n_{s'} v_{t {s'}} {\rm erf}(\zeta),$">|; 

$key = q/displaystylefrac{d_ehat{n}}{dhat{t}}+hat{n},widehat{nabla}cdotwidehat{bfV}_e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.74ex; vertical-align: -1.71ex; " SRC="|."$dir".q|img1368.png"
 ALT="$\displaystyle \frac{d_e\hat{n}}{d\hat{t}} + \hat{n} \widehat{\nabla}\cdot\widehat{\bf V}_e$">|; 

$key = q/displaystylefrac{d_en}{dt}+n,nablacdot{bfV}_e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1142.png"
 ALT="$\displaystyle \frac{d_e n}{dt} + n \nabla\cdot{\bf V}_e$">|; 

$key = q/displaystylefrac{d_ihat{n}}{dhat{t}}+hat{n},widehat{nabla}cdotwidehat{bfV}_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.74ex; vertical-align: -1.71ex; " SRC="|."$dir".q|img1411.png"
 ALT="$\displaystyle \frac{d_i \hat{n}}{d\hat{t}} + \hat{n} \widehat{\nabla}\cdot\widehat{\bf V}_i$">|; 

$key = q/displaystylefrac{d_in}{dt}+n,nablacdot{bfV}_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1149.png"
 ALT="$\displaystyle \frac{d_i n}{dt} + n \nabla\cdot{\bf V}_i$">|; 

$key = q/displaystylefrac{d_sn_s}{dt}+n_s,nablacdot{bfV}_s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1073.png"
 ALT="$\displaystyle \frac{d_s n_s}{dt} + n_s \nabla\cdot{\bf V}_s$">|; 

$key = q/displaystylefrac{d_s}{dt}equivfrac{partial}{partialt}+{bfV}_scdotnabla;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1078.png"
 ALT="$\displaystyle \frac{d_s}{dt} \equiv \frac{\partial}{\partial t} + {\bf V}_s\cdot \nabla$">|; 

$key = q/displaystylefrac{delta_{rmSP}}{a}simleft(frac{1}{epsilon,hat{W},{calS}}right)^{1slash2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3702.png"
 ALT="$\displaystyle \frac{\delta_{\rm SP}}{a}\sim \left(\frac{1}{\epsilon \hat{W} {\cal S}}\right)^{1/2},$">|; 

$key = q/displaystylefrac{delta}{a};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img3681.png"
 ALT="$\displaystyle \frac{\delta}{a}$">|; 

$key = q/displaystylefrac{dgamma}{dt}=epsilon^{-1},omega_{-1}({bfR},{bfU},t)+omega_0({bfR},{bfU},t)+cdots.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img293.png"
 ALT="$\displaystyle \frac{d\gamma}{dt} = \epsilon^{-1} \omega_{-1}({\bf R}, {\bf U}, t)
+ \omega_0({\bf R}, {\bf U}, t) + \cdots.$">|; 

$key = q/displaystylefrac{dhat{mitPsi}}{dhat{t}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.19ex; vertical-align: -1.71ex; " SRC="|."$dir".q|img3757.png"
 ALT="$\displaystyle \frac{d\hat{\mit\Psi}}{d\hat{t}}$">|; 

$key = q/displaystylefrac{dhat{mitPsi}}{dhat{t}}=frac{2^{3slash2}}{sqrt{pi}},S^{1slash2},hat{mitPsi}^{3slash4}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.74ex; vertical-align: -2.30ex; " SRC="|."$dir".q|img3660.png"
 ALT="$\displaystyle \frac{d\hat{\mit\Psi}}{d\hat{t}}= \frac{2^{3/2}}{\sqrt{\pi}} S^{1/2} \hat{\mit\Psi}^{3/4}.$">|; 

$key = q/displaystylefrac{dhat{mitPsi}}{dhat{t}}simhat{v}_0,hat{B}_ast=frac{hat{B}_ast^{,3slash2},S^{1slash2}}{sqrt{pi}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.80ex; vertical-align: -2.30ex; " SRC="|."$dir".q|img3655.png"
 ALT="$\displaystyle \frac{d\hat{\mit\Psi}}{d\hat{t}} \sim \hat{v}_0 \hat{B}_\ast = \frac{\hat{B}_\ast^{ 3/2} S^{1/2}}{\sqrt{\pi}}.$">|; 

$key = q/displaystylefrac{dk_x}{dt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2148.png"
 ALT="$\displaystyle \frac{d k_x}{dt}$">|; 

$key = q/displaystylefrac{dln{mitPsi}}{dhat{t}}=frac{2^{3slash2}}{sqrt{pi}}left(frac{hat{delta}}{hat{mitPsi}^{1slash2}}right)^{1slash2}S^{2slash3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.13ex; vertical-align: -2.30ex; " SRC="|."$dir".q|img3667.png"
 ALT="$\displaystyle \frac{d\ln{\mit\Psi}}{d\hat{t}} = \frac{2^{3/2}}{\sqrt{\pi}}\left(\frac{\hat{\delta}}{\hat{\mit\Psi}^{1/2}}\right)^{1/2} S^{2/3}$">|; 

$key = q/displaystylefrac{dmu}{dt}=frac{d}{dt}!left(frac{m,u_perp^{2}}{2,B}right)=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.52ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img383.png"
 ALT="$\displaystyle \frac{d\mu}{dt}= \frac{d}{dt}\!\left(\frac{ m u_\perp^{2}}{2 B}\right) = 0.$">|; 

$key = q/displaystylefrac{dn}{dt}+n,nablacdot{bfV};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1097.png"
 ALT="$\displaystyle \frac{dn}{dt} + n \nabla\cdot{\bf V}$">|; 

$key = q/displaystylefrac{dn}{dt}+n,nablacdot{bfV}=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1478.png"
 ALT="$\displaystyle \frac{dn}{dt} + n \nabla\cdot{\bf V} = 0,$">|; 

$key = q/displaystylefrac{domega}{dt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2125.png"
 ALT="$\displaystyle \frac{d\omega}{d t}$">|; 

$key = q/displaystylefrac{domega}{dt}equivfrac{partialomega}{partialt}+({bfv}_gcdotnabla),omega=frac{partial{mitOmega}}{partialt}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2121.png"
 ALT="$\displaystyle \frac{d\omega}{dt} \equiv
\frac{\partial\omega}{\partial t} + ({\bf v}_g\cdot\nabla)  \omega =
\frac{\partial {\mit\Omega}}{\partial t}.$">|; 

$key = q/displaystylefrac{dphi}{dz}simeqpmk_0,n,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.80ex; " SRC="|."$dir".q|img1929.png"
 ALT="$\displaystyle \frac{d\phi}{dz} \simeq \pm k_0 n,$">|; 

$key = q/displaystylefrac{dphi}{dz}simeqpmk_0,nleft(1pmfrac{{rmi}}{k_0,n^2}frac{dn}{dz}right)^{1slash2}simeqpmk_0,n+frac{rmi}{2,n}frac{dn}{dz},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1933.png"
 ALT="$\displaystyle \frac{d\phi}{dz} \simeq \pm k_0 n\left(1\pm \frac{{\rm i}}{k_0 \...
...\frac{dn}{dz}
\right)^{1/2}\simeq \pm k_0 n + \frac{\rm i}{2 n}\frac{dn}{dz},$">|; 

$key = q/displaystylefrac{dphi}{dz}simeqpmleft(k_0^{2},n^2pm{rmi},k_0,frac{dn}{dz}right)^{1slash2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1932.png"
 ALT="$\displaystyle \frac{d\phi}{dz} \simeq \pm \left(k_0^{2}  n^2 \pm {\rm i}  k_0  \frac{dn}{dz}\right)^{1/2}.$">|; 

$key = q/displaystylefrac{dp}{dr}=-rho,frac{G,M_odot}{r^{2}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2755.png"
 ALT="$\displaystyle \frac{dp}{dr} = - \rho \frac{G M_\odot}{r^{2}},$">|; 

$key = q/displaystylefrac{drho}{dt}+rho,nablacdot{bfV};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2672.png"
 ALT="$\displaystyle \frac{d\rho}{dt} + \rho \nabla\cdot{\bf V}$">|; 

$key = q/displaystylefrac{dsigma}{d{mitOmega}}=frac{1}{4}left(frac{e_s,e_{s'}}{4pi,epsilon_0,mu_{ss'},u_{ss'}^{2}}right)^2frac{1}{sin^4(chislash2)}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.08ex; vertical-align: -2.42ex; " SRC="|."$dir".q|img732.png"
 ALT="$\displaystyle \frac{d\sigma}{d{\mit\Omega}} = \frac{1}{4}\left(\frac{e_s e_{s'}}{4\pi \epsilon_0 \mu_{ss'} u_{ss'}^{2}}\right)^2 \frac{1}{\sin^4(\chi/2)}.$">|; 

$key = q/displaystylefrac{dsigma}{d{mitOmega}}=frac{1}{4}left(frac{e_s,e_{s'}}{4pi,epsilon_0,mu_{ss'},u_{ss'}^{2}}right)^2frac{1}{sin^4(chislash2)};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.08ex; vertical-align: -2.42ex; " SRC="|."$dir".q|img730.png"
 ALT="$\displaystyle \frac{d\sigma}{d{\mit\Omega}} = \frac{1}{4}\left(\frac{e_s e_{s'}}{4\pi \epsilon_0 \mu_{ss'} u_{ss'}^{2}}\right)^2 \frac{1}{\sin^4(\chi/2)}$">|; 

$key = q/displaystylefrac{dsigma}{d{mitOmega}}=frac{2pi,b}{|d{mitOmega}slashdb|}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.98ex; " SRC="|."$dir".q|img728.png"
 ALT="$\displaystyle \frac{d\sigma}{d{\mit\Omega}} = \frac{2\pi b}{\vert d{\mit\Omega}/db\vert}.$">|; 

$key = q/displaystylefrac{dskew{3}hat{mitPhi}}{dy};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img1609.png"
 ALT="$\displaystyle \frac{d\skew{3}\hat{\mit\Phi}}{dy}$">|; 

$key = q/displaystylefrac{dskew{3}hat{mitPsi}}{dhat{t}},cosxi={skew{3}hat{phi},hat{psi}}+hat{J}(hat{psi}).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.19ex; vertical-align: -1.71ex; " SRC="|."$dir".q|img3506.png"
 ALT="$\displaystyle \frac{d\skew{3}\hat{\mit\Psi}}{d\hat{t}} \cos\xi = \{\skew{3}\hat{\phi},\hat{\psi}\} + \hat{J}(\hat{\psi}).$">|; 

$key = q/displaystylefrac{dskew{3}hat{mitPsi}}{dhat{t}}=gamma,tau_R,skew{3}hat{mitPsi}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.19ex; vertical-align: -1.71ex; " SRC="|."$dir".q|img3610.png"
 ALT="$\displaystyle \frac{d\skew{3}\hat{\mit\Psi}}{d\hat{t}} = \gamma \tau_R  \skew{3}\hat{\mit\Psi}.$">|; 

$key = q/displaystylefrac{du(r_c)}{dr}=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2787.png"
 ALT="$\displaystyle \frac{du(r_c)}{dr} = 0.$">|; 

$key = q/displaystylefrac{du^2}{dr}left(1-frac{u_c^{2}}{u^2}right)=frac{4,u_c^{2}}{r}left(1-frac{r_c}{r}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.52ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2795.png"
 ALT="$\displaystyle \frac{du^2}{dr}\left(1-\frac{u_c^{2}}{u^2}\right) = \frac{4 u_c^{2}}{r}
\left(1-\frac{r_c}{r}\right),$">|; 

$key = q/displaystylefrac{du_x}{dx};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3072.png"
 ALT="$\displaystyle \frac{d u_x}{dx}$">|; 

$key = q/displaystylefrac{du}{dt}=frac{e}{m},E_0,{rme}^{,{rmi},(k,x_0+k,u_0,t-omega,t)},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2307.png"
 ALT="$\displaystyle \frac{du}{dt} = \frac{e}{m} E_0 {\rm e}^{ {\rm i} (k x_0+k u_0 t-\omega t)},$">|; 

$key = q/displaystylefrac{dv_parallel}{dt}=frac{e}{m},E_parallel,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.74ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img219.png"
 ALT="$\displaystyle \frac{d v_\parallel} {dt} = \frac{e}{m}  E_\parallel,$">|; 

$key = q/displaystylefrac{dx}{dt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2144.png"
 ALT="$\displaystyle \frac{dx}{dt}$">|; 

$key = q/displaystylefrac{dz}{dt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2146.png"
 ALT="$\displaystyle \frac{dz}{dt}$">|; 

$key = q/displaystylefrac{d{bfR}}{dt}={bfU}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img294.png"
 ALT="$\displaystyle \frac{d{\bf R}}{dt} = {\bf U}.$">|; 

$key = q/displaystylefrac{d{bfZ}}{dt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img258.png"
 ALT="$\displaystyle \frac{d{\bf Z}}{dt}$">|; 

$key = q/displaystylefrac{d{bfZ}}{dt}=langle{bff}rangle({bfZ},t)+epsilon,langle;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img267.png"
 ALT="$\displaystyle \frac{d{\bf Z}}{dt} = \langle {\bf f}\rangle({\bf Z},t) + \epsilon  \langle$">|; 

$key = q/displaystylefrac{d{bfh}_{ss'}}{dt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img679.png"
 ALT="$\displaystyle \frac{d {\bf h}_{ss'}}{dt}$">|; 

$key = q/displaystylefrac{d{bfk}}{dt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2123.png"
 ALT="$\displaystyle \frac{d{\bf k}}{dt}$">|; 

$key = q/displaystylefrac{d{bfk}}{dt}equivfrac{partial{bfk}}{partialt}+({bfv}_gcdotnabla),{bfk}=-nabla{mitOmega}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2119.png"
 ALT="$\displaystyle \frac{d{\bf k}}{dt}\equiv\frac{\partial {\bf k}}{\partial t} + ({\bf v}_g\cdot\nabla) 
{\bf k} = -\nabla{\mit\Omega}.$">|; 

$key = q/displaystylefrac{d{bfr}}{dt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img275.png"
 ALT="$\displaystyle \frac{d{\bf r}}{dt}$">|; 

$key = q/displaystylefrac{d{bfv}}{dt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img277.png"
 ALT="$\displaystyle \frac{d{\bf v}}{dt}$">|; 

$key = q/displaystylefrac{d{bfz}}{dt}={bff}({bfz},t,tau),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img236.png"
 ALT="$\displaystyle \frac{d{\bf z}}{dt} = {\bf f}({\bf z}, t, \tau),$">|; 

$key = q/displaystylefrac{d{calE}}{dt}=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img412.png"
 ALT="$\displaystyle \frac{d{\cal E}}{dt} = 0,$">|; 

$key = q/displaystylefrac{d{calI}}{dt}=-ointfrac{dH}{ds},ds=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img395.png"
 ALT="$\displaystyle \frac{d{\cal I}}{dt} =-\oint\frac{d H}{ds} ds =0.$">|; 

$key = q/displaystylefrac{d{mitPhi}_1}{dt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2907.png"
 ALT="$\displaystyle \frac{d{\mit\Phi}_1}{dt}$">|; 

$key = q/displaystylefrac{d{mitPhi}_2}{dt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2909.png"
 ALT="$\displaystyle \frac{d{\mit\Phi}_2}{dt}$">|; 

$key = q/displaystylefrac{d{mitPsi}}{dt}=-int_{bfS}nablatimesleft({bfE}+{bfV}times{bfB}right)cdotd{bfS}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img2699.png"
 ALT="$\displaystyle \frac{d{\mit\Psi}}{dt} = - \int_{\bf S}\nabla\times\left({\bf E} + {\bf V}\times
{\bf B}\right)\cdot d{\bf S}.$">|; 

$key = q/displaystylefrac{d{mitPsi}}{dt}=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2701.png"
 ALT="$\displaystyle \frac{d{\mit\Psi}}{dt} = 0,$">|; 

$key = q/displaystylefrac{d{mitPsi}}{dt}simv_0,B_ast,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3636.png"
 ALT="$\displaystyle \frac{d{\mit\Psi}}{dt} \sim v_0 B_\ast,$">|; 

$key = q/displaystylefrac{d}{dp}!left(frac{1}{p^2},frac{dK}{dp}right)-frac{Q,(Q+p^2)}{p^2},K=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3432.png"
 ALT="$\displaystyle \frac{d}{dp}\!\left(\frac{1}{p^2} \frac{dK}{dp}\right) - \frac{Q (Q+p^2)}{p^2} K= 0.$">|; 

$key = q/displaystylefrac{d}{dp}!left(frac{p^{2}}{Q+p^{2}},frac{dskew{3}bar{phi}}{dp}right)=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3406.png"
 ALT="$\displaystyle \frac{d}{dp}\!\left(\frac{p^{2}}{Q+p^{2}} \frac{d\skew{3}\bar{\phi}}{dp} \right) = 0.$">|; 

$key = q/displaystylefrac{d}{dp}!left(frac{p^{2}}{Q+p^{2}}frac{dskew{3}bar{phi}}{dp}right)-Q,p^{2},skew{3}bar{phi}=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3385.png"
 ALT="$\displaystyle \frac{d}{dp}\!\left(\frac{p^{2}}{Q+p^{2}}\frac{d\skew{3}\bar{\phi}}{dp}\right)
-Q p^{2} \skew{3}\bar{\phi} = 0,$">|; 

$key = q/displaystylefrac{d}{dp}!left(frac{p^{2}}{Q+p^{2}}frac{dskew{3}bar{phi}}{dp}right)-left(Q,p^{2}+P,p^{4}right)skew{3}bar{phi}=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3745.png"
 ALT="$\displaystyle \frac{d}{dp}\!\left(\frac{p^{2}}{Q+p^{2}}\frac{d\skew{3}\bar{\phi}}{dp}\right)
-\left(Q p^{2}+ P p^{4}\right)\skew{3}\bar{\phi} = 0.
$">|; 

$key = q/displaystylefrac{d}{dt}!intB_z^{2},dx,dy=-frac{2,eta}{mu_0}int!int|nablaB_z|^{2},dx,dy.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img3231.png"
 ALT="$\displaystyle \frac{d}{dt}\!\int B_z^{2} dx dy = -\frac{2 \eta}{\mu_0}\int\!\int \vert\nabla B_z\vert^{2} dx dy.
$">|; 

$key = q/displaystylefrac{d}{dt}!intchi^2,dV=-2,frac{eta}{mu_0}int|nablachi|^{2},dVleq0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img2972.png"
 ALT="$\displaystyle \frac{d}{dt}\!\int\chi^2 dV = -2 \frac{\eta}{\mu_0}\int\vert\nabla\chi\vert^{2} dV\leq 0.$">|; 

$key = q/displaystylefrac{d}{dt}!intpsi^2,dV=-2,frac{eta}{mu_0}int|nablapsi|^{2},dVleq0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img2964.png"
 ALT="$\displaystyle \frac{d}{dt}\!\int\psi^2 dV = -2 \frac{\eta}{\mu_0}\int \vert\nabla\psi\vert^{2} dV\leq 0.$">|; 

$key = q/displaystylefrac{d}{dt}!intpsi^{2},dx,dy=-frac{2,eta}{mu_0}int!int|nablapsi|^{2},dx,dy,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img3228.png"
 ALT="$\displaystyle \frac{d}{dt}\!\int \psi^{2} dx dy=-\frac{2 \eta}{\mu_0}\int\!\int \vert\nabla\psi\vert^{2} dx dy,
$">|; 

$key = q/displaystylefrac{d}{dt}!left(frac{p}{n^{5slash3}}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img1548.png"
 ALT="$\displaystyle \frac{d}{dt}\!\left(\frac{p}{n^{5/3}}\right)$">|; 

$key = q/displaystylefrac{d}{dt}!left(frac{p}{n^{5slash3}}right)simeq0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img1495.png"
 ALT="$\displaystyle \frac{d}{dt}\!\left(\frac{p}{n^{5/3}}\right) \simeq 0.$">|; 

$key = q/displaystylefrac{d}{dt}!left(frac{p}{rho^{{mitGamma}}}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2674.png"
 ALT="$\displaystyle \frac{d}{dt}\!\left(\frac{p}{\rho^{{\mit\Gamma}}}\right)$">|; 

$key = q/displaystylefrac{d}{dt}langlefrangle=leftlanglefrac{df}{dt}rightrangle,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img369.png"
 ALT="$\displaystyle \frac{d}{dt} \langle f\rangle = \left\langle \frac{df}{dt}\right\rangle,$">|; 

$key = q/displaystylefrac{d}{dv}!left(v^{2},frac{dG_{s'}}{dv}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img896.png"
 ALT="$\displaystyle \frac{d}{dv}\!\left(v^{2} \frac{dG_{s'}}{dv}\right)$">|; 

$key = q/displaystylefrac{d}{dv}!left(v^{2},frac{dH_{s'}}{dv}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img894.png"
 ALT="$\displaystyle \frac{d}{dv}\!\left(v^{2} \frac{dH_{s'}}{dv}\right)$">|; 

$key = q/displaystylefrac{d}{dx}(V_x,B_y-V_y,B_x);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3068.png"
 ALT="$\displaystyle \frac{d}{dx}(V_x B_y-V_y B_x)$">|; 

$key = q/displaystylefrac{e,V}{T}=cosh^{-1}left(1+frac{sigma^2}{16,epsilon_0,n_0,T}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img197.png"
 ALT="$\displaystyle \frac{e V}{T} = \cosh^{-1}\left(1+ \frac{\sigma^2}{16 \epsilon_0 n_0 T}\right).
$">|; 

$key = q/displaystylefrac{epsilon_0,m_e}{e^2},f(U)=Pint_{-infty}^inftyfrac{F_0'(u)}{u-U},du+{rmi},pi,F_0'(U).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.13ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img2532.png"
 ALT="$\displaystyle \frac{\epsilon_0 m_e}{e^2} f(U) = P\int_{-\infty}^\infty\frac{F_0'(u)}{u-U} du + {\rm i} \pi F_0'(U).$">|; 

$key = q/displaystylefrac{gamma}{omega_r};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.35ex; vertical-align: -1.95ex; " SRC="|."$dir".q|img2634.png"
 ALT="$\displaystyle \frac{\gamma}{\omega_r}$">|; 

$key = q/displaystylefrac{hat{psi}(hatx,xi)}{skew{3}hat{mitPsi}}=8left(frac{hat{x}}{hat{W}}right)^2+cosxi.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3461.png"
 ALT="$\displaystyle \frac{\hat{\psi}(\hat x,\xi)}{\skew{3}\hat{\mit\Psi}}=8\left(\frac{\hat{x}}{\hat{W}}\right)^2+\cos\xi.$">|; 

$key = q/displaystylefrac{lambda_D}{L}ll1,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.46ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img57.png"
 ALT="$\displaystyle \frac{\lambda_D}{L} \ll 1,$">|; 

$key = q/displaystylefrac{lambda_{rmmfp}}{lambda_D}simfrac{{mitLambda}}{ln{mitLambda}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.95ex; " SRC="|."$dir".q|img128.png"
 ALT="$\displaystyle \frac{\lambda_{\rm mfp}}{\lambda_D} \sim \frac{{\mit\Lambda}}{\ln{\mit\Lambda}}.$">|; 

$key = q/displaystylefrac{m}{2}frac{dv^2}{dt}=e,{bfv}cdot{bfE}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img365.png"
 ALT="$\displaystyle \frac{m}{2} \frac{d v^2}{dt} = e {\bf v}\cdot{\bf E}.$">|; 

$key = q/displaystylefrac{m}{2}frac{d}{dt}(u_perp^{2}+U_0^{2})=e,U_{0,parallel},E_parallel+e,{bfU}_1cdot{bfE}+e,langle{bfu}cdot(;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img367.png"
 ALT="$\displaystyle \frac{m}{2} \frac{d}{dt} (u_\perp^{2} + U_0^{2}) = e U_{0 \parallel}
 E_\parallel + e  {\bf U}_1\cdot {\bf E} + e \langle
{\bf u}\cdot ($">|; 

$key = q/displaystylefrac{n_e}{n_s};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.41ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img1617.png"
 ALT="$\displaystyle \frac{n_e}{n_s}$">|; 

$key = q/displaystylefrac{n_i}{n_s};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.41ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img1615.png"
 ALT="$\displaystyle \frac{n_i}{n_s}$">|; 

$key = q/displaystylefrac{omega_r}{k}simeqleft(frac{T_e}{m_i}right)^{1slash2}frac{1}{left[1+(k,lambda_{D,e})^{2}right]^{1slash2}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.19ex; vertical-align: -2.54ex; " SRC="|."$dir".q|img2665.png"
 ALT="$\displaystyle \frac{\omega_r}{k} \simeq \left(\frac{T_e}{m_i}\right)^{1/2}\frac{1}{\left[1+(k \lambda_{D e})^{2}\right]^{1/2}},
$">|; 

$key = q/displaystylefrac{p_2}{p_1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img3098.png"
 ALT="$\displaystyle \frac{p_2}{p_1}$">|; 

$key = q/displaystylefrac{partial(m_s,n_s,{bfV}_s)}{partialt}+nablacdot{bfP}_s-e_s,n_s,({bfE}+{bfV}_stimes{bfB})={bfF}_s.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1060.png"
 ALT="$\displaystyle \frac{\partial(m_s  n_s {\bf V}_s)}{\partial t}
+ \nabla\cdot{\bf P}_s -e_s  n_s ({\bf E} + {\bf V}_s\times {\bf B}) ={\bf F}_s.$">|; 

$key = q/displaystylefrac{partial(rho,{bfV})}{partialt}+nablacdot{bfT};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3051.png"
 ALT="$\displaystyle \frac{\partial (\rho {\bf V})}{\partial t} + \nabla\cdot{\bf T}$">|; 

$key = q/displaystylefrac{partialF_1}{partialt}+{rmi},k,u,F_1-frac{e}{m_e},E,frac{partialF_0}{partialu}=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.96ex; " SRC="|."$dir".q|img2245.png"
 ALT="$\displaystyle \frac{\partial F_1}{\partial t} + {\rm i} k u F_1 - \frac{e}{m_e} E 
\frac{\partial F_0}{\partial u} = 0,$">|; 

$key = q/displaystylefrac{partialH_{s'}}{partialv_alpha};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img910.png"
 ALT="$\displaystyle \frac{\partial H_{s'}}{\partial v_\alpha}$">|; 

$key = q/displaystylefrac{partialU}{partialt}+nablacdot{bfu};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3052.png"
 ALT="$\displaystyle \frac{\partial U}{\partial t} + \nabla\cdot {\bf u}$">|; 

$key = q/displaystylefrac{partial^2G_{s'}}{partialv_alpha,v_beta};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.52ex; vertical-align: -2.26ex; " SRC="|."$dir".q|img912.png"
 ALT="$\displaystyle \frac{\partial^2 G_{s'}}{\partial v_\alpha v_\beta}$">|; 

$key = q/displaystylefrac{partial^2hat{psi}}{partialhat{x}^2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3485.png"
 ALT="$\displaystyle \frac{\partial^2\hat{\psi}}{\partial \hat{x}^2}$">|; 

$key = q/displaystylefrac{partialepsilon_r(k,omega_r)}{partialomega}simeqfrac{2}{omega_r}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.95ex; " SRC="|."$dir".q|img2632.png"
 ALT="$\displaystyle \frac{\partial\epsilon_r(k,\omega_r)}{\partial\omega}\simeq \frac{2}{\omega_r}.$">|; 

$key = q/displaystylefrac{partialf_0}{partialv_x'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.19ex; vertical-align: -2.18ex; " SRC="|."$dir".q|img2379.png"
 ALT="$\displaystyle \frac{\partial f_0}{\partial v_x'}$">|; 

$key = q/displaystylefrac{partialf_0}{partialv_y'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.47ex; " SRC="|."$dir".q|img2381.png"
 ALT="$\displaystyle \frac{\partial f_0}{\partial v_y'}$">|; 

$key = q/displaystylefrac{partialf_0}{partialv_z'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.30ex; vertical-align: -2.29ex; " SRC="|."$dir".q|img2383.png"
 ALT="$\displaystyle \frac{\partial f_0}{\partial v_z'}$">|; 

$key = q/displaystylefrac{partialf_1}{partialt}+{bfv}cdotnablaf_1-frac{e}{m_e},{bfE}cdotnabla_vf_0=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.96ex; " SRC="|."$dir".q|img2232.png"
 ALT="$\displaystyle \frac{\partial f_1}{\partial t} + {\bf v}\cdot\nabla f_1
- \frac{e}{m_e} {\bf E}\cdot\nabla_v f_0 =0,$">|; 

$key = q/displaystylefrac{partialf_e}{partialt}+{bfv}cdotnablaf_e-frac{e}{m_e},{bfE}cdotnabla_vf_e=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.96ex; " SRC="|."$dir".q|img2225.png"
 ALT="$\displaystyle \frac{\partial f_e}{\partial t} + {\bf v}\cdot\nabla f_e - \frac{e}{m_e} 
{\bf E}\cdot\nabla_v f_e = 0,$">|; 

$key = q/displaystylefrac{partialf_s}{partialt}+nablacdot({bfv},f_s)+nabla_vcdot({bfa}_s,f_s)=C_s(f).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1056.png"
 ALT="$\displaystyle \frac{\partial f_s}{\partial t} +
\nabla\cdot({\bf v} f_s) +\nabla_v\cdot({\bf a}_s f_s) = C_s(f).$">|; 

$key = q/displaystylefrac{partialf_s}{partialt}=sum_{s'}C_{ss'}(f_s,f_{s'}).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.58ex; vertical-align: -2.62ex; " SRC="|."$dir".q|img849.png"
 ALT="$\displaystyle \frac{\partial f_s}{\partial t} = \sum_{s'} C_{ss'}(f_s,f_{s'}).$">|; 

$key = q/displaystylefrac{partialf_s}{partialv_alpha}=-frac{2,(v_alpha-V_{s,alpha})}{v_{t,s}^{2}},f_s.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.30ex; vertical-align: -2.29ex; " SRC="|."$dir".q|img919.png"
 ALT="$\displaystyle \frac{\partial f_s}{\partial v_\alpha} = -\frac{2 (v_\alpha-V_{s \alpha})}{v_{t s}^{2}} f_s.$">|; 

$key = q/displaystylefrac{partialg}{partialt}+nablacdot{bfg}={mitDelta}g,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1066.png"
 ALT="$\displaystyle \frac{\partial g}{\partial t} + \nabla\cdot {\bf g} = {\mit\Delta} g,$">|; 

$key = q/displaystylefrac{partialhat{U}}{partialhat{t}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.13ex; vertical-align: -1.71ex; " SRC="|."$dir".q|img3483.png"
 ALT="$\displaystyle \frac{\partial\hat{U}}{\partial\hat{t}}$">|; 

$key = q/displaystylefrac{partialhat{psi}}{partialhat{t}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -1.71ex; " SRC="|."$dir".q|img3481.png"
 ALT="$\displaystyle \frac{\partial\hat{\psi}}{\partial\hat{t}}$">|; 

$key = q/displaystylefrac{partialk_alpha}{partialt}+frac{partialomega}{partialr_alpha};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img2116.png"
 ALT="$\displaystyle \frac{\partial k_\alpha}{\partial t} + \frac{\partial\omega}{\partial r_\alpha}$">|; 

$key = q/displaystylefrac{partialk_beta}{partialr_alpha}-frac{partialk_alpha}{partialr_beta};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.26ex; " SRC="|."$dir".q|img2117.png"
 ALT="$\displaystyle \frac{\partial k_\beta}{\partial r_\alpha} - \frac{\partial k_\alpha}{\partial r_\beta}$">|; 

$key = q/displaystylefrac{partialn_s}{partialt}+nablacdot(n_s,{bfV}_s)=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1059.png"
 ALT="$\displaystyle \frac{\partial n_s}{\partial t} + \nabla\cdot(n_s {\bf V}_s) = 0.$">|; 

$key = q/displaystylefrac{partialn}{partialt}+nablacdot(n,{bfV});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1897.png"
 ALT="$\displaystyle \frac{\partial n}{\partial t} + \nabla\cdot (n {\bf V})$">|; 

$key = q/displaystylefrac{partialn}{partialt}+nablacdot(n,{bfV}_e);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1468.png"
 ALT="$\displaystyle \frac{\partial n}{\partial t} + \nabla\cdot(n {\bf V}_e)$">|; 

$key = q/displaystylefrac{partialn}{partialt}+nablacdot(n,{bfV}_i);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1470.png"
 ALT="$\displaystyle \frac{\partial n}{\partial t} + \nabla\cdot(n {\bf V}_i)$">|; 

$key = q/displaystylefrac{partialpsi}{partialt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3263.png"
 ALT="$\displaystyle \frac{\partial\psi}{\partial t}$">|; 

$key = q/displaystylefrac{partialrho}{partialt}+nablacdot(rho,{bfV});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3050.png"
 ALT="$\displaystyle \frac{\partial\rho}{\partial t} + \nabla\cdot(\rho {\bf V})$">|; 

$key = q/displaystylefrac{partialrho}{partialt}+rho_0,nablacdot{bfV};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2704.png"
 ALT="$\displaystyle \frac{\partial\rho}{\partial t} + \rho_0 \nabla\cdot{\bf V}$">|; 

$key = q/displaystylefrac{partials_s}{partialt}+nablacdot{bfs}_s={mitTheta}_s,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1093.png"
 ALT="$\displaystyle \frac{\partial s_s}{\partial t} + \nabla\cdot{\bf s}_s = {\mit\Theta}_s,$">|; 

$key = q/displaystylefrac{partialu_{ss',alpha}}{partialu_{ss',beta}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -2.26ex; " SRC="|."$dir".q|img798.png"
 ALT="$\displaystyle \frac{\partial u_{ss' \alpha}}{\partial u_{ss' \beta}}$">|; 

$key = q/displaystylefrac{partialu_{ss'}}{partialu_{ss',alpha}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img796.png"
 ALT="$\displaystyle \frac{\partial u_{ss'}}{\partial u_{ss' \alpha}}$">|; 

$key = q/displaystylefrac{partialw_{ss',alphabeta}}{partialu_{ss',beta}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.26ex; " SRC="|."$dir".q|img802.png"
 ALT="$\displaystyle \frac{\partial w_{ss' \alpha\beta}}{\partial u_{ss' \beta}}$">|; 

$key = q/displaystylefrac{partial{bfB}}{partialt}-nablatimes({bfV}times{bfB});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3049.png"
 ALT="$\displaystyle \frac{\partial {\bf B}}{\partial t} - \nabla\times ({\bf V}\times {\bf B})$">|; 

$key = q/displaystylefrac{partial{bfB}}{partialt}-nablatimes({bfV}times{bfB})=frac{eta}{mu_0}nabla^2{bfB}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img2889.png"
 ALT="$\displaystyle \frac{\partial {\bf B}}{\partial t} - \nabla\times({\bf V}\times{\bf B})
= \frac{\eta}{\mu_0}\nabla^2{\bf B}.$">|; 

$key = q/displaystylefrac{partial{bfB}}{partialt}=({bfB}cdotnabla),{bfV}-({bfV}cdotnabla),{bfB}+frac{eta}{mu_0},nabla^2{bfB},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img2977.png"
 ALT="$\displaystyle \frac{\partial{\bf B}}{\partial t} = ({\bf B}\cdot\nabla) {\bf V}
-({\bf V}\cdot\nabla) {\bf B} + \frac{\eta}{\mu_0} \nabla^2{\bf B},$">|; 

$key = q/displaystylefrac{partial{bfB}}{partialt}=nablatimes({bfV}times{bfB})+frac{1}{mu_0,sigma},nabla^2{bfB},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img3203.png"
 ALT="$\displaystyle \frac{\partial {\bf B}}{\partial t} = \nabla\times ({\bf V}\times {\bf B})
+ \frac{1}{\mu_0 \sigma} \nabla^2{\bf B},
$">|; 

$key = q/displaystylefrac{partial{bfB}}{partialt}=nablatimes({bfV}times{bfB})+frac{eta}{mu_0},nabla^2{bfB}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img3238.png"
 ALT="$\displaystyle \frac{\partial{\bf B}}{\partial t} = \nabla\times({\bf V}\times{\bf B})+
\frac{\eta}{\mu_0} \nabla^2{\bf B}.$">|; 

$key = q/displaystylefrac{partial{bfB}}{partialt}=nablatimes({bfV}times{bfB})+frac{eta}{mu_0}nabla^2{bfB},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img2921.png"
 ALT="$\displaystyle \frac{\partial {\bf B}}{\partial t} = \nabla\times({\bf V}\times{\bf B})
+ \frac{\eta}{\mu_0}\nabla^2{\bf B},$">|; 

$key = q/displaystylefrac{partial{bfz}}{partialt}+frac{1}{epsilon}frac{partial{bfz}}{partialtau}={bff}({bfz},t,tau),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img244.png"
 ALT="$\displaystyle \frac{\partial{\bf z}}{\partial t} +\frac{1}{\epsilon}\frac{\partial {\bf z}}
{\partial \tau} = {\bf f}({\bf z}, t, \tau),$">|; 

$key = q/displaystylefrac{partial{calF}_s}{partialt}+{bfv}cdotfrac{partial{calF}_s}{partial{bfr}}+{bfa}_scdotfrac{partial{calF}_s}{partial{bfv}}=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img581.png"
 ALT="$\displaystyle \frac{\partial{\cal F}_s}{\partial t} + {\bf v}\cdot \frac{\parti...
...tial {\bf r}}
+ {\bf a}_s\cdot\frac{\partial {\cal F}_s}{\partial {\bf v}} = 0,$">|; 

$key = q/displaystylefrac{partial{calM}}{partialomega};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2133.png"
 ALT="$\displaystyle \frac{\partial{\cal M}}{\partial\omega}$">|; 

$key = q/displaystylefrac{partial{calM}}{partialt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2139.png"
 ALT="$\displaystyle \frac{\partial{\cal M}}{\partial t}$">|; 

$key = q/displaystylefrac{partial{calM}}{partial{bfk}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2135.png"
 ALT="$\displaystyle \frac{\partial{\cal M}}{\partial {\bf k}}$">|; 

$key = q/displaystylefrac{partial{calM}}{partial{bfr}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2137.png"
 ALT="$\displaystyle \frac{\partial{\cal M}}{\partial{\bf r}}$">|; 

$key = q/displaystylefrac{partial{f_s}}{partialt}+{bfv}cdotnablaf_s+{bfa}_scdotnabla_vf_s=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1009.png"
 ALT="$\displaystyle \frac{\partial{f_s}}{\partial t} + {\bf v}\cdot\nabla f_s
+{\bf a}_s\cdot\nabla_v f_s = 0.$">|; 

$key = q/displaystylefrac{partial{f_s}}{partialt}+{bfv}cdotnablaf_s+{bfa}_scdotnabla_vf_s=C_s(f).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1005.png"
 ALT="$\displaystyle \frac{\partial{f_s}}{\partial t} + {\bf v}\cdot\nabla f_s
+ {\bf a}_s\cdot\nabla_vf_s = C_s(f).$">|; 

$key = q/displaystylefrac{partial}{partialt}!left(frac{p}{p_0}-frac{{mitGamma},rho}{rho_0}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2707.png"
 ALT="$\displaystyle \frac{\partial}{\partial t}\!\left(\frac{p}{p_0} - \frac{{\mit\Gamma} \rho}{\rho_0}\right)$">|; 

$key = q/displaystylefrac{pi}{2},t^{2}=frac{1}{2},phi_s'',(omega-omega_s)^{2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img2076.png"
 ALT="$\displaystyle \frac{\pi}{2}  t^{2} = \frac{1}{2}  \phi_s''  (\omega-\omega_s)^{2}.$">|; 

$key = q/displaystylefrac{r_c}{a}=frac{T_0}{T},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img2783.png"
 ALT="$\displaystyle \frac{r_c}{a} = \frac{T_0}{T},$">|; 

$key = q/displaystylefrac{rho_2}{rho_1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img3094.png"
 ALT="$\displaystyle \frac{\rho_2}{\rho_1}$">|; 

$key = q/displaystylefrac{rho_e}{R_E}=frac{sqrt{2,{calE},m_e}}{e,B,R_E}=sqrt{{calE}({rmMeV)}}left(,frac{L}{38.9}right)^3,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -1.95ex; " SRC="|."$dir".q|img450.png"
 ALT="$\displaystyle \frac{\rho_e}{R_E} = \frac{\sqrt{2 {\cal E} m_e}}{e B R_E} =\sqrt{{\cal E}({\rm MeV)}}\left(
 \frac{L}{38.9}\right)^3,$">|; 

$key = q/displaystylefrac{rho_p}{R_E}=frac{sqrt{2,{calE},m_p}}{e,B,R_E}=sqrt{{calE}({rmMeV)}},left(frac{L}{11.1}right)^3,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.52ex; vertical-align: -1.95ex; " SRC="|."$dir".q|img449.png"
 ALT="$\displaystyle \frac{\rho_p}{R_E} = \frac{\sqrt{2 {\cal E} m_p}}{e B R_E} =
\sqrt{{\cal E}({\rm MeV)}} \left( \frac{L}{11.1}\right)^3,$">|; 

$key = q/displaystylefrac{sin^2alpha}{sin^2alpha_{rmeq}}=frac{B}{B_{rmeq}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.97ex; vertical-align: -2.55ex; " SRC="|."$dir".q|img453.png"
 ALT="$\displaystyle \frac{\sin^2\alpha}{\sin^2\alpha_{\rm eq}}=\frac{B}{B_{\rm eq}},$">|; 

$key = q/displaystylefrac{skew{3}hat{mitPsi}_m}{skew{3}hat{mitPsi}_1}=frac{{mitDelta}_1'}{{mitDelta}_m'},frac{I_m}{I_1}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.69ex; vertical-align: -2.28ex; " SRC="|."$dir".q|img3558.png"
 ALT="$\displaystyle \frac{\skew{3}\hat{\mit\Psi}_m}{\skew{3}\hat{\mit\Psi}_1}=\frac{{\mit\Delta}_1'}{{\mit\Delta}_m'} \frac{I_m}{I_1}.$">|; 

$key = q/displaystylefrac{tau_p}{tau}ll1.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.24ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img58.png"
 ALT="$\displaystyle \frac{\tau_p}{\tau}\ll 1.$">|; 

$key = q/displaystylefrac{{bfB}_0cdot{bfB}}{mu_0}=frac{({bfk}cdot{bfV}),B_0^{2}-({bfk}cdot{bfB}_0),({bfB}_0cdot{bfV})}{mu_0,omega}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.52ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img2740.png"
 ALT="$\displaystyle \frac{{\bf B}_0\cdot{\bf B}}{\mu_0} = \frac{({\bf k}\cdot{\bf V}) B_0^{2}
- ({\bf k}\cdot{\bf B}_0) ({\bf B}_0\cdot{\bf V})}
{\mu_0 \omega}.$">|; 

$key = q/displaystylefrac{{bfB}_0cdot{bfB}}{mu_0}=frac{V_A^{2}}{V_S^{2}}left(1-frac{k^2,V_S^{2},cos^2theta}{omega^2}right)p.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.91ex; vertical-align: -2.44ex; " SRC="|."$dir".q|img2742.png"
 ALT="$\displaystyle \frac{{\bf B}_0\cdot{\bf B}}{\mu_0}
=\frac{V_A^{2}}{V_S^{2}} \left(1-\frac{k^2 V_S^{2} \cos^2\theta}
{\omega^2}\right)p.$">|; 

$key = q/displaystylefrac{{mitGamma}-1}{2,{mitGamma}}leqM_1^{2}leqinfty.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3113.png"
 ALT="$\displaystyle \frac{{\mit\Gamma}-1}{2 {\mit\Gamma}}\leq M_1^{2} \leq \infty.$">|; 

$key = q/displaystylefrac{{mitGamma}-1}{{mitGamma}+1}leqrleqfrac{{mitGamma}+1}{{mitGamma}-1},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3111.png"
 ALT="$\displaystyle \frac{{\mit\Gamma}-1}{{\mit\Gamma}+1} \leq r \leq \frac{{\mit\Gamma}+1}{{\mit\Gamma}-1},$">|; 

$key = q/displaystylefrac{{mitOmega}}{2pi},{mitPhi}=frac{{mitOmega}}{2pi},M,I,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img2893.png"
 ALT="$\displaystyle \frac{{\mit\Omega}}{2\pi} {\mit\Phi} = \frac{{\mit\Omega}}{2\pi} M I,$">|; 

$key = q/displaystylefrac{{mitPi}_e^{2}}{k^{2}}frac{m_e}{T_e}=frac{1}{(k,lambda_D)^2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.30ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img2340.png"
 ALT="$\displaystyle \frac{{\mit\Pi}_e^{2}}{k^{2}}\frac{m_e}{T_e} = \frac{1}{(k \lambda_D)^2},$">|; 

$key = q/displaystylefrac{{rmi},E_x}{E_y}=-1.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -2.26ex; " SRC="|."$dir".q|img1766.png"
 ALT="$\displaystyle \frac{{\rm i} E_x}{E_y} = -1.$">|; 

$key = q/displaystylefrac{{rmi},E_x}{E_y}=1.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -2.26ex; " SRC="|."$dir".q|img1765.png"
 ALT="$\displaystyle \frac{{\rm i} E_x}{E_y} = 1.$">|; 

$key = q/displaystylefrac{{rmi},E_x}{E_y}=frac{n^2-S}{D}=frac{2,n^2-(R+L)}{R-L}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.52ex; vertical-align: -2.26ex; " SRC="|."$dir".q|img1767.png"
 ALT="$\displaystyle \frac{{\rm i} E_x}{E_y} = \frac{n^2 -S}{D} = \frac{2 n^2 - (R+L)}{R-L}.$">|; 

$key = q/displaystylefrac{{rmi},V_{x,e}}{V_{y,e}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -2.26ex; " SRC="|."$dir".q|img1883.png"
 ALT="$\displaystyle \frac{{\rm i} V_{x e}}{V_{y e}}$">|; 

$key = q/displaystylefrac{{rmi},V_{x,i}}{V_{y,i}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -2.26ex; " SRC="|."$dir".q|img1881.png"
 ALT="$\displaystyle \frac{{\rm i} V_{x i}}{V_{y i}}$">|; 

$key = q/displaystylefrac{{{mitPi}}_i^{2}}{{{mitOmega}}_i^{2}}=frac{c^2}{B_0^{2}slash(mu_0,rho)}=frac{c^2}{V_A^{2}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.91ex; vertical-align: -2.46ex; " SRC="|."$dir".q|img1810.png"
 ALT="$\displaystyle \frac{{{\mit\Pi}}_i^{2}}{{{\mit\Omega}}_i^{2}} = \frac{c^2}{B_0^{2}/(\mu_0 \rho)}
= \frac{c^2}{V_A^{2}}.$">|; 

$key = q/displaystylefrac{|v_parallel|}{|v_perp|}<(B_{rmmax}slashB_{rmmin}-1)^{1slash2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.98ex; " SRC="|."$dir".q|img432.png"
 ALT="$\displaystyle \frac{\vert v_\parallel\vert}{\vert v_\perp\vert} &lt; (B_{\rm max}/B_{\rm min} - 1)^{1/2}.$">|; 

$key = q/displaystylegamma,B_r;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2980.png"
 ALT="$\displaystyle \gamma B_r$">|; 

$key = q/displaystylegamma,B_theta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2983.png"
 ALT="$\displaystyle \gamma B_\theta$">|; 

$key = q/displaystylegamma,psi_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3302.png"
 ALT="$\displaystyle \gamma \psi_1$">|; 

$key = q/displaystylegamma,rholeft(frac{d^2}{dx^2}-k^2right)phi_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3304.png"
 ALT="$\displaystyle \gamma \rho\left(\frac{d^2}{dx^2}-k^2\right)\phi_1$">|; 

$key = q/displaystylegamma,tau_A;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3679.png"
 ALT="$\displaystyle \gamma \tau_A$">|; 

$key = q/displaystylegamma,tau_Rsimeq{rme}^{,{rmi},pislash3}left(frac{m,{mitOmega},tau_R}{2}right)^{2slash3}-k^2,a^2-{rmi},frac{mu}{2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3033.png"
 ALT="$\displaystyle \gamma \tau_R \simeq {\rm e}^{ {\rm i} \pi/3}\left(\frac{m {\mit\Omega} \tau_R}
{2}\right)^{2/3} - k^2 a^2 - {\rm i} \frac{\mu}{2}.$">|; 

$key = q/displaystylegamma,taull1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3425.png"
 ALT="$\displaystyle \gamma \tau\ll 1$">|; 

$key = q/displaystylegamma=-frac{epsilon_i(k,omega_r)}{partialepsilon_r(k,omega_r)slashpartialomega}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img2607.png"
 ALT="$\displaystyle \gamma = -\frac{\epsilon_i(k,\omega_r)}{\partial\epsilon_r(k,\omega_r)/\partial\omega}.$">|; 

$key = q/displaystylegamma=-frac{epsilon_i(k,omega_r)}{partialepsilon_r(k,omega_r)slashpartialomega}=-frac{omega_r}{2},epsilon_i(k,omega_r),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img2633.png"
 ALT="$\displaystyle \gamma = -\frac{\epsilon_i(k,\omega_r)}{\partial\epsilon_r(k,\omega_r)/\partial\omega} = -\frac{\omega_r}{2} \epsilon_i(k,\omega_r),$">|; 

$key = q/displaystylegamma=L^{-1}left(frac{M}{2pi},{mitOmega}-Rright).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img2898.png"
 ALT="$\displaystyle \gamma = L^{-1}\left(\frac{M}{2\pi} {\mit\Omega} - R\right).$">|; 

$key = q/displaystylegamma=frac{-(L,R'+L',R)pmsqrt{(L,R'+L',R)^{2}+4,R',(L,L'-M^{2}),(M,{mitOmega}slash2pi-R)}}{2,(L,L'-M^{2})}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.58ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img2914.png"
 ALT="$\displaystyle \gamma = \frac{ -(L R'+L' R)\pm \sqrt{(L R'+L' R)^{2 }+ 4 R' (L L'-M^{2}) 
(M {\mit\Omega}/2\pi -R)}}{2 (L L'-M^{2})}.$">|; 

$key = q/displaystylegamma=frac{1}{tau_H^{2slash3},tau_R^{1slash3}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.58ex; vertical-align: -2.66ex; " SRC="|."$dir".q|img3450.png"
 ALT="$\displaystyle \gamma= \frac{1}{\tau_H^{2/3} \tau_R^{1/3}}.$">|; 

$key = q/displaystylegamma=gamma_0+{mitOmega},t,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img308.png"
 ALT="$\displaystyle \gamma = \gamma_0 + {\mit\Omega} t,$">|; 

$key = q/displaystylegamma=kleft(frac{m_e}{m_i}right)^{1slash2}left[U_e-left(frac{T_i}{m_e}right)^{1slash2}right].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.26ex; " SRC="|."$dir".q|img2571.png"
 ALT="$\displaystyle \gamma = k\left(\frac{m_e}{m_i}\right)^{1/2}\left[U_e - \left(\frac{T_i}{m_e}\right)^{1/2}\right].$">|; 

$key = q/displaystylegamma=left[frac{Gamma(1slash4)}{2pi,Gamma(3slash4)}right]^{4slash5}frac{{mitDelta}'^{,4slash5}}{tau_H^{2slash5},tau_R^{3slash5}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.30ex; vertical-align: -2.67ex; " SRC="|."$dir".q|img3412.png"
 ALT="$\displaystyle \gamma = \left[\frac{\Gamma(1/4)}{2\pi \Gamma(3/4)}\right]^{4/5}
\frac{{\mit\Delta}'^{ 4/5}}{\tau_H^{2/5} \tau_R^{3/5}}.$">|; 

$key = q/displaystylegamma_p,tau_Asimhat{delta}_{rmSP}^{-3slash2},{calS}^{-1slash2}simepsilon^{3slash2},{calS}^{1slash4},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.79ex; vertical-align: -0.82ex; " SRC="|."$dir".q|img3713.png"
 ALT="$\displaystyle \gamma_p \tau_A \sim \hat{\delta}_{\rm SP}^{-3/2} {\cal S}^{-1/2}\sim \epsilon^{3/2} {\cal S}^{1/4},$">|; 

$key = q/displaystylegamma_{ss'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img993.png"
 ALT="$\displaystyle \gamma_{ss'}$">|; 

$key = q/displaystylegamma_{ss'}=left(frac{e_s,e_{s'}}{4pi,epsilon_0}right)^2,2pi,ln{mitLambda}_c.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img784.png"
 ALT="$\displaystyle \gamma_{ss'} = \left(\frac{e_s e_{s'}}{4\pi \epsilon_0}\right)^2 2\pi \ln{\mit\Lambda}_c.$">|; 

$key = q/displaystylegammaequiv-{rmi},omegasimeqk,(V-v_e).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2671.png"
 ALT="$\displaystyle \gamma\equiv -{\rm i} \omega \simeq k (V-v_e).
$">|; 

$key = q/displaystyleh(omega)=h_0+deltaleft(frac{omega}{{mitPi}_0}right)^p,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.52ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2208.png"
 ALT="$\displaystyle h(\omega)= h_0 + \delta\left(\frac{\omega}{{\mit\Pi}_0}\right)^p,
$">|; 

$key = q/displaystyleh(omega)=int_0^{z_0(omega)}frac{omega}{left[omega^2-{mitPi}_e^{2}(z)right]^{1slash2}},dz,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.97ex; vertical-align: -2.59ex; " SRC="|."$dir".q|img2203.png"
 ALT="$\displaystyle h(\omega) = \int_0^{z_0(\omega)}\frac{\omega}{\left[\omega^2- {\mit\Pi}_e^{2}(z)\right]^{1/2}} dz,
$">|; 

$key = q/displaystyleh=r^2,skew{3}dot{theta}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img690.png"
 ALT="$\displaystyle h = r^2 \skew{3}\dot{\theta}.$">|; 

$key = q/displaystylehat{B}_ast=2,hat{mitPsi}^{1slash2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.35ex; " SRC="|."$dir".q|img3659.png"
 ALT="$\displaystyle \hat{B}_\ast = 2 \hat{\mit\Psi}^{1/2}.$">|; 

$key = q/displaystylehat{B}_ast=frac{B_{0,y}(Wslash2)}{B_0},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img3656.png"
 ALT="$\displaystyle \hat{B}_\ast = \frac{B_{0 y}(W/2)}{B_0},$">|; 

$key = q/displaystylehat{J}(hat{x},xi)=sum_{m=1,infty}J_m(hat{x}),cos(m,xi),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img3539.png"
 ALT="$\displaystyle \hat{J}(\hat{x},\xi) = \sum_{m=1,\infty}J_m(\hat{x}) \cos(m \xi),$">|; 

$key = q/displaystylehat{J}({mitOmega})=frac{dskew{3}hat{mitPsi}}{dhat{t}},frac{langlecosxirangle}{langle1rangle}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -1.98ex; " SRC="|."$dir".q|img3518.png"
 ALT="$\displaystyle \hat{J}({\mit\Omega}) = \frac{d\skew{3}\hat{\mit\Psi}}{d\hat{t}} \frac{\langle\cos\xi\rangle}{\langle 1\rangle}.$">|; 

$key = q/displaystylehat{J}=hat{J}(hat{psi}).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3505.png"
 ALT="$\displaystyle \hat{J} = \hat{J}(\hat{\psi}).$">|; 

$key = q/displaystylehat{U};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3487.png"
 ALT="$\displaystyle \hat{U}$">|; 

$key = q/displaystylehat{W}=4,skew{3}hat{mitPsi}^{1slash2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3460.png"
 ALT="$\displaystyle \hat{W} = 4 \skew{3}\hat{\mit\Psi}^{1/2}.$">|; 

$key = q/displaystylehat{W}_s=frac{pi}{2},frac{1-hat{k}^2}{hat{k},(2-hat{k}^2)}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.74ex; vertical-align: -2.34ex; " SRC="|."$dir".q|img3606.png"
 ALT="$\displaystyle \hat{W}_s = \frac{\pi}{2} \frac{1-\hat{k}^2}{\hat{k} (2-\hat{k}^2)}.$">|; 

$key = q/displaystylehat{W}_ssimeqfrac{{mitDelta}'(0)}{alpha}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img3605.png"
 ALT="$\displaystyle \hat{W}_s \simeq \frac{{\mit\Delta}'(0)}{\alpha}.$">|; 

$key = q/displaystylehat{bfr};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img1331.png"
 ALT="$\displaystyle \hat{\bf r}$">|; 

$key = q/displaystylehat{delta},frac{dskew{3}hat{mitPsi}}{dhat{t}}={mitDelta}',skew{3}hat{mitPsi},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.19ex; vertical-align: -1.71ex; " SRC="|."$dir".q|img3611.png"
 ALT="$\displaystyle \hat{\delta} \frac{d\skew{3}\hat{\mit\Psi}}{d\hat{t}} = {\mit\Delta}'  \skew{3}\hat{\mit\Psi},$">|; 

$key = q/displaystylehat{delta}=left[frac{2pi,Gamma(3slash4)}{Gamma(1slash4)}right]^{4slash5}{mitDelta}'^{1slash5},S^{-2slash5};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.91ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3612.png"
 ALT="$\displaystyle \hat{\delta}=\left[\frac{2\pi \Gamma(3/4)}{\Gamma(1/4)}\right]^{4/5}{\mit\Delta}'^{1/5} S^{-2/5}$">|; 

$key = q/displaystylehat{delta}_ast;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.35ex; " SRC="|."$dir".q|img3650.png"
 ALT="$\displaystyle \hat{\delta}_\ast$">|; 

$key = q/displaystylehat{delta}_astsimfrac{pi}{hat{k}},frac{hat{v}_0}{hat{v}_ast}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.96ex; " SRC="|."$dir".q|img3649.png"
 ALT="$\displaystyle \hat{\delta}_\ast \sim\frac{\pi}{\hat{k}} \frac{\hat{v}_0}{\hat{v}_\ast}.$">|; 

$key = q/displaystylehat{delta}_psimhat{delta}_{rmSP}^{3slash4},{calS}^{-1slash4}simepsilon^{-3slash4},{calS}^{-5slash8}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.79ex; vertical-align: -0.82ex; " SRC="|."$dir".q|img3720.png"
 ALT="$\displaystyle \hat{\delta}_p \sim \hat{\delta}_{\rm SP}^{3/4} {\cal S}^{-1/4}\sim \epsilon^{-3/4} {\cal S}^{-5/8}.$">|; 

$key = q/displaystylehat{delta}_{rmSP}simepsilon^{-1},{calS}^{-1slash2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3708.png"
 ALT="$\displaystyle \hat{\delta}_{\rm SP} \sim \epsilon^{-1} {\cal S}^{-1/2},$">|; 

$key = q/displaystylehat{delta}gghat{W}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3472.png"
 ALT="$\displaystyle \hat{\delta}\gg \hat{W}.$">|; 

$key = q/displaystylehat{delta}llhat{W}ll1,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img3474.png"
 ALT="$\displaystyle \hat{\delta} \ll \hat{W}\ll 1,$">|; 

$key = q/displaystylehat{gamma}=left[frac{Gamma(1slash4)}{2pi,Gamma(3slash4)}right]^{4slash5}{mitDelta}'^{,4slash5},S^{-3slash5},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.91ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3411.png"
 ALT="$\displaystyle \hat{\gamma} = \left[\frac{\Gamma(1/4)}{2\pi \Gamma(3/4)}\right]^{4/5}
{\mit\Delta}'^{ 4/5} S^{-3/5},$">|; 

$key = q/displaystylehat{gamma}^2left(frac{d^2}{dhat{x}^2}-hat{k}^2right)skew{3}hat{phi};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3740.png"
 ALT="$\displaystyle \hat{\gamma}^2\left(\frac{d^2}{d\hat{x}^2}-\hat{k}^2\right)\skew{3}\hat{\phi}$">|; 

$key = q/displaystylehat{gamma}^{,2}left(frac{d^2}{dhat{x}^2}-hat{k}^2right)skew{3}hat{phi};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3317.png"
 ALT="$\displaystyle \hat{\gamma}^{ 2}\left(\frac{d^2}{d\hat{x}^2}-\hat{k}^2\right)\skew{3}\hat{\phi}$">|; 

$key = q/displaystylehat{gamma}^{2},frac{d^2skew{3}hat{phi}}{dhat{x}^{2}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3339.png"
 ALT="$\displaystyle \hat{\gamma}^{2} \frac{d^2\skew{3}\hat{\phi}}{d\hat{x}^{2}}$">|; 

$key = q/displaystylehat{gamma}ll1llS,hat{gamma}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3326.png"
 ALT="$\displaystyle \hat{\gamma} \ll 1 \ll S \hat{\gamma}.$">|; 

$key = q/displaystylehat{gamma}llS^{-1slash3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3426.png"
 ALT="$\displaystyle \hat{\gamma} \ll S^{-1/3}$">|; 

$key = q/displaystylehat{k}_c,(1+tanhhat{k}_c)=1.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3734.png"
 ALT="$\displaystyle \hat{k}_c (1+\tanh\hat{k}_c )= 1.
$">|; 

$key = q/displaystylehat{mitPsi}(t)=left(frac{t}{tau_{rmSP}}right)^{4},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3661.png"
 ALT="$\displaystyle \hat{\mit\Psi}(t) = \left(\frac{t}{\tau_{\rm SP}}\right)^{4},$">|; 

$key = q/displaystylehat{n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img1327.png"
 ALT="$\displaystyle \hat{n}$">|; 

$key = q/displaystylehat{psi}(hatx,xi,hat{t})=frac{hat{x}^2}{2}+skew{3}hat{mitPsi}(hat{t}),cosxi,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3503.png"
 ALT="$\displaystyle \hat{\psi}(\hat x,\xi,\hat{t})=\frac{\hat{x}^2}{2}+\skew{3}\hat{\mit\Psi}(\hat{t}) \cos\xi,$">|; 

$key = q/displaystylehat{psi}(hatx,xi,hat{t})=frac{hat{x}^2}{2}+skew{3}hat{mitPsi}(hat{t}),cosxi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3458.png"
 ALT="$\displaystyle \hat{\psi}(\hat x,\xi,\hat{t})=\frac{\hat{x}^2}{2}+\skew{3}\hat{\mit\Psi}(\hat{t}) \cos\xi$">|; 

$key = q/displaystylehat{psi}(hat{x});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3358.png"
 ALT="$\displaystyle \hat{\psi}(\hat{x})$">|; 

$key = q/displaystylehat{psi}(hat{x})={mitPsi},{rme}^{-hat{k},|hat{x}|}left(1+hat{k}^{-1},tanh|hat{x}|right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.35ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img3356.png"
 ALT="$\displaystyle \hat{\psi}(\hat{x}) = {\mit\Psi} {\rm e}^{-\hat{k} \vert\hat{x}\vert}\left(1+\hat{k}^{-1} \tanh \vert\hat{x}\vert\right),$">|; 

$key = q/displaystylehat{psi}(hat{x},xi,hat{t})=frac{hat{x}^2}{2}+sum_{m=1,infty}skew{3}hat{mitPsi}_m(hat{t}),cos(m,xi),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.08ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img3543.png"
 ALT="$\displaystyle \hat{\psi}(\hat{x},\xi,\hat{t})=\frac{\hat{x}^2}{2}+\sum_{m=1,\infty}\skew{3}\hat{\mit\Psi}_m(\hat{t}) \cos(m \xi),$">|; 

$key = q/displaystylehat{p}_e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1345.png"
 ALT="$\displaystyle \hat{p}_e$">|; 

$key = q/displaystylehat{p}_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1397.png"
 ALT="$\displaystyle \hat{p}_i$">|; 

$key = q/displaystylehat{t};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img1335.png"
 ALT="$\displaystyle \hat{t}$">|; 

$key = q/displaystylehat{v}_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3652.png"
 ALT="$\displaystyle \hat{v}_0$">|; 

$key = q/displaystylehat{v}_0simfrac{1}{hat{delta}_ast}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.15ex; " SRC="|."$dir".q|img3642.png"
 ALT="$\displaystyle \hat{v}_0 \sim \frac{1}{\hat{\delta}_\ast}.$">|; 

$key = q/displaystylehat{v}_ast;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.35ex; " SRC="|."$dir".q|img3753.png"
 ALT="$\displaystyle \hat{v}_\ast$">|; 

$key = q/displaystylehat{v}_astsimfrac{hat{B}_ast,S}{hat{k}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.35ex; vertical-align: -1.96ex; " SRC="|."$dir".q|img3643.png"
 ALT="$\displaystyle \hat{v}_\ast\sim \frac{\hat{B}_\ast S}{\hat{k}},$">|; 

$key = q/displaystylehat{v}_e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1329.png"
 ALT="$\displaystyle \hat{v}_e$">|; 

$key = q/displaystylehat{v}_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1390.png"
 ALT="$\displaystyle \hat{v}_i$">|; 

$key = q/displaystylehat{z}=(k_0^{2},a)^{1slash3},z.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.57ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img1953.png"
 ALT="$\displaystyle \hat{z} = (k_0^{2} a)^{1/3} z.$">|; 

$key = q/displaystylehat{z}=(k_0^{2},b),z,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.57ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img1972.png"
 ALT="$\displaystyle \hat{z} = (k_0^{2} b) z,$">|; 

$key = q/displaystyleint!{calF}_s({bfr},{bfv},t),d^3{bfv}=n_s({bfr},t),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img579.png"
 ALT="$\displaystyle \int \!{\cal F}_s({\bf r}, {\bf v}, t) d^3
{\bf v} = n_s({\bf r}, t),$">|; 

$key = q/displaystyleintC_{s's},d^3{bfv}_{s'}=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img657.png"
 ALT="$\displaystyle \int C_{s's} d^3{\bf v}_{s'}=0.$">|; 

$key = q/displaystyleintC_{ss'},d^3{bfv}=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img1041.png"
 ALT="$\displaystyle \int C_{ss'}  d^3{\bf v} =0.$">|; 

$key = q/displaystyleintC_{ss'},d^3{bfv}_s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img652.png"
 ALT="$\displaystyle \int C_{ss'} d^3{\bf v}_s$">|; 

$key = q/displaystyleintC_{ss'},d^3{bfv}_s=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img655.png"
 ALT="$\displaystyle \int C_{ss'} d^3{\bf v}_s=0.$">|; 

$key = q/displaystyleintH(v),v_alpha,d^3{bfv};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img938.png"
 ALT="$\displaystyle \int H(v) v_\alpha d^3{\bf v}$">|; 

$key = q/displaystyleintH(v),v_alpha,v_beta,d^3{bfv};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img939.png"
 ALT="$\displaystyle \int H(v) v_\alpha v_\beta d^3{\bf v}$">|; 

$key = q/displaystyleintH(v),v_alpha,v_beta,v_gamma,d^3{bfv};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img941.png"
 ALT="$\displaystyle \int H(v) v_\alpha v_\beta v_\gamma d^3{\bf v}$">|; 

$key = q/displaystyleintK_{ss'},C_{ss'},d^3{bfv}_s=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img660.png"
 ALT="$\displaystyle \int K_{ss'} C_{ss'} d^3{\bf v}_s = 0.$">|; 

$key = q/displaystyleint_0^inftycosleft(pi,t^{2}slash2right),dt=int_0^inftysinleft(pi,t^{2}slash2right),dt=frac{1}{2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.13ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img2077.png"
 ALT="$\displaystyle \int_0^\infty\cos\left(\pi  t^{2}/2\right) dt = \int_0^\infty\sin\left(\pi  t^{2}/2\right) dt
=\frac{1}{2}.$">|; 

$key = q/displaystyleint_0^inftyx,J_n^{2}(s,x),{rme}^{-x^2},dx;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.13ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img2409.png"
 ALT="$\displaystyle \int_0^\infty x J_n^{2}(s x) {\rm e}^{-x^2} dx$">|; 

$key = q/displaystyleint_0^inftyx^3left[J_n'(s,x)right]^2{rme}^{-x^2},dx;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.13ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img2411.png"
 ALT="$\displaystyle \int_0^\infty x^3\left[J_n'(s x)\right]^2{\rm e}^{-x^2} dx$">|; 

$key = q/displaystyleint_0^infty{rme}^{-xi,zeta^{2}},zeta,F_1(zeta),dzeta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.13ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img946.png"
 ALT="$\displaystyle \int_0^\infty {\rm e}^{-\xi \zeta^{2}} \zeta F_1(\zeta) d\zeta$">|; 

$key = q/displaystyleint_0^infty{rme}^{-xi,zeta^{2}},zeta,{rmerf}(zeta),dzeta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.13ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img948.png"
 ALT="$\displaystyle \int_0^\infty {\rm e}^{-\xi \zeta^{2}} \zeta {\rm erf}(\zeta) d\zeta$">|; 

$key = q/displaystyleint_{-infty}^0{rme}^{-t^{2}},dt=frac{pi^{1slash2}}{2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.35ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img2329.png"
 ALT="$\displaystyle \int_{-\infty}^0 {\rm e}^{-t^{2}} dt = \frac{\pi^{1/2}}{2},$">|; 

$key = q/displaystyleint_{-infty}^inftyfrac{F_0'(u)}{u-U_0},du>0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.19ex; vertical-align: -2.05ex; " SRC="|."$dir".q|img2538.png"
 ALT="$\displaystyle \int_{-\infty}^\infty \frac{F_0'(u)}{u-U_0} du&gt;0.$">|; 

$key = q/displaystyleint_{-infty}^inftyfrac{F_0(u)-F_0(U_0)}{(u-U_0)^{2}},du=n_eleft[frac{V^{2}-v_e^{2}}{(V^{2}+v_e^{2})^{2}}right].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.52ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2553.png"
 ALT="$\displaystyle \int_{-\infty}^\infty \frac{F_0(u)-F_0(U_0)}{(u-U_0)^{2}} du = n_e\left[\frac{V^{2}- v_e^{2}}{(V^{2}+ v_e^{2})^{2}}\right].$">|; 

$key = q/displaystyleint_{-infty}^inftyfrac{F_0(u)-F_0(U_0)}{(u-U_0)^{2}},du>0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.05ex; " SRC="|."$dir".q|img2539.png"
 ALT="$\displaystyle \int_{-\infty}^\infty \frac{F_0(u)-F_0(U_0)}{(u-U_0)^{2}} du &gt; 0.$">|; 

$key = q/displaystyleint_{-infty}^inftyfrac{G(u)}{u-{rmi},pslashk},du.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.13ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img2270.png"
 ALT="$\displaystyle \int_{-\infty}^\infty \frac{G(u)}{u-{\rm i} p/k} du.$">|; 

$key = q/displaystyleintfrac{1}{2},m_s,v_s^{2},C_{ss'},d^3{bfv}_s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img1003.png"
 ALT="$\displaystyle \int\frac{1}{2} m_s v_s^{2} C_{ss'} d^3{\bf v}_s$">|; 

$key = q/displaystyleintfrac{1}{2},m_s,v_s^{2},C_{ss'},d^3{bfv}_s=-intfrac{1}{2},m_{s'},v_{s'}^{2},C_{s's},d^3{bfv}_{s'}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img662.png"
 ALT="$\displaystyle \int \frac{1}{2} m_s v_s^{2} C_{ss'} d^3{\bf v}_s = - \int\frac{1}{2} m_{s'} v_{s'}^{2} C_{s's} d^3{\bf v}_{s'}.$">|; 

$key = q/displaystyleintfrac{2,d{mitOmega}}{sin^2(chislash2)}=16pi,ln{mitLambda}_c,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.35ex; vertical-align: -2.35ex; " SRC="|."$dir".q|img771.png"
 ALT="$\displaystyle \int \frac{2 d{\mit\Omega}}{\sin^2(\chi/2)}=16\pi \ln{\mit\Lambda}_c,$">|; 

$key = q/displaystyleintfrac{{bfg}_{ss'},d{mitOmega}}{sin^4(chislash2)};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.35ex; vertical-align: -2.35ex; " SRC="|."$dir".q|img763.png"
 ALT="$\displaystyle \int \frac{{\bf g}_{ss'} d{\mit\Omega}}{\sin^4(\chi/2)}$">|; 

$key = q/displaystyleintfrac{{bfg}_{ss'}{bfg}_{ss'},d{mitOmega}}{sin^4(chislash2)};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.35ex; vertical-align: -2.35ex; " SRC="|."$dir".q|img765.png"
 ALT="$\displaystyle \int \frac{{\bf g}_{ss'}{\bf g}_{ss'} d{\mit\Omega}}{\sin^4(\chi/2)}$">|; 

$key = q/displaystyleintm_s,{bfv},C_{ss'},d^3{bfv}=-intm_{s'},{bfv},C_{s's},d^3{bfv}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img1042.png"
 ALT="$\displaystyle \int m_s {\bf v} C_{ss'} d^3{\bf v} = - \int m_{s'} {\bf v} C_{s's} d^3{\bf v}.$">|; 

$key = q/displaystyleintm_s,{bfv}_s,C_{ss'},d^3{bfv}_s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img1001.png"
 ALT="$\displaystyle \int m_s {\bf v}_s C_{ss'} d^3{\bf v}_s$">|; 

$key = q/displaystyleintm_s,{bfv}_s,C_{ss'},d^3{bfv}_s=-intm_{s'},{bfv}_{s'},C_{s's},d^3{bfv}_{s'}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img659.png"
 ALT="$\displaystyle \int m_s {\bf v}_s C_{ss'} d^3{\bf v}_s = - \int m_{s'} {\bf v}_{s'} C_{s's} d^3{\bf v}_{s'}.$">|; 

$key = q/displaystylej_e=e,n_s,left(frac{T_e}{2pi,m_e}right)^{1slash2}expleft[frac{e,({mitPhi}_w-{mitPhi}_s)}{T_e}right].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1598.png"
 ALT="$\displaystyle j_e= e n_s \left(\frac{T_e}{2\pi m_e}\right)^{1/2} \exp\left[\frac{e ({\mit\Phi}_w-{\mit\Phi}_s)}{T_e}\right].$">|; 

$key = q/displaystylej_i=-e,n_i(0),V_i(0)=-e,n_s,V_s=-e,n_sleft(frac{T_e}{m_i}right)^{1slash2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1592.png"
 ALT="$\displaystyle j_i = -e n_i(0) V_i(0) = -e n_s V_s = - e n_s\left(\frac{T_e}{m_i}\right)^{1/2}.$">|; 

$key = q/displaystylej_parallel={rmi},omega,epsilon_0,frac{{{mitPi}}_e^{2}}{omega^2},E_parallel,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img1700.png"
 ALT="$\displaystyle j_\parallel = {\rm i} \omega \epsilon_0 \frac{{{\mit\Pi}}_e^{2}}{\omega^2} 
E_\parallel,$">|; 

$key = q/displaystylej_pm={rmi},omega,epsilon_0left(frac{{{mitPi}}_e^{2}}{omega^2pmomega,{{mitOmega}}_e+{{mitOmega}}_e,{{mitOmega}}_i}right)E_pm,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.52ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1712.png"
 ALT="$\displaystyle j_\pm = {\rm i} \omega \epsilon_0\left(\frac{{{\mit\Pi}}_e^{2}}...
...\pm \omega {{\mit\Omega}}_e
+ {{\mit\Omega}}_e {{\mit\Omega}}_i}\right)E_\pm,$">|; 

$key = q/displaystylek^2,{mitPhi}=sum_sfrac{e_s}{epsilon_0}intf_{1,s},d^3{bfv}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.58ex; vertical-align: -2.62ex; " SRC="|."$dir".q|img2500.png"
 ALT="$\displaystyle k^2 {\mit\Phi} =\sum_s \frac{e_s}{\epsilon_0}\int f_{1 s} d^3{\bf v}.$">|; 

$key = q/displaystylek^{2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img2509.png"
 ALT="$\displaystyle k^{2}$">|; 

$key = q/displaystylek^{2}=f(U),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2522.png"
 ALT="$\displaystyle k^{2} = f(U),$">|; 

$key = q/displaystylek^{2}=frac{e^2}{epsilon_0,m_e}int_{-infty}^inftyfrac{partialF_0slashpartialu}{u-omegaslashk},du,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -2.05ex; " SRC="|."$dir".q|img2521.png"
 ALT="$\displaystyle k^{2} = \frac{e^2}{\epsilon_0 m_e}\int_{-\infty}^\infty \frac{\partial F_0/\partial u}{u-\omega/k} du,$">|; 

$key = q/displaystylek_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1893.png"
 ALT="$\displaystyle k_i$">|; 

$key = q/displaystylek_p,asimhat{delta}_{SP}^{-5slash4},{calS}^{-1slash4}simepsilon^{5slash4},{calS}^{3slash8}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.84ex; vertical-align: -0.80ex; " SRC="|."$dir".q|img3714.png"
 ALT="$\displaystyle k_p a \sim \hat{\delta}_{SP}^{-5/4} {\cal S}^{-1/4}\sim \epsilon^{5/4} {\cal S}^{3/8}.$">|; 

$key = q/displaystylek_r;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img1891.png"
 ALT="$\displaystyle k_r$">|; 

$key = q/displaystylek_x=k_x(z=0)=frac{omega}{c},S,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img2150.png"
 ALT="$\displaystyle k_x= k_x(z=0) = \frac{\omega}{c} S,$">|; 

$key = q/displaystylek_z=pmfrac{omega}{c}sqrt{n^2-S^2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img2152.png"
 ALT="$\displaystyle k_z = \pm \frac{\omega}{c}\sqrt{n^2-S^2}.$">|; 

$key = q/displaystylek_{ss'}=frac{e_s,e_{s'}}{4pi,epsilon_0},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.41ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img668.png"
 ALT="$\displaystyle k_{ss'} = \frac{e_s e_{s'}}{4\pi \epsilon_0},$">|; 

$key = q/displaystylekappa;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1120.png"
 ALT="$\displaystyle \kappa$">|; 

$key = q/displaystylekappa=frac{5}{2},n,nu,l^{2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img1646.png"
 ALT="$\displaystyle \kappa = \frac{5}{2} n \nu l^{2}.
$">|; 

$key = q/displaystylekappa=frac{5}{4},n,nu,l^{2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img1648.png"
 ALT="$\displaystyle \kappa = \frac{5}{4} n \nu l^{2}.
$">|; 

$key = q/displaystylekappa=kappa_0,T^{5slash2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2761.png"
 ALT="$\displaystyle \kappa = \kappa_0 T^{5/2},$">|; 

$key = q/displaystylekappa_parallel^e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.94ex; " SRC="|."$dir".q|img1200.png"
 ALT="$\displaystyle \kappa_\parallel^e$">|; 

$key = q/displaystylekappa_parallel^i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.79ex; vertical-align: -0.94ex; " SRC="|."$dir".q|img1202.png"
 ALT="$\displaystyle \kappa_\parallel^i$">|; 

$key = q/displaystylekappa_perp^e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.64ex; " SRC="|."$dir".q|img1241.png"
 ALT="$\displaystyle \kappa_\perp^e$">|; 

$key = q/displaystylekappa_perp^i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.64ex; " SRC="|."$dir".q|img1243.png"
 ALT="$\displaystyle \kappa_\perp^i$">|; 

$key = q/displaystylekappa_times^e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.65ex; " SRC="|."$dir".q|img1245.png"
 ALT="$\displaystyle \kappa_\times^e$">|; 

$key = q/displaystylekappa_times^i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.65ex; " SRC="|."$dir".q|img1247.png"
 ALT="$\displaystyle \kappa_\times^i$">|; 

$key = q/displaystyleksimeqfrac{omega}{V_A}+{rmi},frac{omega^2}{2,V_A^{3}}left(frac{1}{mu_0,sigma}+frac{mu}{rho_0}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.63ex; vertical-align: -2.43ex; " SRC="|."$dir".q|img3209.png"
 ALT="$\displaystyle k\simeq \frac{\omega}{V_A} + {\rm i} \frac{\omega^2}{2 V_A^{3}}\left(\frac{1}{\mu_0 \sigma} + \frac{\mu}{\rho_0}\right).
$">|; 

$key = q/displaystylel=frac{1}{sqrt{2},pi,n,sigma^2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -2.30ex; " SRC="|."$dir".q|img1106.png"
 ALT="$\displaystyle l = \frac{1}{\sqrt{2} \pi n \sigma^2}.$">|; 

$key = q/displaystylelambda_D=left(frac{epsilon_0,T}{n,e^2}right)^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img56.png"
 ALT="$\displaystyle \lambda_D = \left(\frac{\epsilon_0 T}{n e^2}\right)^{1/2}$">|; 

$key = q/displaystylelambda_Dequivfrac{1}{{mitPi}}left(frac{T}{m}right)^{1slash2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img55.png"
 ALT="$\displaystyle \lambda_D \equiv \frac{1}{{\mit\Pi}}\left(\frac{T}{m}\right)^{1/2}.$">|; 

$key = q/displaystylelambda_esimlambda_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1423.png"
 ALT="$\displaystyle \lambda_e\sim \lambda_i$">|; 

$key = q/displaystylelambda_s=frac{(k_perp,rho_s)^2}{2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img2462.png"
 ALT="$\displaystyle \lambda_s = \frac{(k_\perp  \rho_s)^2}{2},$">|; 

$key = q/displaystylelambda_s=frac{k_perp^{2},v_s^{2}}{2,{mitOmega}_s^{2}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.52ex; vertical-align: -2.19ex; " SRC="|."$dir".q|img2418.png"
 ALT="$\displaystyle \lambda_s = \frac{k_\perp^{2} v_s^{2}}{2 {\mit\Omega}_s^{2}},$">|; 

$key = q/displaystylelambda_{rmmfp}equivfrac{v_t}{nu}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img123.png"
 ALT="$\displaystyle \lambda_{\rm mfp} \equiv \frac{v_t}{\nu}.$">|; 

$key = q/displaystylelambda_{rmmfp}llL,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.75ex; " SRC="|."$dir".q|img124.png"
 ALT="$\displaystyle \lambda_{\rm mfp} \ll L,$">|; 

$key = q/displaystylelambdabarequivfrac{h}{m,v_t},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.96ex; " SRC="|."$dir".q|img149.png"
 ALT="$\displaystyle \lambdabar \equiv \frac{h}{m v_t},$">|; 

$key = q/displaystylelambdasim1,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img1443.png"
 ALT="$\displaystyle \lambda \sim 1,$">|; 

$key = q/displaystylelambdasimdelta,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img1453.png"
 ALT="$\displaystyle \lambda\sim \delta,$">|; 

$key = q/displaystylelambdasimdelta^{-1}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img1433.png"
 ALT="$\displaystyle \lambda \sim \delta^{-1}.$">|; 

$key = q/displaystylelangle(;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img320.png"
 ALT="$\displaystyle \langle ($">|; 

$key = q/displaystylelangle1rangle;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img3564.png"
 ALT="$\displaystyle \langle 1\rangle$">|; 

$key = q/displaystylelangle;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img250.png"
 ALT="$\displaystyle \langle$">|; 

$key = q/displaystylelanglecos(m,xi)rangle=;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3568.png"
 ALT="$\displaystyle \langle \cos(m \xi)\rangle=$">|; 

$key = q/displaystylelanglecosxirangle=;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3566.png"
 ALT="$\displaystyle \langle\cos\xi\rangle =$">|; 

$key = q/displaystylelangletau_drangle=frac{2pi,L,R_E}{langlev_drangle}simeqfrac{pi,e,B_E,R_E^{2}}{3,{calE},L},(0.35+0.15,sinalpha_{rmeq})^{-1}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -1.98ex; " SRC="|."$dir".q|img484.png"
 ALT="$\displaystyle \langle \tau_d\rangle = \frac{2\pi L R_E}{\langle v_d\rangle}
\...
...i e B_E R_E^{2}}{3 {\cal E} L}  
(0.35 + 0.15 \sin\alpha_{\rm eq})^{-1}.$">|; 

$key = q/displaystylelangletau_drangle_p=langletau_drangle_esimeqfrac{1.05}{{calE}({rmMeV}),L},(1+0.43,sinalpha_{rmeq})^{-1},,,{rmhours}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img485.png"
 ALT="$\displaystyle \langle \tau_d\rangle_p=\langle \tau_d\rangle_e \simeq \frac{1.05}{{\cal E}({\rm MeV}) L}  (1+0.43 \sin\alpha_{\rm eq})^{-1}   {\rm hours}.$">|; 

$key = q/displaystylelanglev_dranglesimeqfrac{6,{calE},L^2}{e,B_E,R_E},(0.35+0.15,sinalpha_{rmeq}).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.13ex; vertical-align: -1.95ex; " SRC="|."$dir".q|img483.png"
 ALT="$\displaystyle \langle v_d\rangle \simeq \frac{6 {\cal E} L^2}{e B_E R_E}
 (0.35 + 0.15 \sin\alpha_{\rm eq}).$">|; 

$key = q/displaystylelanglev_xrangle=+0.223left(frac{{mitOmega}_0}{a}right)y_0^{2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img567.png"
 ALT="$\displaystyle \langle v_x\rangle =+ 0.223\left(\frac{{\mit\Omega}_0}{a}\right)y_0^{2}.
$">|; 

$key = q/displaystylelanglev_xrangle=-left(frac{{mitOmega}_0}{4,a}right)(y_+^{2}+y_-^{2}),(1-alpha),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img559.png"
 ALT="$\displaystyle \langle v_x\rangle = - \left(\frac{{\mit\Omega}_0}{4 a}\right)(y_+^{2}+y_-^{2}) (1-\alpha),
$">|; 

$key = q/displaystylelanglev_{d}rangle=frac{2,{calE}}{e,B_{rmeq},r_{rmeq}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.30ex; vertical-align: -2.27ex; " SRC="|."$dir".q|img535.png"
 ALT="$\displaystyle \langle v_{d}\rangle = \frac{2 {\cal E}}{e B_{\rm eq} r_{\rm eq}}.
$">|; 

$key = q/displaystylelangle{calF}_srangleequivf_s,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img583.png"
 ALT="$\displaystyle \langle {\cal F}_s\rangle\equiv f_s,$">|; 

$key = q/displaystyleleft(!{array}{ccc}P-n^2,&0,&00,&P-n^2,&00,&0,&P{array}!right)left(!{array}{c}E_xE_yE_z{array}!right)={bf0},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 7.70ex; vertical-align: -3.25ex; " SRC="|."$dir".q|img1781.png"
 ALT="$\displaystyle \left(\!\begin{array}{ccc}
P-n^2, &amp; 0, &amp; 0\\\\
0, &amp; P-n^2, &amp; 0 \ ...
...! \right)\left(\!\begin{array}{c} E_x\ E_y\ E_z\end{array}\!\right) = {\bf0},$">|; 

$key = q/displaystyleleft(!{array}{c}a_1a_2a_3{array}!right)={bfU}left(!{array}{c}a_+a_-a_3{array}!right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 7.58ex; vertical-align: -3.25ex; " SRC="|."$dir".q|img1732.png"
 ALT="$\displaystyle \left(\!\begin{array}{c} a_1 \ a_2 \ a_3 \end{array}\! \right) =
{\bf U} \left(\!\begin{array}{c} a_+ \ a_- \ a_3 \end{array}\! \right),$">|; 

$key = q/displaystyleleft(frac{1}{lambda_D}right)^2=frac{1}{2}left[left(frac{1}{lambda_{D,e}}right)^2+left(frac{1}{lambda_{D,i}}right)^2right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.26ex; " SRC="|."$dir".q|img167.png"
 ALT="$\displaystyle \left(\frac{1}{\lambda_D}\right)^2 = \frac{1}{2}\left[\left(\frac{1}{\lambda_{D e}}\right)^2+ \left(\frac{1}{\lambda_{D i}}\right)^2\right],
$">|; 

$key = q/displaystyleleft(frac{dphi}{dz}right)^2=k_0^{2},n^2+{rmi},frac{d^2phi}{dz^{2}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1927.png"
 ALT="$\displaystyle \left(\frac{d\phi}{dz}\right)^2 = k_0^{2}  n^2 +{\rm i} \frac{d^2\phi}
{dz^{2}}.$">|; 

$key = q/displaystyleleft(frac{partialphi}{partialomega}right)_{omega=omega_0}=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.69ex; vertical-align: -2.52ex; " SRC="|."$dir".q|img2079.png"
 ALT="$\displaystyle \left(\frac{\partial\phi}{\partial\omega}\right)_{\omega=\omega_0} = 0,$">|; 

$key = q/displaystyleleft(frac{partial{mitPsi}}{partialt}right)_1=-int_{bfS}nablatimes{bfE}cdotd{bfS}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.28ex; " SRC="|."$dir".q|img2693.png"
 ALT="$\displaystyle \left(\frac{\partial{\mit\Psi}}{\partial t}\right)_1 = -
\int_{\bf S} \nabla \times{\bf E} \cdot d{\bf S}.$">|; 

$key = q/displaystyleleft(frac{partial{mitPsi}}{partialt}right)_1=int_{bfS}frac{partial{bfB}}{partialt}cdotd{bfS}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.28ex; " SRC="|."$dir".q|img2692.png"
 ALT="$\displaystyle \left(\frac{\partial{\mit\Psi}}{\partial t}\right)_1 =
\int_{\bf S} \frac{\partial{\bf B}}{\partial t}\cdot d{\bf S}.$">|; 

$key = q/displaystyleleft(frac{partial{mitPsi}}{partialt}right)_2=int_C{bfB}cdot{bfV}timesd{bfr}=int_C{bfB}times{bfV}cdotd{bfr}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.28ex; " SRC="|."$dir".q|img2697.png"
 ALT="$\displaystyle \left(\frac{\partial{\mit\Psi}}{\partial t}\right)_2 = \int_C {\bf B} \cdot{\bf V}\times d{\bf r} = \int_C {\bf B}\times{\bf V} \cdot d{\bf r}.$">|; 

$key = q/displaystyleleft(frac{partial{mitPsi}}{partialt}right)_2=int_{bfS}nablatimes({bfB}times{bfV})cdotd{bfS}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.28ex; " SRC="|."$dir".q|img2698.png"
 ALT="$\displaystyle \left(\frac{\partial{\mit\Psi}}{\partial t}\right)_2= \int_{\bf S} \nabla\times
({\bf B}\times
{\bf V})\cdot d{\bf S}.$">|; 

$key = q/displaystyleleft(frac{partial}{partial{bfu}_{ss'}}cdot{bfw}_{ss'}right)_alpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.52ex; vertical-align: -2.30ex; " SRC="|."$dir".q|img775.png"
 ALT="$\displaystyle \left(\frac{\partial}{\partial {\bf u}_{ss'}}\cdot{\bf w}_{ss'}\right)_\alpha$">|; 

$key = q/displaystyleleft(frac{u^2}{u_c^{2}}-1right)-lnleft(frac{u}{u_c}right)^2=4,lnleft(frac{r}{r_c}right)+4left(frac{r_c}{r}-1right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2806.png"
 ALT="$\displaystyle \left(\frac{u^2}{u_c^{2}}-1\right)-\ln\left(\frac{u}{u_c}\right)^2
= 4 \ln\left(\frac{r}{r_c}\right) + 4\left(\frac{r_c}{r}-1\right),$">|; 

$key = q/displaystyleleft(frac{u}{u_c}right)^2-lnleft(frac{u}{u_c}right)^2=4,lnleft(frac{r}{r_c}right)+4,frac{r_c}{r}+C,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2796.png"
 ALT="$\displaystyle \left(\frac{u}{u_c}\right)^2 -\ln\left(\frac{u}{u_c}\right)^2 = 4 \ln\left(\frac{r}{r_c}\right)
+ 4 \frac{r_c}{r} + C,$">|; 

$key = q/displaystyleleft(frac{u}{u_c}right)^2simeq4,lnleft(frac{r}{r_c}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2802.png"
 ALT="$\displaystyle \left(\frac{u}{u_c}\right)^2 \simeq 4 \ln \left(\frac{r}{r_c}\right),$">|; 

$key = q/displaystyleleft(hat{delta}+frac{I_1,hat{W}}{2}right)frac{dskew{3}hat{mitPsi}}{dhat{t}}={mitDelta}',skew{3}hat{mitPsi};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.69ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3617.png"
 ALT="$\displaystyle \left(\hat{\delta} + \frac{I_1 \hat{W}}{2}\right)\frac{d\skew{3}\hat{\mit\Psi}}{d\hat{t}} = {\mit\Delta}'  \skew{3}\hat{\mit\Psi}$">|; 

$key = q/displaystyleleft(nabla^2-frac{2}{lambda_D^{2}}right)delta{mitPhi}=-frac{deltarho_{rmext}}{epsilon_0}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.58ex; vertical-align: -2.41ex; " SRC="|."$dir".q|img67.png"
 ALT="$\displaystyle \left(\nabla^2 - \frac{2}{\lambda_D^{2}}\right) \delta {\mit\Phi}
= - \frac{\delta\rho_{\rm ext}}{\epsilon_0}.$">|; 

$key = q/displaystyleleft(nabla^2-frac{2}{lambda_D^{2}}right)delta{mitPhi}=-frac{q,delta({bfr})}{epsilon_0}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.58ex; vertical-align: -2.41ex; " SRC="|."$dir".q|img171.png"
 ALT="$\displaystyle \left(\nabla^2-\frac{2}{\lambda_D^{2}}\right)\delta{\mit\Phi} = - \frac{q \delta({\bf r})}{\epsilon_0}.
$">|; 

$key = q/displaystyleleft[frac{1}{2},rho,V^{2},V_x+frac{mitGamma}{{mitGamma}-1},p,V_x+frac{B_y,(V_x,B_y-V_y,B_x)}{mu_0}right]^2_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.28ex; " SRC="|."$dir".q|img3078.png"
 ALT="$\displaystyle \left[\frac{1}{2} \rho V^{2} V_x + \frac{\mit\Gamma}{{\mit\Gamma}-1} p V_x
+ \frac{B_y (V_x B_y-V_y B_x)}{\mu_0}\right]^2_1$">|; 

$key = q/displaystyleleft[frac{dB_pm}{dy}right]_{y=1_-}^{y=1_+}=pm{rmi},{mitOmega},tau_Rleft(frac{B_++B_-}{2}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.25ex; vertical-align: -2.59ex; " SRC="|."$dir".q|img3016.png"
 ALT="$\displaystyle \left[\frac{d B_\pm}{dy}\right]_{y=1_-}^{y=1_+} =\pm{\rm i} {\mit\Omega} \tau_R\left(
\frac{B_+ +B_-}{2}\right).$">|; 

$key = q/displaystyleleft[frac{partialf_s({bfr},{bfv}_s,t)}{partialt}right]_{s's}d^3{bfr},d^3{bfv}_s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.58ex; vertical-align: -2.31ex; " SRC="|."$dir".q|img625.png"
 ALT="$\displaystyle \left[\frac{\partial f_s({\bf r},{\bf v}_s,t)}{\partial t}\right]_{s's} d^3{\bf r} d^3{\bf v}_s$">|; 

$key = q/displaystyleleft[omega^2-frac{({bfk}cdot{bfB}_0)^2}{mu_0,rho_0}right]{bfV}=;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2719.png"
 ALT="$\displaystyle \left[ \omega^2 - \frac{({\bf k}\cdot{\bf B}_0)^2}{\mu_0 \rho_0}
\right] {\bf V} =$">|; 

$key = q/displaystyleleftlangle{bfa}_scdotfrac{partial{calF}_s}{partial{bfv}}rightrangle=langle{bfa}_sranglecdotfrac{partialf_s}{partial{bfv}}-C_s(f),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img585.png"
 ALT="$\displaystyle \left\langle{\bf a}_s\cdot\frac{\partial {\cal F}_s}{\partial{\bf...
...le
= \langle{\bf a}_s\rangle \cdot\frac{\partial f_s}{\partial {\bf v}}-C_s(f),$">|; 

$key = q/displaystyleleftlangle{bfa}_scdotfrac{partial{calF}_s}{partial{bfv}}rightrangleneqlangle{bfa}_sranglecdotfrac{partialf_s}{partial{bfv}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img584.png"
 ALT="$\displaystyle \left\langle{\bf a}_s\cdot\frac{\partial {\cal F}_s}{\partial {\b...
...t\rangle
\neq \langle{\bf a}_s\rangle\cdot\frac{\partial f_s}{\partial{\bf v}}.$">|; 

$key = q/displaystylelim_{etarightarrow0}gammaproptoeta^{alpha},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.29ex; vertical-align: -1.80ex; " SRC="|."$dir".q|img2926.png"
 ALT="$\displaystyle \lim_{\eta\rightarrow 0}\gamma \propto \eta^{\alpha},$">|; 

$key = q/displaystylellB,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img270.png"
 ALT="$\displaystyle \ll B,$">|; 

$key = q/displaystylellB.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img272.png"
 ALT="$\displaystyle \ll B.$">|; 

$key = q/displaystylelnf_s+lnf_{s'}-lnf_s'-lnf_{s'}';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img867.png"
 ALT="$\displaystyle \ln f_s + \ln f_{s'} - \ln f_s' - \ln f_{s'}'$">|; 

$key = q/displaystylelnf_s+lnf_{s'}-lnf_s'-lnf_{s'}'=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img863.png"
 ALT="$\displaystyle \ln f_s+ \ln f_{s'} - \ln f_s' - \ln f_{s'}'=0.$">|; 

$key = q/displaystylelnf_s=a_s+m_s,{bfb}cdot{bfv}_s+c,m_s,v_s^{2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.51ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img864.png"
 ALT="$\displaystyle \ln f_s = a_s + m_s {\bf b}\cdot{\bf v}_s+ c m_s v_s^{2},$">|; 

$key = q/displaystylelnleft(frac{I}{I_s}+1right)=C+frac{e,V}{T_e},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1622.png"
 ALT="$\displaystyle \ln\left(\frac{I}{I_s}+1\right) = C + \frac{e V}{T_e},$">|; 

$key = q/displaystylelnleft(frac{u}{u_c}right)simeq-2,lnleft(frac{r}{r_c}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2798.png"
 ALT="$\displaystyle \ln\left(\frac{u}{u_c}\right) \simeq -2 \ln\left(\frac{r}{r_c}\right),$">|; 

$key = q/displaystyleln{mitLambda}_c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img841.png"
 ALT="$\displaystyle \ln{\mit\Lambda}_c$">|; 

$key = q/displaystyleln{mitLambda}_c=23-lnleft(n_e^{1slash2},T_i^{-3slash2}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.23ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img846.png"
 ALT="$\displaystyle \ln{\mit\Lambda}_c = 23 - \ln\left(n_e^{1/2} T_i^{-3/2}\right).$">|; 

$key = q/displaystyleln{mitLambda}_c=23.5-lnleft(n_e^{1slash2},T_e^{-5slash4}right)-left[10^{-5}+(lnT_e-2)^2slash16right]^{1slash2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.68ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img840.png"
 ALT="$\displaystyle \ln{\mit\Lambda}_c = 23.5 - \ln\left(n_e^{1/2} T_e^{-5/4}\right)-\left[10^{-5} + (\ln T_e-2)^2/16\right]^{1/2}.$">|; 

$key = q/displaystyleln{mitLambda}_c=intfrac{dchi}{chi},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img820.png"
 ALT="$\displaystyle \ln {\mit\Lambda}_c =\int\frac{d\chi}{\chi},$">|; 

$key = q/displaystyleln{mitLambda}_c=lnleft(frac{b_{rmmax}}{b_{rmmin}}right)=lnleft(frac{lambda_D}{r_c}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img826.png"
 ALT="$\displaystyle \ln{\mit\Lambda}_c = \ln\left(\frac{b_{\rm max}}{b_{\rm min}}\right) = \ln\left(\frac{\lambda_D}{r_c}\right).$">|; 

$key = q/displaystyleln{mitLambda}_c=lnleft(frac{chi_{rmmax}}{chi_{rmmin}}right)=lnleft(frac{b_{rmmax}}{b_{rmmin}}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img772.png"
 ALT="$\displaystyle \ln {\mit\Lambda}_c = \ln\left(\frac{\chi_{\rm max}}{\chi_{\rm min}}\right)=\ln\left(\frac{b_{\rm max}}{b_{\rm min}}\right)$">|; 

$key = q/displaystyleln{mitLambda}_csimeqln{mitLambda}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img827.png"
 ALT="$\displaystyle \ln{\mit\Lambda}_c\simeq \ln {\mit\Lambda}.$">|; 

$key = q/displaystylem,frac{dU_{0,parallel}}{dt}=e,E_parallel-;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.74ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img344.png"
 ALT="$\displaystyle m \frac{dU_{0 \parallel}}{dt} = e E_\parallel -$">|; 

$key = q/displaystylem,frac{d^2deltax}{dt^2}=e,E_x=-m,{mitPi}^{2},deltax,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img48.png"
 ALT="$\displaystyle m \frac{d^2 \delta x}{dt^2} = e E_x = -m {\mit\Pi}^{2} \delta x,$">|; 

$key = q/displaystylem,frac{d{bfU}_0}{dt}=e,E_parallel,{bfb}+e,{bfU}_1times{bfB}-mu,nablaB.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img343.png"
 ALT="$\displaystyle m  \frac{d{\bf U}_0}{dt} = e E_\parallel {\bf b} + e {\bf U}_1\times {\bf B}
-\mu \nabla B.$">|; 

$key = q/displaystylem,frac{d{bfv}}{dt}=e,({bfE}+{bfv}times{bfB}).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img218.png"
 ALT="$\displaystyle m \frac{d{\bf v}}{dt} = e ({\bf E} + {\bf v}\times {\bf B}).$">|; 

$key = q/displaystylem,n,frac{d{bfV}}{dt}+nablap+nablacdot;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1098.png"
 ALT="$\displaystyle m  n \frac{d {\bf V}}{dt} + \nabla p + \nabla\cdot$">|; 

$key = q/displaystylem_e,n,frac{d_e{bfV}_e}{dt}+[delta^{-2}],nablap_e+[zeta^{-1}],nablacdot;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1456.png"
 ALT="$\displaystyle m_e  n \frac{d_e {\bf V}_e}{dt} + [\delta^{-2}] \nabla p_e+
[\zeta^{-1}]  \nabla\cdot$">|; 

$key = q/displaystylem_e,n,frac{d_e{bfV}_e}{dt}+e,n,({bfE}+{bfV}_etimes{bfB});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1437.png"
 ALT="$\displaystyle m_e  n \frac{d_e {\bf V}_e}{dt} + e  n 
({\bf E} + {\bf V}_e\times {\bf B})$">|; 

$key = q/displaystylem_e,n,frac{d_e{bfV}_e}{dt}+nablap_e+[delta^{-1}],e,n,({bfE}+{bfV}_etimes{bfB});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1445.png"
 ALT="$\displaystyle m_e  n \frac{d_e {\bf V}_e}{dt} + \nabla p_e+ [\delta^{-1}] e  n 
({\bf E} + {\bf V}_e\times {\bf B})$">|; 

$key = q/displaystylem_e,n,frac{d_e{bfV}_e}{dt}+nablap_e+nablacdot;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1143.png"
 ALT="$\displaystyle m_e  n \frac{d_e {\bf V}_e}{dt} + \nabla p_e+ \nabla\cdot$">|; 

$key = q/displaystylem_e,n,frac{d{bfV}}{dt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1898.png"
 ALT="$\displaystyle m_e n \frac{d{\bf V}}{dt}$">|; 

$key = q/displaystylem_e,n,frac{partial{bfV}_e}{partialt}+m_e,n,({bfV}_ecdotnabla){bfV}_e+[delta^{-2}],nablap_e+[zeta^{-1}],nablacdot;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1498.png"
 ALT="$\displaystyle m_e  n \frac{\partial {\bf V}_e}{\partial t} +
m_e  n ({\bf V}_e\cdot\nabla){\bf V}_e+
[\delta^{-2}] \nabla p_e+
[\zeta^{-1}]  \nabla\cdot$">|; 

$key = q/displaystylem_e,n,frac{partial{bfV}_e}{partialt}+m_e,n,({bfV}_ecdotnabla){bfV}_e+e,n,({bfE}+{bfV}_etimes{bfB});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1469.png"
 ALT="$\displaystyle m_e  n \frac{\partial {\bf V}_e}{\partial t} + m_e  n 
({\bf V}_e\cdot \nabla ){\bf V}_e + e  n 
({\bf E} + {\bf V}_e\times {\bf B})$">|; 

$key = q/displaystylem_e,n,frac{partial{bfV}_e}{partialt}+m_e,n,({bfV}_ecdotnabla){bfV}_e+nablap_e+[delta^{-1}],e,n,({bfE}+{bfV}_etimes{bfB});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1484.png"
 ALT="$\displaystyle m_e  n \frac{\partial {\bf V}_e}{\partial t} +
m_e  n ({\bf V...
...bf V}_e+
\nabla p_e+ [\delta^{-1}] e  n 
({\bf E} + {\bf V}_e\times {\bf B})$">|; 

$key = q/displaystylem_e,n_e,V_e,frac{dV_e}{dx};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1556.png"
 ALT="$\displaystyle m_e n_e V_e \frac{dV_e}{dx}$">|; 

$key = q/displaystylem_i,n,frac{d_i{bfV}_i}{dt}+[delta^{-2}],nablap_i+[zeta^{-1}],nablacdot;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1462.png"
 ALT="$\displaystyle m_i  n \frac{d_i {\bf V}_i}{dt} + [\delta^{-2}] \nabla p_i +
[\zeta^{-1}] \nabla\cdot$">|; 

$key = q/displaystylem_i,n,frac{d_i{bfV}_i}{dt}+nablap_i+nablacdot;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1150.png"
 ALT="$\displaystyle m_i  n \frac{d_i {\bf V}_i}{dt} + \nabla p_i + \nabla\cdot$">|; 

$key = q/displaystylem_i,n,frac{d_i{bfV}_i}{dt}+nablap_i-[delta^{-1}],e,n,({bfE}+{bfV}_itimes{bfB});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1449.png"
 ALT="$\displaystyle m_i  n \frac{d_i {\bf V}_i}{dt} + \nabla p_i - [\delta^{-1}]  e  n 
({\bf E} + {\bf V}_i\times {\bf B})$">|; 

$key = q/displaystylem_i,n,frac{d_i{bfV}_i}{dt}-e,n,({bfE}+{bfV}_itimes{bfB});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1439.png"
 ALT="$\displaystyle m_i  n \frac{d_i {\bf V}_i}{dt} - e  n 
({\bf E} + {\bf V}_i\times {\bf B})$">|; 

$key = q/displaystylem_i,n,frac{d{bfV}}{dt}+nablap-{bfj}times{bfB}simeq0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1490.png"
 ALT="$\displaystyle m_i  n \frac{d{\bf V}}{dt} + \nabla p - {\bf j}\times{\bf B} \simeq 0.$">|; 

$key = q/displaystylem_i,n,frac{d{bfV}}{dt}-{bfj}times{bfB};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1535.png"
 ALT="$\displaystyle m_i  n \frac{d{\bf V}}{dt} -{\bf j}\times {\bf B}$">|; 

$key = q/displaystylem_i,n,frac{d{bfV}}{dt}-{bfj}times{bfB}simeq{bf0}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1481.png"
 ALT="$\displaystyle m_i  n \frac{d{\bf V}}{dt} -{\bf j}\times {\bf B} \simeq {\bf0}.$">|; 

$key = q/displaystylem_i,n,frac{d{bfV}}{dt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1546.png"
 ALT="$\displaystyle m_i  n \frac{d{\bf V}}{dt}$">|; 

$key = q/displaystylem_i,n,frac{partial{bfV}_i}{partialt}+m_i,n,({bfV}_icdotnabla){bfV}_i+[delta^{-2}],nablap_i+[zeta^{-1}],nablacdot;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1500.png"
 ALT="$\displaystyle m_i  n \frac{\partial {\bf V}_i}{\partial t} +
m_i  n ({\bf V}_i\cdot\nabla) {\bf V}_i +
[\delta^{-2}] \nabla p_i +
[\zeta^{-1}] \nabla\cdot$">|; 

$key = q/displaystylem_i,n,frac{partial{bfV}_i}{partialt}+m_i,n,({bfV}_icdotnabla){bfV}_i-e,n,({bfE}+{bfV}_itimes{bfB});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1471.png"
 ALT="$\displaystyle m_i  n \frac{\partial {\bf V}_i}{\partial t} +m_i  n ({\bf V}_i\cdot
\nabla){\bf V}_i - e  n 
({\bf E} + {\bf V}_i\times {\bf B})$">|; 

$key = q/displaystylem_i,n_e,frac{partial{bfV}}{partialt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1684.png"
 ALT="$\displaystyle m_i  n_e \frac{\partial {\bf V}}{\partial t}$">|; 

$key = q/displaystylem_i,n_i,V_i,frac{dV_i}{dx};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1554.png"
 ALT="$\displaystyle m_i n_i V_i \frac{dV_i}{dx}$">|; 

$key = q/displaystylem_s,ddot{bfr}_s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img664.png"
 ALT="$\displaystyle m_s \ddot{\bf r}_s$">|; 

$key = q/displaystylem_s,frac{d{bfV}_s}{dt}+nu_s,m_s,{bfV}_s=e_s,({bfE}+{bfV}_stimes{bfB}).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1887.png"
 ALT="$\displaystyle m_s \frac{d{\bf V}_s}{dt} + \nu_s m_s {\bf V}_s = e_s ({\bf E}+{\bf V}_s\times {\bf B}).
$">|; 

$key = q/displaystylem_s,n_s,frac{d_s{bfV}_s}{dt}+nablacdot{bfp}_s-e_s,n_s,({bfE}+{bfV}_stimes{bfB});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1074.png"
 ALT="$\displaystyle m_s  n_s \frac{d_s {\bf V}_s}{dt} + \nabla\cdot {\bf p}_s - e_s  n_s 
({\bf E} + {\bf V}_s\times {\bf B})$">|; 

$key = q/displaystylem_s,n_s,frac{d_s{bfV}_s}{dt}+nablap_s+nablacdot;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1085.png"
 ALT="$\displaystyle m_s  n_s \frac{d_s {\bf V}_s}{dt} + \nabla p_s + \nabla\cdot$">|; 

$key = q/displaystylem_s,v_s^{2}+m_{s'},v_{s'}^{2}=m_s,v_s'^{2}+m_{s'},v_{s'}'^{2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.51ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img871.png"
 ALT="$\displaystyle m_s v_s^{2} + m_{s'} v_{s'}^{2} =m_s v_s'^{2}+m_{s'} v_{s'}'^{2}.$">|; 

$key = q/displaystylem_s,{bfv}_s+m_{s'},{bfv}_{s'}=m_s,{bfv}_s'+m_{s'},{bfv}_{s'}',;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img870.png"
 ALT="$\displaystyle m_s {\bf v}_s + m_{s'} {\bf v}_{s'} = m_s {\bf v}_s'+m_{s'} {\bf v}_{s'}',$">|; 

$key = q/displaystylem_srightarrowm_sleft(1+frac{{rmi},nu_s}{omega}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1888.png"
 ALT="$\displaystyle m_s\rightarrow m_s\left(1+\frac{{\rm i} \nu_s}{\omega}\right).
$">|; 

$key = q/displaystylem_{s'},ddot{bfr}_{s'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img666.png"
 ALT="$\displaystyle m_{s'} \ddot{\bf r}_{s'}$">|; 

$key = q/displaystylembox{boldmath{{mu{};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img336.png"
 ALT="$\displaystyle \mbox{\boldmath$\mu$}$">|; 

$key = q/displaystylembox{boldmath{{pi{};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1083.png"
 ALT="$\displaystyle \mbox{\boldmath$\pi$}$">|; 

$key = q/displaystylembox{boldmath{{rho{};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img230.png"
 ALT="$\displaystyle \mbox{\boldmath$\rho$}$">|; 

$key = q/displaystylembox{boldmath{{sigma{};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.12ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img1677.png"
 ALT="$\displaystyle \mbox{\boldmath$\sigma$}$">|; 

$key = q/displaystylembox{boldmath{{zeta{};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img247.png"
 ALT="$\displaystyle \mbox{\boldmath$\zeta$}$">|; 

$key = q/displaystylembox{hspace{1cm}as{rrightarrowinfty{};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.12ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2952.png"
 ALT="$\displaystyle \mbox{\hspace{1cm}as $r\rightarrow\infty$}$">|; 

$key = q/displaystylemu;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1325.png"
 ALT="$\displaystyle \mu$">|; 

$key = q/displaystylemu=(m,{mitOmega}-k,U),tau_R,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3031.png"
 ALT="$\displaystyle \mu= (m {\mit\Omega}-k U) \tau_R,$">|; 

$key = q/displaystylemu=frac{m,u_perp^{2}}{2,B},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.85ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img335.png"
 ALT="$\displaystyle \mu = \frac{m u_\perp^{2}}{2 B},$">|; 

$key = q/displaystylemu>mu_{rmtrap}=frac{{calE}}{B_{rmmax}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img427.png"
 ALT="$\displaystyle \mu&gt; \mu_{\rm trap} = \frac{{\cal E}}{B_{\rm max}}$">|; 

$key = q/displaystylemu_{ss'},ddot{bfr}_{ss'}=k_{ss'},frac{{bfr}_{ss'}}{|{bfr}_{ss'}|^{3}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.98ex; " SRC="|."$dir".q|img678.png"
 ALT="$\displaystyle \mu_{ss'} \ddot{\bf r}_{ss'} = k_{ss'} \frac{{\bf r}_{ss'}}{\vert{\bf r}_{ss'}\vert^{3}}.$">|; 

$key = q/displaystylemu_{ss'}=frac{m_s,m_{s'}}{m_s+m_{s'}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.41ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img599.png"
 ALT="$\displaystyle \mu_{ss'} = \frac{m_s m_{s'}}{m_s+m_{s'}}$">|; 

$key = q/displaystylen(omega,z)=left[1-frac{{mitPi}_e^{2}(z)}{omega^2}right]^{1slash2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.97ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2086.png"
 ALT="$\displaystyle n(\omega,z) = \left[1-\frac{{\mit\Pi}_e^{2}(z)}{\omega^2}\right]^{1/2}.$">|; 

$key = q/displaystylen(z_0)=|S|.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2156.png"
 ALT="$\displaystyle n(z_0) = \vert S\vert.$">|; 

$key = q/displaystylen,V_{ast,e}simrho_e,frac{partialn}{partialx},v_esimfrac{T_e}{e,B}frac{partialn}{partialx}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1532.png"
 ALT="$\displaystyle n V_{\ast e} \sim \rho_e \frac{\partial n}{\partial x} v_e \sim
\frac{T_e}{e B} \frac{\partial n}{\partial x}.$">|; 

$key = q/displaystylen,{bfV};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img985.png"
 ALT="$\displaystyle n {\bf V}$">|; 

$key = q/displaystylen;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img983.png"
 ALT="$\displaystyle n$">|; 

$key = q/displaystylen^2,cos^2theta=1+frac{{{mitPi}}_i^{2}}{{{mitOmega}}_i^{2}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.43ex; " SRC="|."$dir".q|img1808.png"
 ALT="$\displaystyle n^2 \cos^2\theta = 1 + \frac{{{\mit\Pi}}_i^{2}}{{{\mit\Omega}}_i^{2}},$">|; 

$key = q/displaystylen^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img1755.png"
 ALT="$\displaystyle n^2$">|; 

$key = q/displaystylen^2=1+frac{{{mitPi}}_i^{2}}{{{mitOmega}}_i^{2}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.43ex; " SRC="|."$dir".q|img1809.png"
 ALT="$\displaystyle n^2 = 1 + \frac{{{\mit\Pi}}_i^{2}}{{{\mit\Omega}}_i^{2}}.$">|; 

$key = q/displaystylen^2=Lsimeq1-frac{{{mitPi}}_e^{2}}{(omega-{{mitOmega}}_e),(omega-{{mitOmega}}_i)},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.30ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img1830.png"
 ALT="$\displaystyle n^2 = L\simeq 1 - \frac{{{\mit\Pi}}_e^{2}}{(\omega-{{\mit\Omega}}_e) 
(\omega-{{\mit\Omega}}_i)},$">|; 

$key = q/displaystylen^2=Rsimeq1-frac{{{mitPi}}_e^{2}}{(omega+{{mitOmega}}_e),(omega+{{mitOmega}}_i)},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.30ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img1828.png"
 ALT="$\displaystyle n^2 = R \simeq 1 - \frac{{{\mit\Pi}}_e^{2}}{(\omega+{{\mit\Omega}}_e)
 (\omega+{{\mit\Omega}}_i)},$">|; 

$key = q/displaystylen^2=a,z+{calO}left(z^2right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.23ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img1949.png"
 ALT="$\displaystyle n^2 = a z+ {\cal O}\left(z^2\right)$">|; 

$key = q/displaystylen^2=frac{(k_x^{2}+k_z^{2}),c^2}{omega^2}=1-frac{{mitPi}_e^{2}}{omega^2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img2149.png"
 ALT="$\displaystyle n^2 = \frac{(k_x^{2} + k_z^{2}) c^2}{\omega^2} = 1-\frac{{\mit\Pi}_e^{2}}{\omega^2},$">|; 

$key = q/displaystylen^2=frac{BpmF}{2,A},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.46ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img1751.png"
 ALT="$\displaystyle n^2 = \frac{B\pm F}{2 A},$">|; 

$key = q/displaystylen^2=frac{R,L}{S},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1855.png"
 ALT="$\displaystyle n^2 = \frac{R L}{S},$">|; 

$key = q/displaystylen^2=frac{b}{z+{rmi},epsilon}+{calO}(1);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.80ex; " SRC="|."$dir".q|img1969.png"
 ALT="$\displaystyle n^2 = \frac{b}{z + {\rm i} \epsilon} +{\cal O}(1)$">|; 

$key = q/displaystylen^2=frac{k^2,c^2}{omega^2}simeqfrac{{{mitPi}}_e^{2}}{omega,|{{mitOmega}}_e|}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.30ex; vertical-align: -1.98ex; " SRC="|."$dir".q|img1847.png"
 ALT="$\displaystyle n^2 = \frac{k^2 c^2}{\omega^2}\simeq \frac{{{\mit\Pi}}_e^{2}}
{\omega \vert{{\mit\Omega}}_e\vert}.$">|; 

$key = q/displaystylen^2simeqfrac{b}{z+{rmi},epsilon},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.80ex; " SRC="|."$dir".q|img2054.png"
 ALT="$\displaystyle n^2 \simeq \frac{b}{z+ {\rm i} \epsilon},$">|; 

$key = q/displaystylen^{2}=Rsimeq1+frac{{mitPi}_e^{2}}{omega,(|{mitOmega}_e|-omega-{rmi},nu_e)}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.30ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img2051.png"
 ALT="$\displaystyle n^{2} = R \simeq 1+ \frac{{\mit\Pi}_e^{2}}{\omega (\vert{\mit\Omega}_e\vert
-\omega - {\rm i} \nu_e)}.$">|; 

$key = q/displaystylen_e=int_{-infty}^inftyF_0(u),du;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img2548.png"
 ALT="$\displaystyle n_e = \int_{-\infty}^\infty F_0(u) du$">|; 

$key = q/displaystylen_e=n_s,expleft[frac{e,({mitPhi}-{mitPhi}_s)}{T_e}right].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1573.png"
 ALT="$\displaystyle n_e = n_s \exp\left[\frac{e ({\mit\Phi}-{\mit\Phi}_s)}{T_e}\right].$">|; 

$key = q/displaystylen_i(x),V_i(x)=n_s,V_s,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1567.png"
 ALT="$\displaystyle n_i(x) V_i(x) = n_s V_s,$">|; 

$key = q/displaystylen_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1570.png"
 ALT="$\displaystyle n_i$">|; 

$key = q/displaystylen_isimeqn_eequivn,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img36.png"
 ALT="$\displaystyle n_i \simeq n_e \equiv n,$">|; 

$key = q/displaystylen_s({bfr},t)=intf_s({bfr},{bfv},t),d^3{bfv},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img1018.png"
 ALT="$\displaystyle n_s({\bf r},t) = \int f_s({\bf r}, {\bf v},t) d^3{\bf v},$">|; 

$key = q/displaystylen_s,{bfV};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img881.png"
 ALT="$\displaystyle n_s {\bf V}$">|; 

$key = q/displaystylen_s,{bfV}_s({bfr},t)=int{bfv},f_s({bfr},{bfv},t),d^3{bfv}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img1019.png"
 ALT="$\displaystyle n_s {\bf V}_s({\bf r}, t) = \int
{\bf v} f_s({\bf r}, {\bf v},t) d^3{\bf v}.$">|; 

$key = q/displaystylen_s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img879.png"
 ALT="$\displaystyle n_s$">|; 

$key = q/displaystylen_s=n_0,expleft(-e_s,{mitPhi}slashTright),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.58ex; " SRC="|."$dir".q|img59.png"
 ALT="$\displaystyle n_s = n_0 \exp\left(-e_s {\mit\Phi}/T\right),$">|; 

$key = q/displaystylen_s=n_p,{rme}^{-0.5}simeq0.61,n_p.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.68ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1627.png"
 ALT="$\displaystyle n_s = n_p {\rm e}^{-0.5} \simeq 0.61 n_p.$">|; 

$key = q/displaystylenabla^2delta{mitPhi}=-frac{deltarho}{epsilon_0}=-left(frac{deltarho_{rmext}-2,e^2,n_0,delta{mitPhi}slashT}{epsilon_0}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img66.png"
 ALT="$\displaystyle \nabla^2 \delta {\mit\Phi} = - \frac{\delta\rho}{\epsilon_0} =
-\...
...{\delta\rho_{\rm ext} -2  e^2  n_0  \delta{\mit\Phi}/T}{\epsilon_0}
\right),$">|; 

$key = q/displaystylenabla^2{mitPhi}=-frac{e}{epsilon_0}left(n-int!f_e,d^3{bfv}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2228.png"
 ALT="$\displaystyle \nabla^2{\mit\Phi} = -\frac{e}{\epsilon_0}\left(n-\int \!f_e d^3{\bf v}\right).$">|; 

$key = q/displaystylenabla^2{mitPhi}=frac{e}{epsilon_0}int!f_1,d^3{bfv},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img2233.png"
 ALT="$\displaystyle \nabla^2{\mit\Phi} = \frac{e}{\epsilon_0}\int\! f_1 d^3{\bf v},$">|; 

$key = q/displaystylenabla^{2}_vG_{s'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.51ex; vertical-align: -0.66ex; " SRC="|."$dir".q|img812.png"
 ALT="$\displaystyle \nabla^{2}_v G_{s'}$">|; 

$key = q/displaystylenabla^{2}_vH_{s'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.51ex; vertical-align: -0.66ex; " SRC="|."$dir".q|img810.png"
 ALT="$\displaystyle \nabla^{2}_v H_{s'}$">|; 

$key = q/displaystylenabla_vcdot{bfa}_s=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1055.png"
 ALT="$\displaystyle \nabla_v\cdot {\bf a}_s = 0.$">|; 

$key = q/displaystylenabla_{bfk}phi={bfr}-{bfv}_g,t=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2114.png"
 ALT="$\displaystyle \nabla_{\bf k}\phi = {\bf r} - {\bf v}_g t=0,$">|; 

$key = q/displaystylenablacdot{bfB};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img3048.png"
 ALT="$\displaystyle \nabla\cdot{\bf B}$">|; 

$key = q/displaystylenablacdot{bfV};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3242.png"
 ALT="$\displaystyle \nabla\cdot{\bf V}$">|; 

$key = q/displaystylenablacdot{bfV}_s=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1089.png"
 ALT="$\displaystyle \nabla\cdot {\bf V}_s = 0$">|; 

$key = q/displaystylenablacdot{bfq}=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2763.png"
 ALT="$\displaystyle \nabla\cdot{\bf q} = 0.$">|; 

$key = q/displaystylenablacdot{bfq}_{Te}simeqnablacdot(-kappa_parallel^e,nabla_parallelT_e)simeq0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.94ex; " SRC="|."$dir".q|img1504.png"
 ALT="$\displaystyle \nabla\cdot{\bf q}_{Te}\simeq \nabla\cdot(-\kappa_\parallel^e \nabla_\parallel T_e)\simeq 0,$">|; 

$key = q/displaystylenablacdot{bfq}_{Ti}simeqnablacdot(-kappa_parallel^i,nabla_parallelT_i)simeq0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.79ex; vertical-align: -0.94ex; " SRC="|."$dir".q|img1506.png"
 ALT="$\displaystyle \nabla\cdot{\bf q}_{Ti}\simeq \nabla\cdot(-\kappa_\parallel^i \nabla_\parallel T_i)\simeq 0,$">|; 

$key = q/displaystylenablatimesc,{bfB};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img2173.png"
 ALT="$\displaystyle \nabla\times c {\bf B}$">|; 

$key = q/displaystylenablatimes{bfB};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.10ex; " SRC="|."$dir".q|img2682.png"
 ALT="$\displaystyle \nabla\times{\bf B}$">|; 

$key = q/displaystylenablatimes{bfE};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.10ex; " SRC="|."$dir".q|img2175.png"
 ALT="$\displaystyle \nabla\times {\bf E}$">|; 

$key = q/displaystylenu=frac{v_t}{l};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img1128.png"
 ALT="$\displaystyle \nu = \frac{v_t}{l}$">|; 

$key = q/displaystylenu_esimleft(frac{m_i}{m_e}right)^{1slash2}!nu_i.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img120.png"
 ALT="$\displaystyle \nu_e \sim \left(\frac{m_i}{m_e}\right)^{1/2}\!\nu_i.$">|; 

$key = q/displaystylenu_ssimeqsum_{s'}nu_{ss'}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -2.62ex; " SRC="|."$dir".q|img119.png"
 ALT="$\displaystyle \nu_s \simeq \sum_{s'} \nu_{ss'}.$">|; 

$key = q/displaystylenu_{ee}equivfrac{1}{tau_{ee}}=frac{ln{mitLambda}_c,e^{4},n_e}{12,pi^{3slash2},epsilon_0^{2},m_e^{1slash2},T^{3slash2}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.97ex; vertical-align: -2.70ex; " SRC="|."$dir".q|img975.png"
 ALT="$\displaystyle \nu_{ee} \equiv \frac{1}{\tau_{ee}}= \frac{\ln{\mit\Lambda}_c e^{4} n_e}{12 \pi^{3/2} \epsilon_0^{2} m_e^{1/2} T^{3/2}}.$">|; 

$key = q/displaystylenu_{ee}simfrac{ln{mitLambda}}{{mitLambda}},{mitPi}_e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img978.png"
 ALT="$\displaystyle \nu_{ee}\sim \frac{\ln{\mit\Lambda}}{{\mit\Lambda}} {\mit\Pi}_e$">|; 

$key = q/displaystylenu_{ii}equivfrac{1}{tau_{ii}}simfrac{ln{mitLambda}}{{mitLambda}},{mitPi}_i,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.96ex; " SRC="|."$dir".q|img980.png"
 ALT="$\displaystyle \nu_{ii}\equiv \frac{1}{\tau_{ii}}\sim \frac{\ln{\mit\Lambda}}{{\mit\Lambda}} {\mit\Pi}_i,$">|; 

$key = q/displaystylenusimfrac{3,e^4,ln{mitLambda}}{4pi,epsilon_0^{2},m^{1slash2}}frac{n}{T^{3slash2}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.74ex; vertical-align: -2.46ex; " SRC="|."$dir".q|img129.png"
 ALT="$\displaystyle \nu \sim \frac{3 e^4 \ln{\mit\Lambda}}{4\pi \epsilon_0^{2}  m^{1/2}}
\frac{n}{T^{3/2}}.$">|; 

$key = q/displaystylenusimfrac{ln{mitLambda}}{{mitLambda}},{mitPi}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img125.png"
 ALT="$\displaystyle \nu \sim \frac{\ln{\mit\Lambda}}{{\mit\Lambda}} {\mit\Pi}.$">|; 

$key = q/displaystyleomega+{rmi},k,v_isimeqpm{rmi}left(frac{m_e}{m_i}right)^{1slash2},(omega-k,U_e+{rmi},k,v_e).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2566.png"
 ALT="$\displaystyle \omega + {\rm i} k v_i \simeq \pm {\rm i}\left(\frac{m_e}{m_i}\right)^{1/2} (\omega-k U_e+{\rm i} k v_e).$">|; 

$key = q/displaystyleomega,frac{partial{bfu}}{partialgamma}-{mitOmega},{bfu}times{bfb}=frac{e}{m}left({bfE}+{bfU}_0times{bfB}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img296.png"
 ALT="$\displaystyle \omega \frac{\partial{\bf u}}{\partial\gamma} - {\mit\Omega} {\bf u}\times{\bf
b} = \frac{e}{m}\left({\bf E} + {\bf U}_0\times{\bf B}\right).$">|; 

$key = q/displaystyleomega,rho_0,V_z=k,costheta,p.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2741.png"
 ALT="$\displaystyle \omega \rho_0 V_z = k \cos\theta p.$">|; 

$key = q/displaystyleomega,{bfB}+{bfk}times({bfV}times{bfB}_0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2711.png"
 ALT="$\displaystyle \omega {\bf B} + {\bf k}\times({\bf V}\times{\bf B}_0)$">|; 

$key = q/displaystyleomega-omega_{n,s}lesssimk_parallel,v_s.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img2474.png"
 ALT="$\displaystyle \omega - \omega_{n s} \lesssim k_\parallel v_s.$">|; 

$key = q/displaystyleomega-{mitOmega}_ilesssimk_parallel,v_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img2455.png"
 ALT="$\displaystyle \omega-{\mit\Omega}_i\lesssim k_\parallel v_i$">|; 

$key = q/displaystyleomega-|{mitOmega}_e|lesssimk_parallel,v_e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img2454.png"
 ALT="$\displaystyle \omega - \vert{\mit\Omega}_e\vert \lesssim k_\parallel v_e$">|; 

$key = q/displaystyleomega;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2101.png"
 ALT="$\displaystyle \omega$">|; 

$key = q/displaystyleomega=frac{k,V_A,costheta}{sqrt{1+V_A^{2}slashc^2}}simeqk,V_A,costhetaequivk_parallel,V_A,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 7.08ex; vertical-align: -4.12ex; " SRC="|."$dir".q|img1813.png"
 ALT="$\displaystyle \omega = \frac{k V_A \cos\theta}{\sqrt{1+V_A^{2}/c^2}}\simeq k V_A \cos\theta
\equiv k_\parallel V_A,$">|; 

$key = q/displaystyleomega=frac{k,V_A}{sqrt{1+V_A^{2}slashc^2}}simeqk,V_A,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 7.08ex; vertical-align: -4.12ex; " SRC="|."$dir".q|img1814.png"
 ALT="$\displaystyle \omega = \frac{k V_A}{\sqrt{1+V_A^{2}/c^2}}\simeq k V_A,$">|; 

$key = q/displaystyleomega=k,V_+,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img2729.png"
 ALT="$\displaystyle \omega = k V_+,$">|; 

$key = q/displaystyleomega=k,V_-,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img2730.png"
 ALT="$\displaystyle \omega = k V_-,$">|; 

$key = q/displaystyleomega=k,V_A,costheta,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img2725.png"
 ALT="$\displaystyle \omega = k V_A \cos\theta,$">|; 

$key = q/displaystyleomega=k,V_A.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img2736.png"
 ALT="$\displaystyle \omega = k V_A.$">|; 

$key = q/displaystyleomega={mitOmega}({bfk},{bfr},t):;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2107.png"
 ALT="$\displaystyle \omega = {\mit\Omega}({\bf k}, {\bf r}, t):$">|; 

$key = q/displaystyleomega^2+{{mitOmega}}_e,omega-{{mitPi}}_e^{2}simeq0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.51ex; vertical-align: -0.65ex; " SRC="|."$dir".q|img1841.png"
 ALT="$\displaystyle \omega^2+{{\mit\Omega}}_e \omega- {{\mit\Pi}}_e^{2}\simeq 0,$">|; 

$key = q/displaystyleomega^2={{mitPi}}_e^{2}+k^2c^2,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.51ex; vertical-align: -0.65ex; " SRC="|."$dir".q|img1795.png"
 ALT="$\displaystyle \omega^2 = {{\mit\Pi}}_e^{2} + k^2 c^2,$">|; 

$key = q/displaystyleomega^2rightarrow{mitPi}_e^{2}+{mitOmega}_e^{2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.51ex; vertical-align: -0.65ex; " SRC="|."$dir".q|img2489.png"
 ALT="$\displaystyle \omega^2\rightarrow {\mit\Pi}_e^{2} + {\mit\Omega}_e^{2}.$">|; 

$key = q/displaystyleomega^2simeq{mitPi}_e^{2}left[1+3,(k,lambda_D)^2right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.29ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img2295.png"
 ALT="$\displaystyle \omega^2 \simeq {\mit\Pi}_e^{2}\left[1+ 3 (k \lambda_D)^2\right],$">|; 

$key = q/displaystyleomega^{2}={mitPi}_i^{2},frac{(k,lambda_D)^2}{1+(k,lambda_D)^2}=frac{T_e}{m_i}frac{k^{2}}{1+(k,lambda_D)^{2}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img2342.png"
 ALT="$\displaystyle \omega^{2} ={\mit\Pi}_i^{2} \frac{(k \lambda_D)^2}{1+(k \lambda_D)^2}
= \frac{T_e}{m_i} \frac{k^{2}}{1+(k \lambda_D)^{2}}.$">|; 

$key = q/displaystyleomega_1simeq|{{mitOmega}}_e|slash2+sqrt{{{mitOmega}}_e^{2}slash4+{{mitPi}}_e^{2}}>|{{mitOmega}}_e|.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.33ex; " SRC="|."$dir".q|img1843.png"
 ALT="$\displaystyle \omega_1 \simeq \vert{{\mit\Omega}}_e\vert/2 + \sqrt{{{\mit\Omega}}_e^{2}/4
+{{\mit\Pi}}_e^{2}}&gt;\vert{{\mit\Omega}}_e\vert.$">|; 

$key = q/displaystyleomega_2simeq-|{{mitOmega}}_e|slash2+sqrt{{{mitOmega}}_e^{2}slash4+{{mitPi}}_e^{2}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.33ex; " SRC="|."$dir".q|img1851.png"
 ALT="$\displaystyle \omega_2 \simeq -\vert{{\mit\Omega}}_e\vert/2 +
\sqrt{{{\mit\Omega}}_e^{2}/4 + {{\mit\Pi}}_e^{2}}.$">|; 

$key = q/displaystyleomega_r=omega_{r,n}equivn,{mitOmega}_ileft(1-frac{T_{parallel,i}}{T_{perp,i}}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2647.png"
 ALT="$\displaystyle \omega_r= \omega_{r n} \equiv n {\mit\Omega}_i\left(1-\frac{T_{\parallel i}}{T_{\perp i}}\right).$">|; 

$key = q/displaystyleomega_rsimeqk,c_s,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2585.png"
 ALT="$\displaystyle \omega_r \simeq k c_s,$">|; 

$key = q/displaystyleomega_rsimeq{mitPi}_e,frac{k_parallel}{k}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.74ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img2631.png"
 ALT="$\displaystyle \omega_r \simeq {\mit\Pi}_e \frac{k_\parallel}{k}.$">|; 

$key = q/displaystyleomega_{n,s}=n,{mitOmega}_s,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2466.png"
 ALT="$\displaystyle \omega_{n s} = n {\mit\Omega}_s,$">|; 

$key = q/displaystyleomega_{r,n}>left(n-frac{1}{2}right){mitOmega}_i,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2648.png"
 ALT="$\displaystyle \omega_{r n} &gt; \left(n-\frac{1}{2}\right){\mit\Omega}_i,$">|; 

$key = q/displaystyleomega_{rmLH}<omega_2<omega_{rmUH}<omega_1,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1869.png"
 ALT="$\displaystyle \omega_{\rm LH} &lt; \omega_2 &lt; \omega_{\rm UH} &lt; \omega_1,$">|; 

$key = q/displaystyleomega_{rmUH}=sqrt{{{mitPi}}_e^{2}+{{mitOmega}}_e^{2}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.33ex; " SRC="|."$dir".q|img1862.png"
 ALT="$\displaystyle \omega_{\rm UH} = \sqrt{{{\mit\Pi}}_e^{2} + {{\mit\Omega}}_e^{2}}.$">|; 

$key = q/displaystyleomegasimeqk,V_S,costheta.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2738.png"
 ALT="$\displaystyle \omega \simeq k V_S \cos\theta.$">|; 

$key = q/displaystyleomegasimeqkleft(frac{m_e}{m_i}right)^{1slash2}v_e+{rmi},kleft[left(frac{m_e}{m_i}right)^{1slash2}U_e-v_iright].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.26ex; " SRC="|."$dir".q|img2567.png"
 ALT="$\displaystyle \omega\simeq k\left(\frac{m_e}{m_i}\right)^{1/2}v_e + {\rm i} k\left[\left(\frac{m_e}{m_i}\right)^{1/2}U_e-v_i\right].$">|; 

$key = q/displaystyleomegasimeq{mitPi}_e-{rmi},sum_sfrac{nu_s,{mitPi}_s^{2}}{2,{mitPi}_e^{2}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.91ex; vertical-align: -2.62ex; " SRC="|."$dir".q|img1895.png"
 ALT="$\displaystyle \omega \simeq {\mit\Pi}_e-{\rm i} \sum_s\frac{\nu_s {\mit\Pi}_s^{2}}{2 {\mit\Pi}_e^{2}}.
$">|; 

$key = q/displaystylep(infty)=p(a),expleft[-frac{7}{5},frac{G,M_odot,m_p}{2,T(a),a}right]=p(a),expleft[-frac{14}{5},frac{T_0}{T(a)}right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2772.png"
 ALT="$\displaystyle p(\infty) = p(a) \exp\left[-\frac{7}{5} \frac{G M_\odot m_p}{2 T(a) a}
\right] = p(a) \exp\left[-\frac{14}{5} \frac{T_0}{T(a)}\right],$">|; 

$key = q/displaystylep(r)=p(a)expleft{frac{7}{5},frac{G,M_odot,m_p}{2,T(a),a}left[left(frac{a}{r}right)^{5slash7}-1right]right}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2770.png"
 ALT="$\displaystyle p(r) = p(a) \exp\left\{\frac{7}{5} \frac{G M_\odot m_p}{2 T(a) a}
\left[\left(\frac{a}{r}\right)^{5/7}-1\right]\right\}.$">|; 

$key = q/displaystylep,bar{F}_1+{rmi},k,u,bar{F}_1=frac{e}{m_e},bar{E},frac{partialF_0}{partialu}+F_1(u,t=0),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.96ex; " SRC="|."$dir".q|img2253.png"
 ALT="$\displaystyle p \bar{F}_1 + {\rm i} k u \bar{F}_1 = \frac{e}{m_e} \bar{E} \frac{\partial
F_0}{\partial u} + F_1(u,t=0),$">|; 

$key = q/displaystylep,n^{-{mitGamma}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1900.png"
 ALT="$\displaystyle p n^{-{\mit\Gamma}}$">|; 

$key = q/displaystylep;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2716.png"
 ALT="$\displaystyle p$">|; 

$key = q/displaystylep=2,n,T.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2760.png"
 ALT="$\displaystyle p = 2 n T.$">|; 

$key = q/displaystylep=frac{2,rho,T}{m_p},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.19ex; vertical-align: -2.26ex; " SRC="|."$dir".q|img2776.png"
 ALT="$\displaystyle p = \frac{2 \rho T}{m_p},$">|; 

$key = q/displaystylep_infty=frac{2,rho_infty,T}{m_p},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.19ex; vertical-align: -2.26ex; " SRC="|."$dir".q|img2801.png"
 ALT="$\displaystyle p_\infty= \frac{2 \rho_\infty T}{m_p},$">|; 

$key = q/displaystylep_s(b),db=n_{s'},u_{ss'},2pi,b,db.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img725.png"
 ALT="$\displaystyle p_s(b) db = n_{s'} u_{ss'} 2\pi b db.$">|; 

$key = q/displaystylep_s({mitOmega}),d{mitOmega}=n_{s'},u_{ss'},frac{dsigma}{d{mitOmega}},d{mitOmega}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img721.png"
 ALT="$\displaystyle p_s({\mit\Omega}) d{\mit\Omega} = n_{s'} u_{ss'} \frac{d\sigma}{d{\mit\Omega}} d{\mit\Omega}.$">|; 

$key = q/displaystylep_s({mitOmega}),left|frac{d{mitOmega}}{db}right|=p_s(b),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.85ex; vertical-align: -1.84ex; " SRC="|."$dir".q|img726.png"
 ALT="$\displaystyle p_s({\mit\Omega}) \left\vert\frac{d{\mit\Omega}}{db}\right\vert = p_s(b),$">|; 

$key = q/displaystylep_sequivfrac{1}{3},{rmTr},({bfp}_s).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1029.png"
 ALT="$\displaystyle p_s\equiv \frac{1}{3} {\rm Tr} ({\bf p}_s).$">|; 

$key = q/displaystylepequivn,T,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img144.png"
 ALT="$\displaystyle p \equiv n T,$">|; 

$key = q/displaystylephantom{=}+(1+lambda_e^{2})^2,delta_e,zeta_e,widehat{w}_U+(1+lambda_e^{2}),delta_e,widehat{w}_T.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.51ex; vertical-align: -0.65ex; " SRC="|."$dir".q|img1374.png"
 ALT="$\displaystyle \phantom{=}+ (1+\lambda_e^{2})^2 \delta_e \zeta_e 
\widehat{w}_U + (1+\lambda_e^{2}) \delta_e \widehat{w}_T.$">|; 

$key = q/displaystylephantom{=}+A',left[{rmsgn}(epsilon)-1right],hat{z}^{1slash4},expleft[-{rmi}left(2sqrt{hat{z}}+frac{3}{4},piright)right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2029.png"
 ALT="$\displaystyle \phantom{=}+A' 
\left[{\rm sgn}(\epsilon) - 1\right] \hat{z}^{1/4} \exp\left[
-{\rm i}\left(2\sqrt{\hat{z}} + \frac{3}{4} \pi\right)\right],$">|; 

$key = q/displaystylephantom{=}+c,(m_s,v_s^{2}+m_{s'},v_{s'}^{2}-m_s,v_s'^{2}-m_{s'},v_{s'}'^{2}).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.51ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img869.png"
 ALT="$\displaystyle \phantom{=}+ c (m_s v_s^{2} + m_{s'} v_{s'}^{2}-m_s v_s'^{2}-m_{s'} v_{s'}'^{2}).$">|; 

$key = q/displaystylephantom{=}timesexpleft{,{rmi}left[(n,{mitOmega}+k_parallel,v_parallel-omega),(t'-t)+(m-n),theta,right],right}dt',;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img2392.png"
 ALT="$\displaystyle \phantom{=}\times \exp\left\{ {\rm i}\left[(n {\mit\Omega} + k_\parallel v_\parallel-\omega)
 (t'-t) + (m-n) \theta \right] \right\}dt',$">|; 

$key = q/displaystylephantom{=}timesexpleft{{rmi},left[(n,{mitOmega}_s+k_parallel,v_parallel-omega),(t'-t)+(m-n),thetaright]right}d^3{bfv},dt'.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.51ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img2511.png"
 ALT="$\displaystyle \phantom{=} \times\exp\left\{{\rm i} \left[(n {\mit\Omega}_s+k_...
...allel v_\parallel-\omega) (t'-t)+(m-n) \theta\right]\right\}d^3{\bf v} dt'.$">|; 

$key = q/displaystylephantom{=}timesexpleft{{rmi},left[(n,{mitOmega}_s+k_parallel,v_parallel-omega),(t'-t)+(m-n),thetaright]right}dt'.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img2504.png"
 ALT="$\displaystyle \phantom{=} \times\exp\left\{{\rm i} \left[(n {\mit\Omega}_s+k_\parallel v_\parallel-\omega) (t'-t)+(m-n) \theta\right]\right\}dt'.$">|; 

$key = q/displaystylephi(omega)=phi_s+frac{1}{2},phi''_s,(omega-omega_s)^2+cdots.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img2072.png"
 ALT="$\displaystyle \phi(\omega) = \phi_s + \frac{1}{2}  \phi''_s (\omega-\omega_s)^2+\cdots.$">|; 

$key = q/displaystylephi(omega,z,t)=frac{omega}{c}int_z^{a}!n(omega,z),dz'-omega,t.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -2.17ex; " SRC="|."$dir".q|img2067.png"
 ALT="$\displaystyle \phi(\omega, z,t) = \frac{\omega}{c} \int_z^{a} \!n(\omega, z) dz' - \omega  t.$">|; 

$key = q/displaystylephi(x,y,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3294.png"
 ALT="$\displaystyle \phi(x,y,t)$">|; 

$key = q/displaystylephi(z)=pmk_0,n,z.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1920.png"
 ALT="$\displaystyle \phi(z) = \pm k_0 n z.$">|; 

$key = q/displaystylephi(z)simeqpmk_0!int^z!n,dz'+{rmi},logleft(n^{1slash2}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img1934.png"
 ALT="$\displaystyle \phi(z)\simeq \pm k_0\! \int^z \!n dz' +{\rm i} \log\left(n^{1/2}\right).$">|; 

$key = q/displaystylephi={bfk}cdot{bfr}-{mitOmega},t,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2110.png"
 ALT="$\displaystyle \phi = {\bf k}\cdot{\bf r} - {\mit\Omega} t,$">|; 

$key = q/displaystylepi_{e,alphabeta};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1211.png"
 ALT="$\displaystyle \pi_{e \alpha\beta}$">|; 

$key = q/displaystylepi_{i,alphabeta};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1213.png"
 ALT="$\displaystyle \pi_{i \alpha\beta}$">|; 

$key = q/displaystylepi_{xy}=pi_{yx}=-eta,frac{dV_y}{dx},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1641.png"
 ALT="$\displaystyle \pi_{xy}=\pi_{yx} = -\eta \frac{dV_y}{dx},
$">|; 

$key = q/displaystylepllQ^{-1slash4},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3405.png"
 ALT="$\displaystyle p \ll Q^{-1/4},$">|; 

$key = q/displaystylepsi(x,y,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3290.png"
 ALT="$\displaystyle \psi(x,y,t)$">|; 

$key = q/displaystylepsi=frac{mu_0,I,d}{2pi},frac{sintheta}{r}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img524.png"
 ALT="$\displaystyle \psi = \frac{\mu_0 I d}{2\pi} \frac{\sin\theta}{r}.
$">|; 

$key = q/displaystylepsirightarrowfrac{1}{r};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img2951.png"
 ALT="$\displaystyle \psi\rightarrow \frac{1}{r}$">|; 

$key = q/displaystyleq^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.56ex; " SRC="|."$dir".q|img2994.png"
 ALT="$\displaystyle q^2$">|; 

$key = q/displaystyleq^2=n^2-S^{2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.56ex; " SRC="|."$dir".q|img2186.png"
 ALT="$\displaystyle q^2 = n^2-S^{2},
$">|; 

$key = q/displaystyleq_times^isimn,v_i,rho_i,frac{partialT_i}{partialx}simfrac{n,T_i}{m_i,|{mitOmega}_i|},frac{partialT_i}{partialx}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.98ex; " SRC="|."$dir".q|img1259.png"
 ALT="$\displaystyle q_\times^i \sim n v_i  \rho_i \frac{\partial T_i}{\partial x}
...
... \frac{n T_i}{m_i \vert{\mit\Omega}_i\vert} \frac{\partial T_i}{\partial x}.$">|; 

$key = q/displaystyleq_x=-kappa,frac{dT}{dx},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1645.png"
 ALT="$\displaystyle q_x = - \kappa \frac{dT}{dx},
$">|; 

$key = q/displaystyler,u_phi-frac{r,B_r,B_phi}{mu_0,rho,u_r}=L,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.13ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img2860.png"
 ALT="$\displaystyle r u_\phi -\frac{r B_r B_\phi}{\mu_0 \rho u_r} = L,$">|; 

$key = q/displaystyler,u_phi=frac{L,M_A^{2}-{mitOmega},r^{2}}{M_A^{2}-1},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.80ex; vertical-align: -2.41ex; " SRC="|."$dir".q|img2864.png"
 ALT="$\displaystyle r u_\phi = \frac{L M_A^{2} - {\mit\Omega} r^{2}}{M_A^{2} - 1},$">|; 

$key = q/displaystyler-r_0=-frac{u_s}{{mitOmega}},(phi-phi_0),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.01ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img2825.png"
 ALT="$\displaystyle r-r_0 = -\frac{u_s}{{\mit\Omega}} (\phi-\phi_0),$">|; 

$key = q/displaystyler;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.00ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img3099.png"
 ALT="$\displaystyle r$">|; 

$key = q/displaystyler=r_{rmeq},cos^2vartheta,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.62ex; vertical-align: -0.75ex; " SRC="|."$dir".q|img439.png"
 ALT="$\displaystyle r = r_{\rm eq} \cos^2\vartheta,$">|; 

$key = q/displaystyler^{2},rho,u=I,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2777.png"
 ALT="$\displaystyle r^{2} \rho u = I,$">|; 

$key = q/displaystyler_1,r_2=-frac{{mitGamma},({mitGamma}+1),beta_1,M_1^{2}}{2,(2-{mitGamma})}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img3142.png"
 ALT="$\displaystyle r_1 r_2= -\frac{{\mit\Gamma} ({\mit\Gamma}+1) \beta_1 M_1^{2}}{2 (2-{\mit\Gamma})}.$">|; 

$key = q/displaystyler_cequivfrac{e^2}{4pi,epsilon_0,T},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img73.png"
 ALT="$\displaystyle r_c\equiv \frac{e^2}{4\pi \epsilon_0  T},$">|; 

$key = q/displaystyler_dequivn^{-1slash3}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img72.png"
 ALT="$\displaystyle r_d \equiv n^{-1/3}.$">|; 

$key = q/displaystylerangle=frac{u_perp^{2}}{2,{mitOmega}^{2}},({bfI}-{bfb}{bfb}),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.85ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img329.png"
 ALT="$\displaystyle \rangle = \frac{u_\perp^{2}}{2 {\mit\Omega}^{2}}
 ({\bf I} - {\bf b}{\bf b}),$">|; 

$key = q/displaystylerangle=frac{u_perp^{2}}{2,{mitOmega}^{2}},left({bfI}-{bfb},{bfb}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.85ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img505.png"
 ALT="$\displaystyle \rangle = \frac{u_\perp^{2}}{2 {\mit\Omega}^{2}} \left({\bf I}- {\bf b} {\bf b}\right).
$">|; 

$key = q/displaystylerangle=langle{bfu}rangle={bf0}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img287.png"
 ALT="$\displaystyle \rangle = \langle {\bf u} \rangle = {\bf0}.$">|; 

$key = q/displaystylerho,frac{d{bfV}}{dt}+nablap-frac{(nablatimes{bfB})times{bfB}}{mu_0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img2702.png"
 ALT="$\displaystyle \rho \frac{d{\bf V}}{dt} + \nabla p - \frac{(\nabla\times{\bf B})\times {\bf B}}{\mu_0}$">|; 

$key = q/displaystylerho,frac{d{bfV}}{dt}+nablap-{bfj}times{bfB};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2673.png"
 ALT="$\displaystyle \rho \frac{d{\bf V}}{dt} + \nabla p - {\bf j}\times {\bf B}$">|; 

$key = q/displaystylerho,frac{d{bfV}}{dt}=-nablacdot{bfP},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2687.png"
 ALT="$\displaystyle \rho \frac{d{\bf V}}{dt} = -\nabla\cdot{\bf P},$">|; 

$key = q/displaystylerho,frac{d{bfV}}{dt}=-nablap+nablacdot{bfT},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2685.png"
 ALT="$\displaystyle \rho \frac{d{\bf V}}{dt} = -\nabla p + \nabla\cdot{\bf T},$">|; 

$key = q/displaystylerho,frac{d{bfV}}{dt}={bfj}times{bfb}-nablap+mu,nabla^2{bfV}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3201.png"
 ALT="$\displaystyle \rho \frac{d{\bf V}}{dt} = {\bf j}\times {\bf b} -\nabla p + \mu \nabla^2{\bf V}.
$">|; 

$key = q/displaystylerho,frac{partialU}{partialt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3265.png"
 ALT="$\displaystyle \rho \frac{\partial U}{\partial t}$">|; 

$key = q/displaystylerho,u,frac{du}{dr}=-frac{dp}{dr}-rho,frac{G,M_odot}{r^{2}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2774.png"
 ALT="$\displaystyle \rho u \frac{du}{dr} = -\frac{dp}{dr} - \rho \frac{G M_\odot}{r^{2}},$">|; 

$key = q/displaystylerho,|nabla{bfB}|;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img269.png"
 ALT="$\displaystyle \rho \vert\nabla{\bf B}\vert$">|; 

$key = q/displaystylerho;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2714.png"
 ALT="$\displaystyle \rho$">|; 

$key = q/displaystylerho=-nablacdot{bfP},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2170.png"
 ALT="$\displaystyle \rho = -\nabla\cdot{\bf P},
$">|; 

$key = q/displaystylerho_0,frac{partial{bfV}}{partialt}+nablap-frac{(nablatimes{bfB})times{bfB}_0}{mu_0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img2705.png"
 ALT="$\displaystyle \rho_0 \frac{\partial {\bf V}}{\partial t} + \nabla p -
\frac{(\nabla\times{\bf B})\times {\bf B}_0}{\mu_0}$">|; 

$key = q/displaystylerho_c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img571.png"
 ALT="$\displaystyle \rho_c$">|; 

$key = q/displaystylerho_esimleft(frac{m_e}{m_i}right)^{1slash2}!rho_i.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img136.png"
 ALT="$\displaystyle \rho_e \sim \left(\frac{m_e}{m_i}\right)^{1/2}\!\rho_i.$">|; 

$key = q/displaystylerhoequivfrac{v_t}{mitOmega},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.01ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img134.png"
 ALT="$\displaystyle \rho\equiv \frac{v_t}{\mit\Omega},$">|; 

$key = q/displaystylerholeft[frac{partial{bfV}}{partialt}+({bfV}cdotnabla){bfV}right]+nablap-{bfj}times{bfB}-mu,nabla^2{bfV}=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3736.png"
 ALT="$\displaystyle \rho\left[\frac{\partial {\bf V}}{\partial t} + ({\bf V}\cdot\nabla) {\bf V}\right]+\nabla p-{\bf j}\times {\bf B} -\mu \nabla^2{\bf V}=0,
$">|; 

$key = q/displaystylerholeft[frac{partial{bfV}}{partialt}+({bfV}cdotnabla){bfV}right]+nablap-{bfj}times{bfB};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3243.png"
 ALT="$\displaystyle \rho\left[\frac{\partial {\bf V}}{\partial t} + ({\bf V}\cdot\nabla) {\bf V}\right]+\nabla p-{\bf j}\times {\bf B}$">|; 

$key = q/displaystylerhosimeqn,m_p,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2758.png"
 ALT="$\displaystyle \rho\simeq n m_p,$">|; 

$key = q/displaystylerightarrow-frac{1}{xi_n},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img2426.png"
 ALT="$\displaystyle \rightarrow -\frac{1}{\xi_n},$">|; 

$key = q/displaystylerightarrowfrac{1}{xi_n^{2}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.13ex; vertical-align: -2.18ex; " SRC="|."$dir".q|img2428.png"
 ALT="$\displaystyle \rightarrow \frac{1}{\xi_n^{2}}$">|; 

$key = q/displaystylerightarrowfrac{hat{psi}}{hat{x}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img3361.png"
 ALT="$\displaystyle \rightarrow \frac{\hat{\psi}}{\hat{x}},$">|; 

$key = q/displaystylerightarrow{mitPsi}'left[1+frac{mitDelta}{2},|hat{x}|+{calO}(hat{x}^{,2})right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3376.png"
 ALT="$\displaystyle \rightarrow{\mit\Psi}'\left[1+\frac{\mit\Delta}{2} \vert\hat{x}\vert+{\cal O}(\hat{x}^{ 2})\right],$">|; 

$key = q/displaystylerightarrow{mitPsi}left[1+frac{{mitDelta}'}{2},|hat{x}|+{calO}(hat{x}^{,2})right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3359.png"
 ALT="$\displaystyle \rightarrow {\mit\Psi}\left[1 + \frac{{\mit\Delta}'}{2} \vert\hat{x}\vert +{\cal O}(\hat{x}^{ 2})\right],$">|; 

$key = q/displaystyles^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img2996.png"
 ALT="$\displaystyle s^2$">|; 

$key = q/displaystyles_s=-intf_s,lnf_s,d^3{bfv}_s.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img989.png"
 ALT="$\displaystyle s_s= -\int f_s \ln f_s d^3{\bf v}_s.
$">|; 

$key = q/displaystyles_s=n_sleft[lnleft(frac{T_s^{3slash2}}{n_s}right)+frac{3}{2}lnleft(frac{2pi}{m_s}right)+frac{3}{2}right].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.69ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img991.png"
 ALT="$\displaystyle s_s= n_s\left[\ln\left(\frac{T_s^{3/2}}{n_s}\right) +\frac{3}{2}\ln\left(\frac{2\pi}{m_s}\right)+\frac{3}{2}\right].
$">|; 

$key = q/displaystyles_s=n_slnleft(frac{T_s^{3slash2}}{n_s}right)+c,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.69ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1091.png"
 ALT="$\displaystyle s_s = n_s\ln\left(\frac{T_s^{3/2}}{n_s}\right)+c,$">|; 

$key = q/displaystylesigma'({bfv}_s',{bfv}_{s'}';{bfv}_s,{bfv}_{s'})=sigma'({bfv}_s,{bfv}_{s'};{bfv}_s',{bfv}_{s'}').;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img612.png"
 ALT="$\displaystyle \sigma' ({\bf v}_s',{\bf v}_{s'}';{\bf v}_s,{\bf v}_{s'})=\sigma' ({\bf v}_s,{\bf v}_{s'}; {\bf v}_s',{\bf v}_{s'}').$">|; 

$key = q/displaystylesigma'({bfv}_{s'},{bfv}_s;{bfv}_{s'}',{bfv}_s')=sigma'({bfv}_s,{bfv}_{s'};{bfv}_s',{bfv}_{s'}').;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img649.png"
 ALT="$\displaystyle \sigma'({\bf v}_{s'}, {\bf v}_s; {\bf v}_{s'}', {\bf v}_s')= \sigma'({\bf v}_s, {\bf v}_{s'}; {\bf v}_s', {\bf v}_{s'}').$">|; 

$key = q/displaystylesigma=frac{e^2,n_e}{m_e,nu_e}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -1.96ex; " SRC="|."$dir".q|img1658.png"
 ALT="$\displaystyle \sigma = \frac{e^2 n_e}{m_e \nu_e}.
$">|; 

$key = q/displaystylesigma_parallel=1.96,frac{n,e^2,tau_e}{m_e}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -1.96ex; " SRC="|."$dir".q|img1165.png"
 ALT="$\displaystyle \sigma_\parallel = 1.96 \frac{n  e^2 \tau_e}{m_e}.$">|; 

$key = q/displaystylesigma_perp=0.51,sigma_parallel=frac{n,e^2,tau_e}{m_e}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -1.96ex; " SRC="|."$dir".q|img1226.png"
 ALT="$\displaystyle \sigma_\perp = 0.51 \sigma_\parallel = \frac{n e^2 \tau_e}{m_e}.$">|; 

$key = q/displaystylesim(k,a)^{-1slash3},{calS}^{-1slash3}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3685.png"
 ALT="$\displaystyle \sim (k a)^{-1/3} {\cal S}^{-1/3}.$">|; 

$key = q/displaystylesim(k,a)^{-3slash5},{calS}^{-2slash5},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3682.png"
 ALT="$\displaystyle \sim (k a)^{-3/5} {\cal S}^{-2/5},$">|; 

$key = q/displaystylesimV,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img1428.png"
 ALT="$\displaystyle \sim V,$">|; 

$key = q/displaystylesimdelta,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img1426.png"
 ALT="$\displaystyle \sim \delta,$">|; 

$key = q/displaystylesimeq+frac{nablap_i}{e,n}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img1511.png"
 ALT="$\displaystyle \simeq +\frac{\nabla p_i}{e n} .$">|; 

$key = q/displaystylesimeq-frac{nablap_e}{e,n},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img1509.png"
 ALT="$\displaystyle \simeq - \frac{\nabla p_e}{e n},$">|; 

$key = q/displaystylesimeq-frac{{{mitPi}}_e^{2}}{omega^2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img1803.png"
 ALT="$\displaystyle \simeq -\frac{{{\mit\Pi}}_e^{2}}{\omega^2}.$">|; 

$key = q/displaystylesimeq0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img1802.png"
 ALT="$\displaystyle \simeq 0,$">|; 

$key = q/displaystylesimeq1+frac{{{mitPi}}_i^{2}}{{{mitOmega}}_i^{2}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.43ex; " SRC="|."$dir".q|img1800.png"
 ALT="$\displaystyle \simeq 1 +\frac{{{\mit\Pi}}_i^{2}}{{{\mit\Omega}}_i^{2}},$">|; 

$key = q/displaystylesimeq1-frac{{{mitPi}}_e^{2}}{omega^2+omega,{{mitOmega}}_e+{{mitOmega}}_e,{{mitOmega}}_i},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.30ex; vertical-align: -1.96ex; " SRC="|."$dir".q|img1718.png"
 ALT="$\displaystyle \simeq 1 - \frac{{{\mit\Pi}}_e^{2}}
{\omega^2+\omega {{\mit\Omega}}_e + {{\mit\Omega}}_e {{\mit\Omega}}_i},$">|; 

$key = q/displaystylesimeq1-frac{{{mitPi}}_e^{2}}{omega^2-omega,{{mitOmega}}_e+{{mitOmega}}_e,{{mitOmega}}_i},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.30ex; vertical-align: -1.96ex; " SRC="|."$dir".q|img1720.png"
 ALT="$\displaystyle \simeq 1 - \frac{{{\mit\Pi}}_e^{2}}
{\omega^2-\omega {{\mit\Omega}}_e+
{{\mit\Omega}}_e {{\mit\Omega}}_i },$">|; 

$key = q/displaystylesimeq1-frac{{{mitPi}}_e^{2}}{omega^2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img1722.png"
 ALT="$\displaystyle \simeq 1- \frac{{{\mit\Pi}}_e^{2}}{\omega^2}.$">|; 

$key = q/displaystylesimeqfrac{1}{2,c}sum_sfrac{nu_s,{mitPi}_s^{2}}{omega^2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.91ex; vertical-align: -2.62ex; " SRC="|."$dir".q|img1894.png"
 ALT="$\displaystyle \simeq \frac{1}{2 c}\sum_s \frac{\nu_s {\mit\Pi}_s^{2}}{\omega^2},$">|; 

$key = q/displaystylesimeqfrac{1}{2sqrt{pi}},|hat{z}|^{1slash4},expleft(+2sqrt{|hat{z}|}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -2.30ex; " SRC="|."$dir".q|img2016.png"
 ALT="$\displaystyle \simeq \frac{1}{2\sqrt{\pi}} \vert\hat{z}\vert^{1/4} \exp\left(+2\sqrt{\vert\hat{z}\vert}\right),$">|; 

$key = q/displaystylesimeqfrac{1}{sqrt{pi}},hat{z}^{1slash4},cosleft(2sqrt{z}-frac{3}{4},piright),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.52ex; vertical-align: -2.30ex; " SRC="|."$dir".q|img2023.png"
 ALT="$\displaystyle \simeq \frac{1}{\sqrt{\pi}} \hat{z}^{1/4} \cos\left(2\sqrt{z}-\frac{3}{4} \pi\right),$">|; 

$key = q/displaystylesimeqfrac{1}{sqrt{pi}},hat{z}^{1slash4},sinleft(2sqrt{z}-frac{3}{4},piright),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.52ex; vertical-align: -2.30ex; " SRC="|."$dir".q|img2025.png"
 ALT="$\displaystyle \simeq \frac{1}{\sqrt{\pi}} \hat{z}^{1/4} \sin\left(2\sqrt{z}
-\frac{3}{4} \pi\right),$">|; 

$key = q/displaystylesimeqfrac{omega}{c}left(1-frac{{mitPi}_e^{2}}{2,omega^2}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.52ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1892.png"
 ALT="$\displaystyle \simeq \frac{\omega}{c}\left(1-\frac{{\mit\Pi}_e^{2}}{2 \omega^2}\right),$">|; 

$key = q/displaystylesimeqfrac{sqrt{pi}}{2},|hat{z}|^{1slash4},expleft(-2sqrt{|hat{z}|}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img2018.png"
 ALT="$\displaystyle \simeq \frac{\sqrt{\pi}}{2} \vert\hat{z}\vert^{1/4} \exp\left(-2\sqrt{\vert\hat{z}\vert}\right),$">|; 

$key = q/displaystylesimeqmpn^{1slash2},expleft(pm{rmi},k_0!int^z!n,dz'right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1943.png"
 ALT="$\displaystyle \simeq \mp n^{1/2} \exp\left(\pm {\rm i} k_0\! \int^z\! n dz'\right),$">|; 

$key = q/displaystylesimeqmpq^{1slash2},expleft(pm{rmi},k_0int_0^zq,dz'right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2189.png"
 ALT="$\displaystyle \simeq \mp q^{1/2} \exp\left(\pm {\rm i} k_0\int_0^z q dz'\right),$">|; 

$key = q/displaystylesimeqn,q^{-1slash2},expleft(pm{rmi},k_0int_0^zq,dz'right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2196.png"
 ALT="$\displaystyle \simeq n q^{-1/2} \exp\left(\pm {\rm i} k_0\int_0^z q dz'\right),$">|; 

$key = q/displaystylesimeqn^{-1slash2},expleft(pm{rmi},k_0!int^z!n,dz'right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1941.png"
 ALT="$\displaystyle \simeq n^{-1/2} \exp\left(\pm {\rm i}  k_0 \!\int^z \!n dz'\right),$">|; 

$key = q/displaystylesimeqpmn^{-1},q^{1slash2},expleft(pm{rmi},k_0int_0^zq,dz'right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2198.png"
 ALT="$\displaystyle \simeq \pm n^{-1} q^{1/2} \exp\left(\pm {\rm i} k_0\int_0^z q dz'\right),$">|; 

$key = q/displaystylesimeqq^{-1slash2},expleft(pm{rmi},k_0int_0^zq,dz'right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2188.png"
 ALT="$\displaystyle \simeq q^{-1/2} \exp\left(\pm {\rm i} k_0\int_0^z q dz'\right),$">|; 

$key = q/displaystylesimeq{bfV}_E+{bfV}_{ast,e},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1520.png"
 ALT="$\displaystyle \simeq {\bf V}_E + {\bf V}_{\ast e},$">|; 

$key = q/displaystylesimeq{bfV}_E+{bfV}_{ast,i}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1522.png"
 ALT="$\displaystyle \simeq {\bf V}_E + {\bf V}_{\ast i}.$">|; 

$key = q/displaystylesimfrac{hat{B}_ast,S}{hat{k},P^{1slash2}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.35ex; vertical-align: -1.96ex; " SRC="|."$dir".q|img3754.png"
 ALT="$\displaystyle \sim \frac{\hat{B}_\ast S}{\hat{k} P^{1/2}},$">|; 

$key = q/displaystylesimlambda,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img1424.png"
 ALT="$\displaystyle \sim \lambda,$">|; 

$key = q/displaystylesimleft(frac{hat{B}_ast,S}{pi,P^{1slash2}}right)^{1slash2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.02ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3755.png"
 ALT="$\displaystyle \sim \left(\frac{\hat{B}_\ast S}{\pi P^{1/2}}\right)^{1/2},$">|; 

$key = q/displaystylesimleft(frac{hat{B}_ast,S}{pi}right)^{1slash2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.02ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3653.png"
 ALT="$\displaystyle \sim \left(\frac{\hat{B}_\ast S}{\pi}\right)^{1/2}.$">|; 

$key = q/displaystylesimleft(frac{pi,P^{1slash2}}{hat{B}_ast,S}right)^{1slash2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.91ex; vertical-align: -2.23ex; " SRC="|."$dir".q|img3756.png"
 ALT="$\displaystyle \sim \left(\frac{\pi P^{1/2}}{\hat{B}_\ast S}\right)^{1/2},$">|; 

$key = q/displaystylesimleft(frac{pi}{hat{B}_ast,S}right)^{1slash2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.23ex; " SRC="|."$dir".q|img3651.png"
 ALT="$\displaystyle \sim \left(\frac{\pi}{\hat{B}_\ast S}\right)^{1/2},$">|; 

$key = q/displaystylesimv_t,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1430.png"
 ALT="$\displaystyle \sim v_t,$">|; 

$key = q/displaystylesim{mitOmega}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1432.png"
 ALT="$\displaystyle \sim {\mit\Omega}.$">|; 

$key = q/displaystylesin^2alpha_l=frac{cos^6vartheta_E}{(1+3sin^2vartheta_E)^{1slash2}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.52ex; vertical-align: -2.29ex; " SRC="|."$dir".q|img461.png"
 ALT="$\displaystyle \sin^2\alpha_l = \frac{\cos^6\vartheta_E}{(1+3\sin^2\vartheta_E)^{1/2}},$">|; 

$key = q/displaystylesin^2alpha_l=left(4,L^6-3,L^5right)^{-1slash2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.68ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img466.png"
 ALT="$\displaystyle \sin^2\alpha_l = \left(4 L^6 - 3 L^5\right)^{-1/2}.$">|; 

$key = q/displaystylesin^2alpha_{rmeq}=frac{B_{rmeq}}{B_m}=frac{cos^6vartheta_m}{(1+3,sin^2vartheta_m)^{1slash2}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.52ex; vertical-align: -2.29ex; " SRC="|."$dir".q|img458.png"
 ALT="$\displaystyle \sin^2\alpha_{\rm eq} = \frac{B_{\rm eq}}{B_m} = \frac{\cos^6\vartheta_m}
{(1+3 \sin^2\vartheta_m)^{1/2}},$">|; 

$key = q/displaystyleskew{3}bar{phi}(p)=Aleft[1-frac{2,Gamma(3slash4)}{Gamma(1slash4)},Q^{1slash4},p+{calO}(p^{2})right].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3403.png"
 ALT="$\displaystyle \skew{3}\bar{\phi}(p) = A\left[1- \frac{2 \Gamma(3/4)}{\Gamma(1/4)}  Q^{1/4} p + {\cal O}(p^{2})\right].$">|; 

$key = q/displaystyleskew{3}bar{phi}(p)=Bleft(-frac{Q}{p}+pright)+C+{calO}(p^{2}),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3407.png"
 ALT="$\displaystyle \skew{3}\bar{\phi}(p) = B \left(-\frac{Q}{p} + p\right) + C +{\cal O}(p^{2}),$">|; 

$key = q/displaystyleskew{3}bar{phi}(p)=frac{a_{-1}}{p}+a_0+a_{-1}left(frac{Q^2}{2}-frac{1}{Q}right)p+frac{a_0,Q^2,p^2}{6}+{calO}(p^3).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3430.png"
 ALT="$\displaystyle \skew{3}\bar{\phi}(p)= \frac{a_{-1}}{p}+a_0+a_{-1}\left(\frac{Q^2}{2}-\frac{1}{Q}\right)p + \frac{a_0 Q^2 p^2}{6}+{\cal O}(p^3).$">|; 

$key = q/displaystyleskew{3}bar{phi}(p)=frac{a_{-1}}{p}+a_0+{calO}(p),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img3387.png"
 ALT="$\displaystyle \skew{3}\bar{\phi}(p) = \frac{a_{-1}}{p} + a_0 + {\cal O}(p),$">|; 

$key = q/displaystyleskew{3}bar{phi}=A,left[frac{2,Gamma(3slash4)}{Gamma(1slash4)},frac{Q^{5slash4}}{p}+1+{calO}(p)right].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.52ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3409.png"
 ALT="$\displaystyle \skew{3}\bar{\phi} = A \left[\frac{2 \Gamma(3/4)}{\Gamma(1/4)}  \frac{Q^{5/4}}{p} + 1 + {\cal O}(p)\right].$">|; 

$key = q/displaystyleskew{3}dot{r}=-frac{dot{z}}{z^{2}}=-r^{2},frac{dz}{dtheta},frac{dtheta}{dt}=-h,frac{dz}{dtheta}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.80ex; " SRC="|."$dir".q|img695.png"
 ALT="$\displaystyle \skew{3}\dot{r} = -\frac{\dot{z}}{z^{2}} = -r^{2} \frac{dz}{d\theta} \frac{d\theta}{dt} = -h \frac{dz}{d\theta}.$">|; 

$key = q/displaystyleskew{3}hat{delta}simfrac{1}{S^{1slash3},delta_p}simleft(frac{hat{gamma}}{S}right)^{1slash4}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.91ex; vertical-align: -2.26ex; " SRC="|."$dir".q|img3419.png"
 ALT="$\displaystyle \skew{3}\hat{\delta} \sim \frac{1}{S^{1/3} \delta_p} \sim \left(
\frac{\hat{\gamma}}{S}\right)^{1/4}.$">|; 

$key = q/displaystyleskew{3}hat{mitPhi}(0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1611.png"
 ALT="$\displaystyle \skew{3}\hat{\mit\Phi}(0)$">|; 

$key = q/displaystyleskew{3}hat{phi}(hat{x});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3360.png"
 ALT="$\displaystyle \skew{3}\hat{\phi}(\hat{x})$">|; 

$key = q/displaystyleskew{3}hat{phi}(hat{x})=2,{rmi}left[frac{a_0}{S^{1slash3},hat{x}}+frac{pi,a_{-1}}{2},{rmsgn}(hat{x})+{calO}(hat{x}^2)right].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.35ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img3392.png"
 ALT="$\displaystyle \skew{3}\hat{\phi}(\hat{x})= 2 {\rm i}\left[\frac{a_0}{S^{1/3} \hat{x}} + \frac{\pi a_{-1}}{2} {\rm sgn}(\hat{x})
+{\cal O}(\hat{x}^2)\right].$">|; 

$key = q/displaystyleskew{3}hat{phi}(s,k,xi)=frac{{mitDelta}'}{I_1},H(s,k,xi),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.85ex; vertical-align: -1.95ex; " SRC="|."$dir".q|img3593.png"
 ALT="$\displaystyle \skew{3}\hat{\phi}(s,k,\xi) = \frac{{\mit\Delta}'}{I_1} H(s,k,\xi),$">|; 

$key = q/displaystyleskew{3}hat{phi};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3327.png"
 ALT="$\displaystyle \skew{3}\hat{\phi}$">|; 

$key = q/displaystylesqrt{2pi,z},I_m(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3023.png"
 ALT="$\displaystyle \sqrt{2\pi z} I_m(z)$">|; 

$key = q/displaystylesqrt{a,hat{z}},,I_1!left(2sqrt{a,hat{z}}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.23ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img2015.png"
 ALT="$\displaystyle \sqrt{a \hat{z}}  I_1\!\left(2\sqrt{a \hat{z}}\right)$">|; 

$key = q/displaystylesqrt{a,hat{z}},,K_1!left(2sqrt{a,hat{z}}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.23ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img2017.png"
 ALT="$\displaystyle \sqrt{a \hat{z}}  K_1\!\left(2\sqrt{a \hat{z}}\right)$">|; 

$key = q/displaystylesqrt{a,hat{z}},I_1!left(2sqrt{a,hat{z}}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.23ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img2006.png"
 ALT="$\displaystyle \sqrt{a \hat{z}}  I_1\!\left(2\sqrt{a \hat{z}}\right)$">|; 

$key = q/displaystylesqrt{a,hat{z}},K_1!left(2sqrt{a,hat{z}}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.23ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img2010.png"
 ALT="$\displaystyle \sqrt{a \hat{z}} K_1\!\left(2\sqrt{a \hat{z}}\right)$">|; 

$key = q/displaystylesqrt{frac{2,z}{pi}},K_m(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -1.82ex; " SRC="|."$dir".q|img3021.png"
 ALT="$\displaystyle \sqrt{\frac{2 z}{\pi}} K_m(z)$">|; 

$key = q/displaystylesqrt{hat{z}},,J_1!left(2sqrt{hat{z}}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.23ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img2022.png"
 ALT="$\displaystyle \sqrt{\hat{z}}  J_1\!\left(2\sqrt{\hat{z}}\right)$">|; 

$key = q/displaystylesqrt{hat{z}},,Y_1!left(2sqrt{hat{z}}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.23ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img2024.png"
 ALT="$\displaystyle \sqrt{\hat{z}}  Y_1\!\left(2\sqrt{\hat{z}}\right)$">|; 

$key = q/displaystylesqrt{hat{z}},J_1!left(2sqrt{hat{z}}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.23ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img2004.png"
 ALT="$\displaystyle \sqrt{\hat{z}} J_1\!\left(2\sqrt{\hat{z}}\right)$">|; 

$key = q/displaystylesqrt{hat{z}},Y_1!left(2sqrt{hat{z}}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.23ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img2008.png"
 ALT="$\displaystyle \sqrt{\hat{z}} Y_1\!\left(2\sqrt{\hat{z}}\right)$">|; 

$key = q/displaystylesum_s(w_s+{bfV}_scdot{bfF}_s)=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -2.62ex; " SRC="|."$dir".q|img1053.png"
 ALT="$\displaystyle \sum_s (w_s + {\bf V}_s\cdot{\bf F}_s) = 0.$">|; 

$key = q/displaystylesum_s{bfF}_s={bf0}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -2.62ex; " SRC="|."$dir".q|img1046.png"
 ALT="$\displaystyle \sum_s {\bf F}_s = {\bf0}.$">|; 

$key = q/displaystylesum_{n=-infty,infty}{rme}^{-lambda_s},I_n(lambda_s)=1.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -2.80ex; " SRC="|."$dir".q|img2516.png"
 ALT="$\displaystyle \sum_{n=-\infty,\infty} {\rm e}^{-\lambda_s} I_n(\lambda_s) = 1.$">|; 

$key = q/displaystylet=frac{1}{c}int_z^aleft[frac{partial(omega,n)}{partialomega}right]_{omega=omega_0}dz'.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.74ex; vertical-align: -2.52ex; " SRC="|."$dir".q|img2080.png"
 ALT="$\displaystyle t = \frac{1}{c} \int_z^a \left[\frac{\partial(\omega  n)}{\partial\omega}
\right]_{\omega=\omega_0} dz'.$">|; 

$key = q/displaystylet=int_z^afrac{dz'}{u_z}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -2.17ex; " SRC="|."$dir".q|img2083.png"
 ALT="$\displaystyle t =\int_z^a \frac{dz'}{u_z}.$">|; 

$key = q/displaystyletan^2theta=-frac{P,(n^2-R),(n^2-L)}{(S,n^2-R,L),(n^2-P)}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img1754.png"
 ALT="$\displaystyle \tan^2\theta = -\frac{P (n^2-R) (n^2-L)}{(S n^2 - R L) (n^2-P)}.$">|; 

$key = q/displaystyletan^2theta=-frac{P}{S}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1775.png"
 ALT="$\displaystyle \tan^2\theta = -\frac{P}{S}.$">|; 

$key = q/displaystyletanh(e,{mitPhi}slash4,T)=tanh(e,Vslash4,T),{rme}^{-|x|slashlambda_D},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img198.png"
 ALT="$\displaystyle \tanh(e {\mit\Phi}/4 T)= \tanh(e V/4 T) {\rm e}^{-\vert x\vert/\lambda_D},
$">|; 

$key = q/displaystyletau=tslashepsilon.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img239.png"
 ALT="$\displaystyle \tau = t/\epsilon.$">|; 

$key = q/displaystyletau_H=frac{L}{V};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3039.png"
 ALT="$\displaystyle \tau_H = \frac{L}{V}$">|; 

$key = q/displaystyletau_H=frac{k^{-1}}{(B_0^{2}slashmu_0,rho)^{1slash2}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.74ex; vertical-align: -2.46ex; " SRC="|."$dir".q|img3307.png"
 ALT="$\displaystyle \tau_H = \frac{k^{-1}}{(B_0^{2}/\mu_0 \rho)^{1/2}},$">|; 

$key = q/displaystyletau_M=frac{rho_0,a^2}{mu};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.35ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img3743.png"
 ALT="$\displaystyle \tau_M = \frac{\rho_0 a^2}{\mu}
$">|; 

$key = q/displaystyletau_R;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img2992.png"
 ALT="$\displaystyle \tau_R$">|; 

$key = q/displaystyletau_R=frac{mu_0,a^2}{eta},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.35ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img3308.png"
 ALT="$\displaystyle \tau_R = \frac{\mu_0 a^2}{\eta},$">|; 

$key = q/displaystyletau_b(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img546.png"
 ALT="$\displaystyle \tau_b(t)$">|; 

$key = q/displaystyletau_b=4int_0^{vartheta_m}frac{dvartheta}{|v_parallel|}frac{ds}{dvartheta},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.58ex; vertical-align: -2.19ex; " SRC="|."$dir".q|img470.png"
 ALT="$\displaystyle \tau_b = 4\int_0^{\vartheta_m} \frac{d\vartheta}{\vert v_\parallel\vert}\frac{ds}{d\vartheta},$">|; 

$key = q/displaystyletau_b=frac{2pi,L}{sinalphasqrt{2,{calE}slashm}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -2.30ex; " SRC="|."$dir".q|img538.png"
 ALT="$\displaystyle \tau_b = \frac{2\pi L}{\sin\alpha\sqrt{2 {\cal E}/m}}.
$">|; 

$key = q/displaystyletau_b=frac{sqrt{2},pi,r_{rmeq}}{({calE}slashm)^{1slash2}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.58ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img534.png"
 ALT="$\displaystyle \tau_b =\frac{ \sqrt{2} \pi r_{\rm eq}}{({\cal E}/m)^{1/2}}.
$">|; 

$key = q/displaystyletau_bsim2pisqrt{frac{m_e}{e,k^2,{mitPhi}_0}}=2pisqrt{frac{m_e}{e,k,E_0}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.23ex; " SRC="|."$dir".q|img2316.png"
 ALT="$\displaystyle \tau_b \sim 2\pi\sqrt{\frac{m_e}{e k^2 {\mit\Phi}_0}} =
2\pi\sqrt{\frac{m_e}{e k E_0}},$">|; 

$key = q/displaystyletau_bsimeqfrac{L,R_E}{({calE}slashm)^{1slash2}},(3.7-1.6sinalpha_{rmeq}).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.85ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img473.png"
 ALT="$\displaystyle \tau_b \simeq \frac{L R_E}{({\cal E}/m)^{1/2}}  (3.7-1.6\sin\alpha_{\rm eq}).$">|; 

$key = q/displaystyletau_e=frac{6!sqrt{2}pi^{3slash2},epsilon_0^{2},sqrt{m_e},,T_e^{3slash2}}{ln{mitLambda}_c,e^4,n},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.63ex; vertical-align: -1.96ex; " SRC="|."$dir".q|img1136.png"
 ALT="$\displaystyle \tau_e = \frac{6\!\sqrt{2}\pi^{3/2} \epsilon_0^{2} \sqrt{m_e}  T_e^{3/2}}
{\ln{\mit\Lambda}_c  e^4  n},$">|; 

$key = q/displaystyletau_i=frac{12pi^{3slash2},epsilon_0^{2},sqrt{m_i},,T_i^{3slash2}}{ln{mitLambda}_c,e^4,n},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.63ex; vertical-align: -1.96ex; " SRC="|."$dir".q|img1137.png"
 ALT="$\displaystyle \tau_i = \frac{ 12\pi^{3/2} \epsilon_0^{2} \sqrt{m_i}  T_i^{3/2}}
{\ln{\mit\Lambda}_c  e^4  n},$">|; 

$key = q/displaystyletau_psimfrac{1}{gamma_p}simepsilon^{-3slash2},tau_A^{5slash4},tau_R^{-1slash4}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.19ex; vertical-align: -2.26ex; " SRC="|."$dir".q|img3717.png"
 ALT="$\displaystyle \tau_p \sim\frac{1}{\gamma_p} \sim \epsilon^{-3/2} \tau_A^{5/4} \tau_R^{-1/4}.$">|; 

$key = q/displaystyletau_{ee}=frac{12pi^{3slash2},epsilon_0^{2},m_e^{1slash2},T^{3slash2}}{ln{mitLambda}_c,e^{4},n_e},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.63ex; vertical-align: -1.96ex; " SRC="|."$dir".q|img969.png"
 ALT="$\displaystyle \tau_{ee} =\frac{12\pi^{3/2} \epsilon_0^{2} m_e^{1/2} T^{3/2}}{\ln{\mit\Lambda}_c e^{4} n_e},$">|; 

$key = q/displaystyletau_{ee}simtau_{ei}sim(m_eslashm_i)^{1slash2},tau_{ii}sim(m_islashm_e),tau_{ie},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img974.png"
 ALT="$\displaystyle \tau_{ee}\sim \tau_{ei}\sim (m_e/m_i)^{1/2} \tau_{ii}\sim (m_i/m_e) \tau_{ie},$">|; 

$key = q/displaystyletau_{ei}=frac{6!sqrt{2}pi^{3slash2},epsilon_0^{2},m_e^{1slash2},T^{3slash2}}{ln{mitLambda}_c,e^{4},n_e},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.63ex; vertical-align: -1.96ex; " SRC="|."$dir".q|img970.png"
 ALT="$\displaystyle \tau_{ei} =\frac{6\!\sqrt{2}\pi^{3/2} \epsilon_0^{2} m_e^{1/2} T^{3/2}}{\ln{\mit\Lambda}_c e^{4} n_e},$">|; 

$key = q/displaystyletau_{ie}=frac{6!sqrt{2}pi^{3slash2},epsilon_0^{2},m_i,T^{3slash2}}{ln{mitLambda}_c,e^{4},n_e,m_e^{1slash2}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.02ex; vertical-align: -2.36ex; " SRC="|."$dir".q|img973.png"
 ALT="$\displaystyle \tau_{ie} =\frac{6\!\sqrt{2}\pi^{3/2} \epsilon_0^{2} m_i T^{3/2}}{\ln{\mit\Lambda}_c e^{4} n_e m_e^{1/2}},$">|; 

$key = q/displaystyletau_{ii}=frac{12pi^{3slash2},epsilon_0^{2},m_i^{1slash2},T^{3slash2}}{ln{mitLambda}_c,e^{4},n_e},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.63ex; vertical-align: -1.96ex; " SRC="|."$dir".q|img972.png"
 ALT="$\displaystyle \tau_{ii} =\frac{12\pi^{3/2} \epsilon_0^{2} m_i^{1/2} T^{3/2}}{\ln{\mit\Lambda}_c e^{4} n_e},$">|; 

$key = q/displaystyletau_{rmSP}=sqrt{2pi},tau_H^{1slash2},tau_R^{1slash2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.79ex; vertical-align: -0.77ex; " SRC="|."$dir".q|img3663.png"
 ALT="$\displaystyle \tau_{\rm SP} = \sqrt{2\pi} \tau_H^{1/2} \tau_R^{1/2}.$">|; 

$key = q/displaystyletau_{rmSP}simepsilon^{-1},tau_A^{1slash2},tau_R^{1slash2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.68ex; vertical-align: -0.77ex; " SRC="|."$dir".q|img3718.png"
 ALT="$\displaystyle \tau_{\rm SP} \sim \epsilon^{-1} \tau_A^{1/2} \tau_R^{1/2},$">|; 

$key = q/displaystyletau_{rmohm}=mu_0,sigma,L^2,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2882.png"
 ALT="$\displaystyle \tau_{\rm ohm} = \mu_0 \sigma L^2,$">|; 

$key = q/displaystyletau_{ss'}=frac{3pi^{1slash2},m_s,mu_{ss'},(v_{t,s}^{2}+v_{t,{s'}}^{2})^{3slash2}}{8,gamma_{ss'},n_{s'}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.52ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img967.png"
 ALT="$\displaystyle \tau_{ss'} = \frac{3\pi^{1/2} m_s \mu_{ss'} (v_{t s}^{2}+v_{t {s'}}^{2})^{3/2}}{8 \gamma_{ss'} n_{s'}}.$">|; 

$key = q/displaystyletausimfrac{1}{n,r_c^{2},v_t}simfrac{epsilon_0^{2}sqrt{m},,T^{3slash2}}{e^4,n}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.63ex; vertical-align: -2.18ex; " SRC="|."$dir".q|img1141.png"
 ALT="$\displaystyle \tau \sim \frac{1}{n r_c^{2} v_t} \sim \frac{\epsilon_0^{2}\sqrt{m}  T^{3/2}}
{e^4 n}.$">|; 

$key = q/displaystyletausimfrac{l}{v_t}simfrac{1}{n,sigma^2,v_t},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.96ex; " SRC="|."$dir".q|img1139.png"
 ALT="$\displaystyle \tau \sim \frac{l}{v_t} \sim \frac{1}{n \sigma^2 v_t},$">|; 

$key = q/displaystyletausimtau_R,hat{delta}^{2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3424.png"
 ALT="$\displaystyle \tau \sim \tau_R \hat{\delta}^{2}.$">|; 

$key = q/displaystyletimes[sigma'({bfv}_s',{bfv}_{s'}';{bfv}_s,{bfv}_{s'}),d^3{bfv}_s,d^3{bfv}_{s'}].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.51ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img627.png"
 ALT="$\displaystyle \times[\sigma' ({\bf v}_s', {\bf v}_{s'}';{\bf v}_s,{\bf v}_{s'}) d^3{\bf v}_s d^3{\bf v}_{s'}].$">|; 

$key = q/displaystyletimes[sigma'({bfv}_s,{bfv}_{s'};{bfv}_s',{bfv}_{s'}'),d^3{bfv}_s',d^3{bfv}_{s'}'].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.51ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img619.png"
 ALT="$\displaystyle \times[\sigma' ({\bf v}_s, {\bf v}_{s'};{\bf v}_s',{\bf v}_{s'}') d^3{\bf v}_s' d^3{\bf v}_{s'}'].$">|; 

$key = q/displaystyletimes{bfb})cdot(;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img372.png"
 ALT="$\displaystyle \times{\bf b})\cdot ($">|; 

$key = q/displaystyletimes{bfb})times(;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img321.png"
 ALT="$\displaystyle \times{\bf b})\times ($">|; 

$key = q/displaystyletimes{bfb}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img314.png"
 ALT="$\displaystyle \times {\bf b}.$">|; 

$key = q/displaystyleu-u_0=frac{e}{m},E_0,t,{rme}^{,{rmi},k,x_0},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img2310.png"
 ALT="$\displaystyle u -u_0 = \frac{e}{m} E_0 t {\rm e}^{ {\rm i} k x_0},$">|; 

$key = q/displaystyleu-u_0=frac{e}{m},E_0left[frac{{rme}^{,{rmi},(k,x_0+k,u_0,t-omega,t)}-{rme}^{,{rmi},k,x_0}}{{rmi},(k,u_0-omega)}right].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.52ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2308.png"
 ALT="$\displaystyle u-u_0 = \frac{e}{m} E_0\left[\frac{{\rm e}^{ {\rm i} (k x_0+k...
...,t-\omega t)}
- {\rm e}^{ {\rm i} k x_0}}{{\rm i} (k u_0-\omega)}\right].$">|; 

$key = q/displaystyleu>V_A,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img2836.png"
 ALT="$\displaystyle u &gt; V_A,$">|; 

$key = q/displaystyleu^2(r_c)=u_c^{2}equivfrac{2,T}{m_p},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.19ex; vertical-align: -2.26ex; " SRC="|."$dir".q|img2786.png"
 ALT="$\displaystyle u^2(r_c) = u_c^{2} \equiv \frac{2 T}{m_p},$">|; 

$key = q/displaystyleu^2=u_0^{2}left[1+frac{2,u_c^{2},x^2}{u_0^{2}-u_c^{2}}+{calO}(x^3)right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.80ex; vertical-align: -2.46ex; " SRC="|."$dir".q|img3215.png"
 ALT="$\displaystyle u^2 = u_0^{2}\left[1+\frac{2 u_c^{2} x^2}{u_0^{2}-u_c^{2}} + {\cal O}(x^3)\right],
$">|; 

$key = q/displaystyleu^2=u_c^{2}left[1pm2,x+{calO}(x^2)right];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.29ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img3214.png"
 ALT="$\displaystyle u^2= u_c^{2}\left[1\pm 2 x + {\cal O}(x^2)\right]
$">|; 

$key = q/displaystyleu_infty=left(frac{2,E_{ss'}}{mu_{ss'}}right)^{1slash2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img697.png"
 ALT="$\displaystyle u_\infty = \left(\frac{2 E_{ss'}}{\mu_{ss'}}\right)^{1/2},$">|; 

$key = q/displaystyleu_phi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2817.png"
 ALT="$\displaystyle u_\phi$">|; 

$key = q/displaystyleu_phi=frac{{mitOmega},r}{u_{r,A}}frac{u_{r,A}-u_r}{1-M_A^{2}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.30ex; vertical-align: -2.41ex; " SRC="|."$dir".q|img2874.png"
 ALT="$\displaystyle u_\phi = \frac{{\mit\Omega} r}{u_{r A}} \frac{u_{r A} - u_r}{1-M_A^{2}}.$">|; 

$key = q/displaystyleu_phi={mitOmega},r;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2846.png"
 ALT="$\displaystyle u_\phi = {\mit\Omega} r$">|; 

$key = q/displaystyleu_phi={mitOmega},r_Aleft(frac{r_A}{r}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.29ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img2847.png"
 ALT="$\displaystyle u_\phi = {\mit\Omega} r_A\left(\frac{r_A}{r}\right)$">|; 

$key = q/displaystyleu_phirightarrow{mitOmega},r_Aleft(frac{r_A}{r}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.29ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img2877.png"
 ALT="$\displaystyle u_\phi \rightarrow {\mit\Omega} r_A\left(\frac{r_A}{r}\right)$">|; 

$key = q/displaystyleu_phirightarrow{mitOmega},r_Aleft(frac{r_A}{r}right)left(1-frac{u_{r,A}}{u_r}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2876.png"
 ALT="$\displaystyle u_\phi \rightarrow {\mit\Omega} r_A\left(\frac{r_A}{r}\right)\left(1-\frac{u_{r A}}
{u_r}\right)$">|; 

$key = q/displaystyleu_r;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img2814.png"
 ALT="$\displaystyle u_r$">|; 

$key = q/displaystyleu_theta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2816.png"
 ALT="$\displaystyle u_\theta$">|; 

$key = q/displaystyleu_z(omega,z)=cleft[1-frac{{mitPi}_e^{2}(z)}{omega^2}right]^{1slash2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.97ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2088.png"
 ALT="$\displaystyle u_z(\omega,z) = c \left[1-\frac{{\mit\Pi}_e^{2}(z)}{\omega^2}\right]^{1/2}.$">|; 

$key = q/displaystyleu_z(omega_0,z)=cleftslashleft(frac{partial[omega,n(omega,z)]}{partialomega}right)_{omega=omega_0}right..;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.74ex; vertical-align: -2.52ex; " SRC="|."$dir".q|img2084.png"
 ALT="$\displaystyle u_z(\omega_0,z) = c\left/ \left(\frac{\partial[\omega  n(\omega,z)]}{\partial\omega}
\right)_{\omega=\omega_0}\right..$">|; 

$key = q/displaystyleu_{ss'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img997.png"
 ALT="$\displaystyle u_{ss'}$">|; 

$key = q/displaystyleuproptofrac{1}{r^{2}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img2799.png"
 ALT="$\displaystyle u\propto \frac{1}{r^{2}}.$">|; 

$key = q/displaystyleusimeq2,u_cleft[lnleft(frac{r}{r_c}right)right]^{1slash2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2803.png"
 ALT="$\displaystyle u \simeq 2 u_c\left[\ln\left(\frac{r}{r_c}\right)\right]^{1/2}.$">|; 

$key = q/displaystylev_0simfrac{E_z}{B_ast}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.74ex; vertical-align: -1.88ex; " SRC="|."$dir".q|img3632.png"
 ALT="$\displaystyle v_0 \sim \frac{E_z}{B_\ast}.$">|; 

$key = q/displaystylev_1^{2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.66ex; " SRC="|."$dir".q|img3172.png"
 ALT="$\displaystyle v_1^{2}$">|; 

$key = q/displaystylev_1^{2}simeqfrac{r_m}{{mitGamma}-1},frac{2,V_{S,1}^{2}+sin^2theta_1,[{mitGamma}+(2-{mitGamma}),r_m],V_{A,1}^{2}}{r_m-r}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.58ex; vertical-align: -1.96ex; " SRC="|."$dir".q|img3186.png"
 ALT="$\displaystyle v_1^{2} \simeq \frac{r_m}{{\mit\Gamma}-1} \frac{2 V_{S 1}^{2}+\sin^2\theta_1 [{\mit\Gamma}
+ (2-{\mit\Gamma}) r_m] V_{A 1}^{2}}{r_m-r}.$">|; 

$key = q/displaystylev_dsimdelta,v_t.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1551.png"
 ALT="$\displaystyle v_d \sim \delta v_t.$">|; 

$key = q/displaystylev_esimv_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1429.png"
 ALT="$\displaystyle v_e \sim v_i$">|; 

$key = q/displaystylev_g=frac{domega}{dk}=2,c,frac{sqrt{omega,|{{mitOmega}}_e|}}{{{mitPi}}_e}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.30ex; vertical-align: -1.96ex; " SRC="|."$dir".q|img1848.png"
 ALT="$\displaystyle v_g = \frac{d\omega}{dk} = 2 c \frac{\sqrt{\omega \vert{{\mit\Omega}}_e\vert}}{{{\mit\Pi}}_e}.$">|; 

$key = q/displaystylev_parallel;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img532.png"
 ALT="$\displaystyle v_\parallel$">|; 

$key = q/displaystylev_perp;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img530.png"
 ALT="$\displaystyle v_\perp$">|; 

$key = q/displaystylev_t=sqrt{frac{2,T}{m}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -1.81ex; " SRC="|."$dir".q|img1129.png"
 ALT="$\displaystyle v_t = \sqrt{\frac{2 T}{m}}$">|; 

$key = q/displaystylev_z(omega,z)=frac{c}{n(omega,z)}=cleft[1-frac{{mitPi}_e^{2}(z)}{omega^2}right]^{-1slash2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.97ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2087.png"
 ALT="$\displaystyle v_z(\omega,z) = \frac{c}{n(\omega,z)} = c\left[1-\frac{{\mit\Pi}_e^{2}(z)}{\omega^2}\right]^{-1/2}.$">|; 

$key = q/displaystylev_z,u_z=c^2.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2089.png"
 ALT="$\displaystyle v_z u_z = c^2.$">|; 

$key = q/displaystylev_{t,i}simleft(frac{m_e}{m_i}right)^{1slash2}v_{t,e}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img40.png"
 ALT="$\displaystyle v_{t i} \sim \left(\frac{m_e}{m_i}\right)^{1/2}v_{t e}.$">|; 

$key = q/displaystylev_{t,s}equivleft(frac{2,T}{m_s}right)^{1slash2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img39.png"
 ALT="$\displaystyle v_{t s} \equiv \left(\frac{2 T}{m_s}\right)^{1/2}.$">|; 

$key = q/displaystylevarphi';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3597.png"
 ALT="$\displaystyle \varphi'$">|; 

$key = q/displaystylevarphi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3595.png"
 ALT="$\displaystyle \varphi$">|; 

$key = q/displaystylew_T;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img1302.png"
 ALT="$\displaystyle w_T$">|; 

$key = q/displaystylew_U;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1300.png"
 ALT="$\displaystyle w_U$">|; 

$key = q/displaystylew_e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1161.png"
 ALT="$\displaystyle w_e$">|; 

$key = q/displaystylew_e=-w_i+w_U+w_T,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1299.png"
 ALT="$\displaystyle w_e = -w_i + w_U + w_T,$">|; 

$key = q/displaystylew_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1159.png"
 ALT="$\displaystyle w_i$">|; 

$key = q/displaystylew_isimeq0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1496.png"
 ALT="$\displaystyle w_i \simeq 0,$">|; 

$key = q/displaystylew_isimfrac{n}{tau_e},frac{2,m_e}{m_i},frac{3}{2},(T_e-T_i).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.96ex; " SRC="|."$dir".q|img1194.png"
 ALT="$\displaystyle w_i \sim \frac{n}{\tau_e}  \frac{2 m_e}{m_i} \frac{3}{2}  (T_e-T_i).$">|; 

$key = q/displaystylew_sequivsum_{s'}w_{ss'}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -2.62ex; " SRC="|."$dir".q|img1050.png"
 ALT="$\displaystyle w_s \equiv \sum_{s'} w_{ss'}.$">|; 

$key = q/displaystylew_{ss',alphabeta};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img800.png"
 ALT="$\displaystyle w_{ss' \alpha\beta}$">|; 

$key = q/displaystylew_{ss',alphabeta}=frac{delta_{alphabeta}}{u_{ss'}}-frac{u_{ss',alpha},u_{ss',beta}}{u_{ss'}^{3}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.52ex; vertical-align: -2.44ex; " SRC="|."$dir".q|img795.png"
 ALT="$\displaystyle w_{ss' \alpha\beta} = \frac{\delta_{\alpha\beta}}{u_{ss'}} - \frac{u_{ss' \alpha} u_{ss' \beta}}{u_{ss'}^{3}}.$">|; 

$key = q/displaystylew_{ss'}+w_{s's}+({bfV}_s-{bfV}_{s'})cdot{bfF}_{ss'}=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1052.png"
 ALT="$\displaystyle w_{ss'} +w_{s's} +({\bf V}_s-{\bf V}_{s'})\cdot {\bf F}_{ss'} = 0,$">|; 

$key = q/displaystylew_{ss'}equivintfrac{1}{2},m_s,u_s^{2},C_{ss'},d^3{bfv}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img1049.png"
 ALT="$\displaystyle w_{ss'} \equiv \int \frac{1}{2} m_s u_s^{2} C_{ss'} d^3{\bf v}.$">|; 

$key = q/displaystylewidehat{bfB};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img1339.png"
 ALT="$\displaystyle \widehat{\bf B}$">|; 

$key = q/displaystylewidehat{bfE};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img1341.png"
 ALT="$\displaystyle \widehat{\bf E}$">|; 

$key = q/displaystylewidehat{bfF}_T;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.51ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img1355.png"
 ALT="$\displaystyle \widehat{\bf F}_T$">|; 

$key = q/displaystylewidehat{bfF}_U;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.57ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1353.png"
 ALT="$\displaystyle \widehat{\bf F}_U$">|; 

$key = q/displaystylewidehat{bfU};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img1343.png"
 ALT="$\displaystyle \widehat{\bf U}$">|; 

$key = q/displaystylewidehat{bfV}_e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.57ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1337.png"
 ALT="$\displaystyle \widehat{\bf V}_e$">|; 

$key = q/displaystylewidehat{bfV}_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.57ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1393.png"
 ALT="$\displaystyle \widehat{\bf V}_i$">|; 

$key = q/displaystylewidehat{bfq}_{Te};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1349.png"
 ALT="$\displaystyle \widehat{\bf q}_{Te}$">|; 

$key = q/displaystylewidehat{bfq}_{Ue};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1351.png"
 ALT="$\displaystyle \widehat{\bf q}_{Ue}$">|; 

$key = q/displaystylewidehat{bfq}_{i};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1401.png"
 ALT="$\displaystyle \widehat{\bf q}_{i}$">|; 

$key = q/displaystylewidehat{mbox{boldmathpi}}_e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1347.png"
 ALT="$\displaystyle \widehat{\mbox{\boldmath$\pi$}}_e$">|; 

$key = q/displaystylewidehat{mbox{boldmathpi}}_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1399.png"
 ALT="$\displaystyle \widehat{\mbox{\boldmath$\pi$}}_i$">|; 

$key = q/displaystylewidehat{nabla};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img1333.png"
 ALT="$\displaystyle \widehat{\nabla}$">|; 

$key = q/displaystylewidehat{w}_T;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img1361.png"
 ALT="$\displaystyle \widehat{w}_T$">|; 

$key = q/displaystylewidehat{w}_U;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1359.png"
 ALT="$\displaystyle \widehat{w}_U$">|; 

$key = q/displaystylewidehat{w}_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1357.png"
 ALT="$\displaystyle \widehat{w}_i$">|; 

$key = q/displaystylewidetilde{cosxi}equivcosxi-frac{langlecosxirangle}{langle1rangle},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.98ex; " SRC="|."$dir".q|img3519.png"
 ALT="$\displaystyle \widetilde{\cos\xi} \equiv \cos\xi - \frac{\langle \cos\xi\rangle}{\langle 1\rangle},$">|; 

$key = q/displaystylex'-x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img2371.png"
 ALT="$\displaystyle x'-x$">|; 

$key = q/displaystylex_0=2,Sint_0^{z_0(S)}frac{dz}{sqrt{n^2(z)-S^2}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.13ex; vertical-align: -2.70ex; " SRC="|."$dir".q|img2157.png"
 ALT="$\displaystyle x_0 = 2 S\int_0^{z_0(S)} \frac{dz}{\sqrt{n^2(z)-S^2}}.$">|; 

$key = q/displaystylex_0=2,h_0,tantheta+frac{2}{alpha},sin2theta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img2217.png"
 ALT="$\displaystyle x_0 = 2 h_0 \tan\theta + \frac{2}{\alpha} \sin2\theta
$">|; 

$key = q/displaystylex_m(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img544.png"
 ALT="$\displaystyle x_m(t)$">|; 

$key = q/displaystylexi_n=frac{omega-n,{mitOmega}_s}{k_parallel,v_s}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.13ex; vertical-align: -2.19ex; " SRC="|."$dir".q|img2421.png"
 ALT="$\displaystyle \xi_n = \frac{\omega - n {\mit\Omega}_s}{k_\parallel v_s} .$">|; 

$key = q/displaystylexsimeq1+3,y^{2}-{rmi},epsilon(1,y).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2656.png"
 ALT="$\displaystyle x\simeq 1 + 3 y^{2}-{\rm i} \epsilon(1,y).
$">|; 

$key = q/displaystyley'-y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2373.png"
 ALT="$\displaystyle y'-y$">|; 

$key = q/displaystyley;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1981.png"
 ALT="$\displaystyle y$">|; 

$key = q/displaystyley^2,frac{d^2B_pm}{dy^2}+y,frac{dB_pm}{dy}-left[(mpm1)^2+q^2,y^2right]B_pm=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.35ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img2999.png"
 ALT="$\displaystyle y^2 \frac{d^2 B_\pm}{dy^2} + y \frac{d B_\pm}{dy} -\left[(m\pm 1)^2 + q^2 y^2\right]B_\pm = 0$">|; 

$key = q/displaystyley^2,frac{d^2B_pm}{dy^2}+y,frac{dB_pm}{dy}-left[(mpm1)^2+s^2,y^2right]B_pm=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.35ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img3001.png"
 ALT="$\displaystyle y^2 \frac{d^2 B_\pm}{dy^2} + y \frac{d B_\pm}{dy} -\left[(m\pm 1)^2 + s^2 y^2\right]B_\pm = 0$">|; 

$key = q/displaystylez'-z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.27ex; " SRC="|."$dir".q|img2375.png"
 ALT="$\displaystyle z'-z$">|; 

$key = q/displaystylez({mitPi}_e)=frac{2}{pi}int_0^{pislash2}h({mitPi}_e,sinalpha),dalpha.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img2207.png"
 ALT="$\displaystyle z({\mit\Pi}_e) = \frac{2}{\pi}\int_0^{\pi/2}h({\mit\Pi}_e \sin\alpha) d\alpha.
$">|; 

$key = q/displaystylez,frac{d^2K}{dz^2}-frac{1}{2},frac{dK}{dz}-frac{1}{4},(Q^{3slash2}+z),K=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -1.80ex; " SRC="|."$dir".q|img3435.png"
 ALT="$\displaystyle z \frac{d^2K}{dz^2} -\frac{1}{2} \frac{dK}{dz} -\frac{1}{4} (Q^{3/2}+z) K = 0,$">|; 

$key = q/displaystylez,frac{d^2L}{dz^2}+left(-frac{1}{2}-zright)frac{dL}{dz}-frac{1}{4}left(Q^{3slash2}-1right)L=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3439.png"
 ALT="$\displaystyle z \frac{d^2 L}{dz^2} + \left(-\frac{1}{2}-z\right)\frac{dL}{dz} - \frac{1}{4}\left(Q^{3/2}-1\right)L = 0,$">|; 

$key = q/displaystylez=Q^{1slash2},p^2.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3434.png"
 ALT="$\displaystyle z = Q^{1/2} p^2.$">|; 

$key = q/displaystylez_0(omega)=frac{2}{pi}int_0^{pislash2}h(omega,sinalpha),dalpha,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img2206.png"
 ALT="$\displaystyle z_0(\omega) = \frac{2}{\pi}\int_0^{\pi/2}h(\omega \sin\alpha) d\alpha,
$">|; 

$key = q/displaystylezeta_e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1323.png"
 ALT="$\displaystyle \zeta_e$">|; 

$key = q/displaystylezeta_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1388.png"
 ALT="$\displaystyle \zeta_i$">|; 

$key = q/displaystyle{A,B}equivfrac{partialA}{partialhat{x}},frac{partialB}{partialxi}-frac{partialA}{partialxi},frac{partialB}{partialhat{x}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img3489.png"
 ALT="$\displaystyle \{A, B\} \equiv \frac{\partial A}{\partial\hat{x}} \frac{\partia...
...rtial\xi} - \frac{\partial A}{\partial\xi} \frac{\partial B}{\partial\hat{x}}.$">|; 

$key = q/displaystyle{bfA}({bfr})={bfA}({bfR})+(;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img399.png"
 ALT="$\displaystyle {\bf A}({\bf r}) = {\bf A}({\bf R}) + ($">|; 

$key = q/displaystyle{bfA}_{ss'}={bfB}_{ss'},f_s-{bfD}_{ss'}cdotfrac{partialf_s}{partial{bfv}_s},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img786.png"
 ALT="$\displaystyle {\bf A}_{ss'} = {\bf B}_{ss'} f_s-{\bf D}_{ss'}\cdot \frac{\partial f_s}{\partial {\bf v}_s},$">|; 

$key = q/displaystyle{bfB}(r,theta,z,t)={bfB}(r),exp[,{rmi},(m,theta-k,z)+gamma,t].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.58ex; " SRC="|."$dir".q|img2979.png"
 ALT="$\displaystyle {\bf B}(r,\theta,z,t) = {\bf B}(r) \exp[ {\rm i} (m \theta -k  z)+\gamma t].$">|; 

$key = q/displaystyle{bfB};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img2178.png"
 ALT="$\displaystyle {\bf B}$">|; 

$key = q/displaystyle{bfB}=frac{mu_0}{4pi}frac{M_E}{r^3}(-2costheta,-sintheta,,0),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img434.png"
 ALT="$\displaystyle {\bf B} = \frac{\mu_0}{4\pi} \frac{M_E}{r^3} (-2\cos\theta, -\sin\theta,  0),$">|; 

$key = q/displaystyle{bfB}=nablapsitimes{bfe}_z,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img523.png"
 ALT="$\displaystyle {\bf B} = \nabla\psi\times {\bf e}_z,
$">|; 

$key = q/displaystyle{bfB}=omega^{-1},{bfk}times{bfE}={bf0}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2501.png"
 ALT="$\displaystyle {\bf B} = \omega^{-1} {\bf k}\times {\bf E} = {\bf0}.$">|; 

$key = q/displaystyle{bfB}_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3275.png"
 ALT="$\displaystyle {\bf B}_0$">|; 

$key = q/displaystyle{bfB}_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3088.png"
 ALT="$\displaystyle {\bf B}_1$">|; 

$key = q/displaystyle{bfB}_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3090.png"
 ALT="$\displaystyle {\bf B}_2$">|; 

$key = q/displaystyle{bfB}_p;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2939.png"
 ALT="$\displaystyle {\bf B}_p$">|; 

$key = q/displaystyle{bfB}_t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2945.png"
 ALT="$\displaystyle {\bf B}_t$">|; 

$key = q/displaystyle{bfB}_{ss'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img787.png"
 ALT="$\displaystyle {\bf B}_{ss'}$">|; 

$key = q/displaystyle{bfB}cdotnablaT_esimeq0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1505.png"
 ALT="$\displaystyle {\bf B}\cdot\nabla T_e\simeq 0.$">|; 

$key = q/displaystyle{bfB}cdotnablaT_isimeq0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1507.png"
 ALT="$\displaystyle {\bf B}\cdot\nabla T_i\simeq 0.$">|; 

$key = q/displaystyle{bfB}cdotnablansimeq0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1515.png"
 ALT="$\displaystyle {\bf B}\cdot\nabla n\simeq 0.$">|; 

$key = q/displaystyle{bfB}cdotnablapsimeq0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1513.png"
 ALT="$\displaystyle {\bf B}\cdot\nabla p \simeq 0.$">|; 

$key = q/displaystyle{bfD}_{ss'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img789.png"
 ALT="$\displaystyle {\bf D}_{ss'}$">|; 

$key = q/displaystyle{bfE}({bfr},t)={bfE}_{bfk},exp[,{rmi},({bfk}cdot{bfr}-omega,t)],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.58ex; " SRC="|."$dir".q|img1662.png"
 ALT="$\displaystyle {\bf E} ({\bf r}, t) = {\bf E}_{\bf k}  \exp[ {\rm i} ({\bf k}
\cdot{\bf r} - \omega  t)],$">|; 

$key = q/displaystyle{bfE}+{bfU}_0times{bfB}={bf0}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img297.png"
 ALT="$\displaystyle {\bf E} + {\bf U}_0\times {\bf B} = {\bf0}.$">|; 

$key = q/displaystyle{bfE}+{bfV}_etimes{bfB};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1508.png"
 ALT="$\displaystyle {\bf E} + {\bf V}_e\times{\bf B}$">|; 

$key = q/displaystyle{bfE}+{bfV}_itimes{bfB};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1510.png"
 ALT="$\displaystyle {\bf E} + {\bf V}_i\times {\bf B}$">|; 

$key = q/displaystyle{bfE}+{bfV}times{bfB};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img1482.png"
 ALT="$\displaystyle {\bf E} + {\bf V}\times {\bf B}$">|; 

$key = q/displaystyle{bfE}+{bfV}times{bfB}=eta,{bfj}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2888.png"
 ALT="$\displaystyle {\bf E} + {\bf V} \times{\bf B} = \eta {\bf j}.$">|; 

$key = q/displaystyle{bfE}+{bfV}times{bfB}={bf0},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img2689.png"
 ALT="$\displaystyle {\bf E} + {\bf V}\times {\bf B} = {\bf0},$">|; 

$key = q/displaystyle{bfE}+{bfV}times{bfB}={bf0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img2700.png"
 ALT="$\displaystyle {\bf E} + {\bf V}\times{\bf B} ={\bf0}$">|; 

$key = q/displaystyle{bfE}+{bfV}times{bfB}_0={bf0}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1819.png"
 ALT="$\displaystyle {\bf E} + {\bf V} \times {\bf B}_0 = {\bf0}.$">|; 

$key = q/displaystyle{bfE}+{bfV}times{bfB}simeq{bf0}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img1493.png"
 ALT="$\displaystyle {\bf E} + {\bf V}\times {\bf B} \simeq {\bf0}.$">|; 

$key = q/displaystyle{bfE};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img1686.png"
 ALT="$\displaystyle {\bf E}$">|; 

$key = q/displaystyle{bfE}=-nabla{mitPhi}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2227.png"
 ALT="$\displaystyle {\bf E} = -\nabla{\mit\Phi}.$">|; 

$key = q/displaystyle{bfE}=-nabla{mitPhi}=-{rmi},{mitPhi},{bfk}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2499.png"
 ALT="$\displaystyle {\bf E} = -\nabla{\mit\Phi} =-{\rm i} {\mit\Phi} {\bf k}.$">|; 

$key = q/displaystyle{bfE}=-{bfV}times{bfB}_0+frac{{bfj}times{bfB}_0}{n_e,e}-{rmi},frac{omega,m_e}{n_e,e^2},{bfj}+frac{nu_e,m_e}{n_e,e^2},{bfj},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.96ex; " SRC="|."$dir".q|img2047.png"
 ALT="$\displaystyle {\bf E} = - {\bf V}\times{\bf B}_0 + \frac{{\bf j}\times{\bf B}_0...
...,\frac{\omega m_e}{n_e e^2} {\bf j} + \frac{\nu_e m_e}{n_e  e^2} {\bf j},$">|; 

$key = q/displaystyle{bfE}=-{bfu}times{bfB}=u_s,B_phi,{bfe}_theta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2832.png"
 ALT="$\displaystyle {\bf E} = - {\bf u} \times {\bf B} = u_s B_\phi {\bf e}_\theta$">|; 

$key = q/displaystyle{bfF};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img1157.png"
 ALT="$\displaystyle {\bf F}$">|; 

$key = q/displaystyle{bfF}=q,{bfv}times{bfB},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.56ex; " SRC="|."$dir".q|img133.png"
 ALT="$\displaystyle {\bf F} = q {\bf v}\times {\bf B},$">|; 

$key = q/displaystyle{bfF}={bfF}_U+{bfF}_T,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1291.png"
 ALT="$\displaystyle {\bf F} = {\bf F}_U+{\bf F}_T,$">|; 

$key = q/displaystyle{bfF}_0({bfZ},t)+frac{partialmbox{boldmathzeta}_0}{partialtau}={bff}({bfZ},t,tau).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.74ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img260.png"
 ALT="$\displaystyle {\bf F}_0({\bf Z}, t) +\frac{\partial\mbox{\boldmath$\zeta$}_0}{\partial\tau}
= {\bf f} ({\bf Z}, t, \tau).$">|; 

$key = q/displaystyle{bfF}_0({bfZ},t)=langle{bff}({bfZ},t,tau)rangleequivlangle{bff}rangle({bfZ},t).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img261.png"
 ALT="$\displaystyle {\bf F}_0({\bf Z}, t) =\langle {\bf f}({\bf Z}, t,\tau)\rangle\equiv \langle {\bf f}\rangle({\bf Z},t).$">|; 

$key = q/displaystyle{bfF}_1({bfZ},t)=langle;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img264.png"
 ALT="$\displaystyle {\bf F}_1({\bf Z},t) =\langle$">|; 

$key = q/displaystyle{bfF}_T;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img1294.png"
 ALT="$\displaystyle {\bf F}_T$">|; 

$key = q/displaystyle{bfF}_U;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1292.png"
 ALT="$\displaystyle {\bf F}_U$">|; 

$key = q/displaystyle{bfF}_sequivsum_{s'}{bfF}_{ss'}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -2.62ex; " SRC="|."$dir".q|img1044.png"
 ALT="$\displaystyle {\bf F}_s \equiv \sum_{s'} {\bf F}_{ss'}.$">|; 

$key = q/displaystyle{bfF}_{s's}=-{bfF}_{ss'},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img931.png"
 ALT="$\displaystyle {\bf F}_{s's} = - {\bf F}_{ss'},$">|; 

$key = q/displaystyle{bfF}_{ss'}'=intm_a,({bfv}_s-{bfU}),C_{ss'},d^3{bfv}_s={bfF}_{ss'}-{bfU}int,m_s,C_{ss'},d^3{bfv}_s={bfF}_{ss'},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img951.png"
 ALT="$\displaystyle {\bf F}_{ss'}' = \int m_a ({\bf v}_s-{\bf U}) C_{ss'} d^3{\bf v}_s= {\bf F}_{ss'}- {\bf U}\int m_s C_{ss'} d^3{\bf v}_s = {\bf F}_{ss'},$">|; 

$key = q/displaystyle{bfF}_{ss'}({bfr},t)=intm_s,{bfv}_s,C_{ss'},d^3{bfv}_s,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img927.png"
 ALT="$\displaystyle {\bf F}_{ss'}({\bf r},t)=\int m_s {\bf v}_s C_{ss'} d^3{\bf v}_s,$">|; 

$key = q/displaystyle{bfF}_{ss'}({bfr},t)=intm_{s'},{bfv}_{s'},C_{s's},d^3{bfv}_{s'},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img928.png"
 ALT="$\displaystyle {\bf F}_{ss'}({\bf r},t)=\int m_{s'} {\bf v}_{s'} C_{s's} d^3{\bf v}_{s'},$">|; 

$key = q/displaystyle{bfF}_{ss'}=-frac{8,gamma_{ss'},n_s,n_{s'}}{3pi^{1slash2},mu_{ss'},(v_{t,s}^2+v_{t,{s'}}^2)^{3slash2}},{bfV}_s.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.35ex; vertical-align: -2.42ex; " SRC="|."$dir".q|img950.png"
 ALT="$\displaystyle {\bf F}_{ss'} = - \frac{8 \gamma_{ss'} n_s n_{s'}}{3\pi^{1/2} \mu_{ss'} (v_{t s}^2+v_{t {s'}}^2)^{3/2}} {\bf V}_s.$">|; 

$key = q/displaystyle{bfF}_{ss'}=-frac{8,gamma_{ss'},n_s,n_{s'}}{3pi^{1slash2},mu_{ss'},(v_{t,s}^{2}+v_{t,{s'}}^{2})^{3slash2}},{bfV}_{ss'}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.35ex; vertical-align: -2.42ex; " SRC="|."$dir".q|img955.png"
 ALT="$\displaystyle {\bf F}_{ss'} = - \frac{8 \gamma_{ss'} n_s n_{s'}}{3\pi^{1/2} \mu_{ss'} (v_{t s}^{2}+v_{t {s'}}^{2})^{3/2}} {\bf V}_{ss'}.$">|; 

$key = q/displaystyle{bfF}_{ss'}=-frac{m_s,n_s}{tau_{ss'}},{bfV}_{ss'}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.41ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img966.png"
 ALT="$\displaystyle {\bf F}_{ss'} = - \frac{m_s n_s}{\tau_{ss'}} {\bf V}_{ss'}.$">|; 

$key = q/displaystyle{bfF}_{ss'}=-{bfF}_{s's},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1045.png"
 ALT="$\displaystyle {\bf F}_{ss'} = -{\bf F}_{s's},$">|; 

$key = q/displaystyle{bfF}_{ss'}equivintm_s,{bfv},C_{ss'},d^3{bfv}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img1043.png"
 ALT="$\displaystyle {\bf F}_{ss'}\equiv \int m_s {\bf v} C_{ss'} d^3{\bf v}.$">|; 

$key = q/displaystyle{bfJ}_{ss'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img999.png"
 ALT="$\displaystyle {\bf J}_{ss'}$">|; 

$key = q/displaystyle{bfJ}_{ss'}=frac{partialf_s}{partial{bfv}_s},frac{f_{s'}}{m_s}-frac{f_s}{m_{s'}},frac{partialf_{s'}}{partial{bfv}_{s'}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img750.png"
 ALT="$\displaystyle {\bf J}_{ss'} = \frac{\partial f_s}{\partial {\bf v}_s} \frac{f_{s'}}{m_s} -\frac{f_s}{m_{s'}} \frac{\partial f_{s'}}{\partial {\bf v}_{s'}}.$">|; 

$key = q/displaystyle{bfK}=left({array}{ccc}S,&-{rmi},D,&0{rmi},D,&S,&00,&0,&P{array}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 7.58ex; vertical-align: -3.25ex; " SRC="|."$dir".q|img1735.png"
 ALT="$\displaystyle {\bf K} = \left(\begin{array}{ccc}
S,&amp;-{\rm i} D,&amp;0\\\\
{\rm i} D, &amp; S,&amp;0\\\\
0,&amp;0,&amp;P\end{array}\right),$">|; 

$key = q/displaystyle{bfK}={bfI}+frac{{rmi},{mbox{boldmathsigma}}}{epsilon_0,omega};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img1680.png"
 ALT="$\displaystyle {\bf K} = {\bf I} + \frac{{\rm i} {\mbox{\boldmath$\sigma$}}}{\epsilon_0 \omega}$">|; 

$key = q/displaystyle{bfK}={bfU},{bfK}_{rmcirc},{bfU}^dag.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1734.png"
 ALT="$\displaystyle {\bf K} = {\bf U}  {\bf K}_{\rm circ}  {\bf U}^\dag .$">|; 

$key = q/displaystyle{bfK}_{rmcirc}=left({array}{ccc}R,&0,&00,&L,&00,&0,&P{array}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 7.58ex; vertical-align: -3.25ex; " SRC="|."$dir".q|img1716.png"
 ALT="$\displaystyle {\bf K}_{\rm circ} = \left(\begin{array}{ccc}
R,&amp;0,&amp;0\\\\
0,&amp;L,&amp;0\\\\
0,&amp;0,&amp;P\end{array}\right),$">|; 

$key = q/displaystyle{bfK}cdot{bfE}={bfE}+frac{{rmi}}{omega,epsilon_0},{bfj}={bfE}+frac{{rmi}}{omega,epsilon_0}sum_se_sint{bfv},f_{1,s},d^3{bfv},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.58ex; vertical-align: -2.62ex; " SRC="|."$dir".q|img2396.png"
 ALT="$\displaystyle {\bf K}\cdot{\bf E} ={\bf E} + \frac{{\rm i}}{\omega \epsilon_0}...
...frac{{\rm i}}{\omega \epsilon_0}
\sum_s e_s\int {\bf v} f_{1 s} d^3{\bf v},$">|; 

$key = q/displaystyle{bfM}(,{rmi},partialslashpartialt,-{rmi},nabla,{bfr},t),{mbox{boldmathpsi}}={bf0}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2092.png"
 ALT="$\displaystyle {\bf M}( {\rm i} \partial/\partial t, -{\rm i} \nabla,
{\bf r}, t) {\mbox{\boldmath$\psi$}} = {\bf0}.$">|; 

$key = q/displaystyle{bfM}(omega,{bfk},{bfr},t),{mbox{boldmathpsi}}={bf0},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2098.png"
 ALT="$\displaystyle {\bf M}(\omega, {\bf k}, {\bf r}, t)  {\mbox{\boldmath$\psi$}} = {\bf0},$">|; 

$key = q/displaystyle{bfM}=left(frac{c}{omega}right)^2{bfk}{bfk}-left(frac{c,k}{omega}right)^2{bfI}+{bfK}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1682.png"
 ALT="$\displaystyle {\bf M} = \left(\frac{c}{\omega}\right)^2{\bf k}{\bf k} - \left(\frac{c k}{\omega}\right)^2{\bf I} +
{\bf K}.$">|; 

$key = q/displaystyle{bfM}_k({bfr},t)=int{bfvvcdotsv},f_s({bfr},{bfv},t),d^3{bfv},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img1012.png"
 ALT="$\displaystyle {\bf M}_k({\bf r}, t) = \int {\bf v v\cdots v} f_s({\bf r},{\bf v}, t) d^3{\bf v},$">|; 

$key = q/displaystyle{bfM}cdot{bfE}=({bfn}cdot{bfE}),{bfn}-n^2,{bfE}+{bfK}cdot{bfE}={bf0}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1739.png"
 ALT="$\displaystyle {\bf M}\cdot{\bf E} =({\bf n}\cdot{\bf E}) {\bf n} - n^2 {\bf E}+ {\bf K}\cdot{\bf E} = {\bf0}.$">|; 

$key = q/displaystyle{bfM}cdot{bfE}={bf0},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img1681.png"
 ALT="$\displaystyle {\bf M}\cdot{\bf E} = {\bf0},$">|; 

$key = q/displaystyle{bfM}cdot{bfE}equivleft[left(frac{c}{omega}right)^2{bfk}{bfk}-left(frac{c,k}{omega}right)^2{bfI}+{bfK}right]cdot{bfE}={bf0},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.26ex; " SRC="|."$dir".q|img2442.png"
 ALT="$\displaystyle {\bf M}\cdot {\bf E} \equiv \left[\left(\frac{c}{\omega}\right)^2...
...-\left(\frac{c k}{\omega}\right)^2{\bf I}+{\bf K}\right]\cdot{\bf E} = {\bf0},$">|; 

$key = q/displaystyle{bfP}=epsilon_0,(n^2-1),{bfE},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2169.png"
 ALT="$\displaystyle {\bf P} =\epsilon_0 (n^2-1) {\bf E},
$">|; 

$key = q/displaystyle{bfP}=left({array}{ccc}p+B^{2}slash2,mu_0,&0,&0[0.5ex]0,&p+B^{2}slash2,mu_0,&0[0.5ex]0,&0,&p-B^{2}slash2,mu_0{array}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 8.70ex; vertical-align: -3.75ex; " SRC="|."$dir".q|img2688.png"
 ALT="$\displaystyle {\bf P} = \left(\begin{array}{ccc}
p + B^{2}/2 \mu_0, &amp; 0, &amp;0\ ...
... &amp;p + B^{2}/2 \mu_0,&amp; 0\ [0.5ex]
0,&amp;0,&amp; p - B^{2}/2 \mu_0\end{array}\right).$">|; 

$key = q/displaystyle{bfP}_s({bfr},t)=intm_s,{bfv}{bfv},f_s({bfr},{bfv},t),d^3{bfv}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img1022.png"
 ALT="$\displaystyle {\bf P}_s({\bf r}, t) = \int
m_s {\bf v}{\bf v}  f_s({\bf r}, {\bf v},t) d^3{\bf v}.$">|; 

$key = q/displaystyle{bfP}_s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1034.png"
 ALT="$\displaystyle {\bf P}_s$">|; 

$key = q/displaystyle{bfQ}_s({bfr},t)=intfrac{1}{2},m_s,v^2,{bfv},f_s({bfr},{bfv},t),d^3{bfv}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img1023.png"
 ALT="$\displaystyle {\bf Q}_s({\bf r}, t) = \int
\frac{1}{2} m_s v^2 {\bf v}  f_s({\bf r}, {\bf v},t) d^3{\bf v}.$">|; 

$key = q/displaystyle{bfQ}_s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.48ex; " SRC="|."$dir".q|img1036.png"
 ALT="$\displaystyle {\bf Q}_s$">|; 

$key = q/displaystyle{bfR}(t)=left(v_{0,parallel},t+frac{e}{m},E_parallel,frac{t^{2}}{2}right){bfb}+{bfv}_E,,t.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img233.png"
 ALT="$\displaystyle {\bf R}(t)=\left(v_{0 \parallel }  t + \frac{e}{m}  E_\parallel  \frac{t^{2}}{2}\right)
{\bf b} + {\bf v}_E   t.$">|; 

$key = q/displaystyle{bfR}_{ss'}=frac{m_s,{bfr}_s+m_{s'},{bfr}_{s'}}{m_s+m_{s'}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img677.png"
 ALT="$\displaystyle {\bf R}_{ss'} = \frac{m_s {\bf r}_s+m_{s'} {\bf r}_{s'}}{m_s+m_{s'}}$">|; 

$key = q/displaystyle{bfT}=rho,{bfV},{bfV}+left(p+frac{B^{2}}{2,mu_0}right){bfI}-frac{{bfB},{bfB}}{mu_0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3053.png"
 ALT="$\displaystyle {\bf T} = \rho {\bf V} {\bf V} + \left(p+ \frac{B^{2}}{2 \mu_0}\right){\bf I}- \frac{{\bf B} {\bf B}}{\mu_0}$">|; 

$key = q/displaystyle{bfU}=frac{1}{sqrt{2}}left({array}{ccc}1,&1,&0{rmi},&-{rmi},&00,&0,&sqrt{2}{array}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 7.58ex; vertical-align: -3.26ex; " SRC="|."$dir".q|img1733.png"
 ALT="$\displaystyle {\bf U} = \frac{1}{\sqrt{2}}\left(\begin{array}{ccc}
1,&amp;1,&amp;0\\\\
{\rm i}, &amp; -{\rm i},&amp;0\\\\
0,&amp;0,&amp;\sqrt{2}\end{array}\right).$">|; 

$key = q/displaystyle{bfU}_0=U_{0,parallel},{bfb}+{bfv}_E,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img300.png"
 ALT="$\displaystyle {\bf U}_0 = U_{0 \parallel}  {\bf b} + {\bf v}_E,$">|; 

$key = q/displaystyle{bfU}_{1,perp}=frac{{bfb}}{{mitOmega}}timesleft(frac{d{bfU}_0}{dt}+frac{mu}{m},nablaBright).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img347.png"
 ALT="$\displaystyle {\bf U}_{1 \perp} = \frac{{\bf b}}{{\mit\Omega}} \times\left(
\frac{d{\bf U}_0}{dt} + \frac{\mu}{m} \nabla B\right).$">|; 

$key = q/displaystyle{bfU}_{rmcurv}=frac{U_{0,parallel}^{2}}{{mitOmega}},{bfb}times({bfb}cdotnabla),{bfb},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.30ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img356.png"
 ALT="$\displaystyle {\bf U}_{\rm curv} = \frac{U_{0 \parallel}^{2}}{{\mit\Omega}} 
{\bf b}\times ({\bf b}\cdot\nabla) {\bf b},$">|; 

$key = q/displaystyle{bfU}_{rmgrad}=frac{mu}{m,{mitOmega}},{bfb}timesnablaB,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img353.png"
 ALT="$\displaystyle {\bf U}_{\rm grad} = \frac{\mu}{m {\mit\Omega}} 
{\bf b}\times \nabla B,$">|; 

$key = q/displaystyle{bfU}_{rmpolz}=frac{1}{{mitOmega}}frac{d}{dt}!left(frac{{bfE}_perp}{B}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img359.png"
 ALT="$\displaystyle {\bf U}_{\rm polz} = \frac{1}{{\mit\Omega}}
\frac{d}{dt}\!\left(\frac{{\bf E}_\perp}
{B}\right)$">|; 

$key = q/displaystyle{bfU}_{rmpolz}=frac{{bfb}}{{mitOmega}}timesfrac{d{bfv}_E}{dt},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img358.png"
 ALT="$\displaystyle {\bf U}_{\rm polz} = \frac{{\bf b}}{{\mit\Omega}}\times \frac{d{\bf v}_E}{dt},$">|; 

$key = q/displaystyle{bfU}_{ss'}=frac{m_s,{bfv}_s+m_{s'},{bfv}_{s'}}{m_s+m_{s'}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img591.png"
 ALT="$\displaystyle {\bf U}_{ss'} = \frac{m_s {\bf v}_s+m_{s'} {\bf v}_{s'}}{m_s+m_{s'}}.$">|; 

$key = q/displaystyle{bfV};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img2936.png"
 ALT="$\displaystyle {\bf V}$">|; 

$key = q/displaystyle{bfV}=frac{m_i,{bfV}_i+m_e,{bfV}_e}{m_i+m_e},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.96ex; " SRC="|."$dir".q|img1472.png"
 ALT="$\displaystyle {\bf V} = \frac{m_i {\bf V}_i + m_e {\bf V}_e}{m_i+ m_e},$">|; 

$key = q/displaystyle{bfV}_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3084.png"
 ALT="$\displaystyle {\bf V}_1$">|; 

$key = q/displaystyle{bfV}_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3086.png"
 ALT="$\displaystyle {\bf V}_2$">|; 

$key = q/displaystyle{bfV}_esimeq{bfV}-[delta],frac{{bfj}}{n,e}+{calO}left(frac{m_e}{m_i}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1489.png"
 ALT="$\displaystyle {\bf V}_e \simeq {\bf V} - [\delta] \frac{{\bf j}}{n e} + {\cal O}\left(\frac{m_e}
{m_i}\right).$">|; 

$key = q/displaystyle{bfV}_esimeq{bfV}-frac{{bfj}}{ne}+{calO}!left(frac{m_e}{m_i}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1477.png"
 ALT="$\displaystyle {\bf V}_e \simeq {\bf V} - \frac{{\bf j}}{ne} + {\cal O}\!\left(\frac{m_e}{m_i}\right).$">|; 

$key = q/displaystyle{bfV}_isimeq{bfV}+{calO}left(frac{m_e}{m_i}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1476.png"
 ALT="$\displaystyle {\bf V}_i \simeq {\bf V} + {\cal O}\left(\frac{m_e}{m_i}\right),$">|; 

$key = q/displaystyle{bfV}_p;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2941.png"
 ALT="$\displaystyle {\bf V}_p$">|; 

$key = q/displaystyle{bfV}_t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2947.png"
 ALT="$\displaystyle {\bf V}_t$">|; 

$key = q/displaystyle{bfV}_{ast,e}=frac{T_e,nablantimes{bfb}}{e,n,B}+frac{nablaT_etimes{bfb}}{e,B}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img1529.png"
 ALT="$\displaystyle {\bf V}_{\ast e} = \frac{T_e \nabla n\times{\bf b}}{e n B} + \frac{
\nabla T_e\times{\bf b}}{e B}.$">|; 

$key = q/displaystyle{bfV}_{ast,e}equivfrac{nablap_etimes{bfB}}{e,n,B^{2}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img1524.png"
 ALT="$\displaystyle {\bf V}_{\ast e} \equiv \frac{\nabla p_e \times{\bf B}}
{e n B^{2}},$">|; 

$key = q/displaystyle{bfV}_{ast,i}equiv-frac{nablap_itimes{bfB}}{e,n,B^{2}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img1525.png"
 ALT="$\displaystyle {\bf V}_{\ast i} \equiv -\frac{\nabla p_i
\times{\bf B}}
{e n B^{2}},$">|; 

$key = q/displaystyle{bfV}_{perp,e};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1519.png"
 ALT="$\displaystyle {\bf V}_{\perp e}$">|; 

$key = q/displaystyle{bfV}_{perp,i};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1521.png"
 ALT="$\displaystyle {\bf V}_{\perp i}$">|; 

$key = q/displaystyle{bfa}_s=frac{e_s}{m_s},({bfE}+{bfv}times{bfB}).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.41ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img1008.png"
 ALT="$\displaystyle {\bf a}_s = \frac{e_s}{m_s} ({\bf E} + {\bf v}\times{\bf B}).$">|; 

$key = q/displaystyle{bfa}_s=frac{e_s}{m_s},({bfE}+{bfv}times{bfB});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.41ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img582.png"
 ALT="$\displaystyle {\bf a}_s = \frac{e_s}{m_s} ({\bf E} + {\bf v}\times{\bf B})$">|; 

$key = q/displaystyle{bfa}_scdotnabla_vf_s=nabla_vcdot({bfa}_s,f_s).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1054.png"
 ALT="$\displaystyle {\bf a}_s\cdot\nabla_v f_s = \nabla_v\cdot({\bf a}_s f_s).$">|; 

$key = q/displaystyle{bfb};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img874.png"
 ALT="$\displaystyle {\bf b}$">|; 

$key = q/displaystyle{bfb}times({bfe}_pmtimes{bfb});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1710.png"
 ALT="$\displaystyle {\bf b}\times ({\bf e}_\pm\times{\bf b})$">|; 

$key = q/displaystyle{bfdelta}simfrac{e,{bfE}_{perp}}{m},({mitDelta}t)^2simfrac{{bfE}_perp}{{mitOmega},B}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img361.png"
 ALT="$\displaystyle {\bf\delta} \sim
\frac{e {\bf E}_{\perp}}{m} ({\mit\Delta} t)^2 \sim \frac{{\bf E}_\perp}{
{\mit\Omega} B}.$">|; 

$key = q/displaystyle{bfe}_+;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img1703.png"
 ALT="$\displaystyle {\bf e}_+$">|; 

$key = q/displaystyle{bfe}_-;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.12ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img1705.png"
 ALT="$\displaystyle {\bf e}_-$">|; 

$key = q/displaystyle{bfe}_pmtimes{bfb};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img1708.png"
 ALT="$\displaystyle {\bf e}_\pm\times{\bf b}$">|; 

$key = q/displaystyle{bfg}_{ss'}simequ_{ss'}left[(coschi-1),{bfl}+sinchi,cosphi,{bfm}+sinchi,sinphi,{bfn}right].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.60ex; " SRC="|."$dir".q|img762.png"
 ALT="$\displaystyle {\bf g}_{ss'} \simeq u_{ss'}\left[(\cos\chi-1) {\bf l} + \sin\chi \cos\phi {\bf m} +\sin\chi \sin\phi {\bf n}\right].$">|; 

$key = q/displaystyle{bfh}_{ss'}=h,{bfe}_z,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img689.png"
 ALT="$\displaystyle {\bf h}_{ss'} = h {\bf e}_z,$">|; 

$key = q/displaystyle{bfh}_{ss'}={bfr}_{ss'}timesdot{bfr}_{ss'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img683.png"
 ALT="$\displaystyle {\bf h}_{ss'} = {\bf r}_{ss'}\times\dot{\bf r}_{ss'}$">|; 

$key = q/displaystyle{bfj};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.54ex; " SRC="|."$dir".q|img573.png"
 ALT="$\displaystyle {\bf j}$">|; 

$key = q/displaystyle{bfj}=-n,e,{bfU},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.54ex; " SRC="|."$dir".q|img1473.png"
 ALT="$\displaystyle {\bf j} = -n e {\bf U},$">|; 

$key = q/displaystyle{bfj}=;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.54ex; " SRC="|."$dir".q|img1676.png"
 ALT="$\displaystyle {\bf j} =$">|; 

$key = q/displaystyle{bfj}=frac{partial{bfP}}{partialt}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2171.png"
 ALT="$\displaystyle {\bf j} = \frac{\partial{\bf P}}{\partial t}.
$">|; 

$key = q/displaystyle{bfj}=sigma,{bfE},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.54ex; " SRC="|."$dir".q|img1657.png"
 ALT="$\displaystyle {\bf j} = \sigma {\bf E},
$">|; 

$key = q/displaystyle{bfj}_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.54ex; " SRC="|."$dir".q|img3277.png"
 ALT="$\displaystyle {\bf j}_0$">|; 

$key = q/displaystyle{bfj}_astequiv-e,n,({bfV}_{ast,e}-{bfV}_{ast,i})=-frac{nablaptimes{bfB}}{B^{2}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img1528.png"
 ALT="$\displaystyle {\bf j}_\ast \equiv - e n ({\bf V}_{\ast e}-{\bf V}_{\ast i})
=-\frac{\nabla p\times{\bf B}}{B^{2}},$">|; 

$key = q/displaystyle{bfj}times{bfB}simeqnablap,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1512.png"
 ALT="$\displaystyle {\bf j}\times {\bf B} \simeq \nabla p,$">|; 

$key = q/displaystyle{bfk};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img2099.png"
 ALT="$\displaystyle {\bf k}$">|; 

$key = q/displaystyle{bfk}cdot{bfr}-omega,t={rmconstant},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img1665.png"
 ALT="$\displaystyle {\bf k}\cdot{\bf r} - \omega  t = {\rm constant},$">|; 

$key = q/displaystyle{bfk}times{bfB};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.10ex; " SRC="|."$dir".q|img1671.png"
 ALT="$\displaystyle {\bf k}\times{\bf B}$">|; 

$key = q/displaystyle{bfk}times{bfB}=-frac{omega}{c^2},{bfK}cdot{bfE},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img1679.png"
 ALT="$\displaystyle {\bf k}\times{\bf B} = -\frac{\omega}{c^2} {\bf K}\cdot{\bf E},$">|; 

$key = q/displaystyle{bfk}times{bfE};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.10ex; " SRC="|."$dir".q|img1673.png"
 ALT="$\displaystyle {\bf k}\times{\bf E}$">|; 

$key = q/displaystyle{bfn}=frac{c}{omega},{bfk};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img1738.png"
 ALT="$\displaystyle {\bf n} = \frac{c}{\omega} {\bf k}$">|; 

$key = q/displaystyle{bfp}:nabla{bfV}_sequivp_{s,alphabeta},frac{partialV_{s,beta}}{partialr_alpha}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.13ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img1079.png"
 ALT="$\displaystyle {\bf p} : \nabla {\bf V}_s \equiv p_{s \alpha\beta}  \frac{\partial V_{s \beta}}{\partial r_\alpha}.$">|; 

$key = q/displaystyle{bfp}=m,{bfv}+e,{bfA},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img397.png"
 ALT="$\displaystyle {\bf p} = m {\bf v} +e {\bf A},$">|; 

$key = q/displaystyle{bfp}_s({bfr},t)=intm_s,{bfu}_s{bfu}_s,f_s({bfr},{bfv},t),d^3{bfv},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img1027.png"
 ALT="$\displaystyle {\bf p}_s({\bf r}, t) = \int
m_s {\bf u}_s{\bf u}_s  f_s({\bf r}, {\bf v},t) d^3{\bf v},$">|; 

$key = q/displaystyle{bfp}_s=p_s,{bfI}+;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1082.png"
 ALT="$\displaystyle {\bf p}_s = p_s {\bf I} +$">|; 

$key = q/displaystyle{bfq}=-kappa,nablaT.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1115.png"
 ALT="$\displaystyle {\bf q} = - \kappa \nabla T.$">|; 

$key = q/displaystyle{bfq}_e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1196.png"
 ALT="$\displaystyle {\bf q}_e$">|; 

$key = q/displaystyle{bfq}_e={bfq}_{Te}+{bfq}_{Ue},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1307.png"
 ALT="$\displaystyle {\bf q}_e = {\bf q}_{Te} + {\bf q}_{Ue},$">|; 

$key = q/displaystyle{bfq}_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1198.png"
 ALT="$\displaystyle {\bf q}_i$">|; 

$key = q/displaystyle{bfq}_s({bfr},t)=intfrac{1}{2},m_s,u_s^{2},{bfu}_s,f_s({bfr},{bfv},t),d^3{bfv}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img1028.png"
 ALT="$\displaystyle {\bf q}_s({\bf r}, t) = \int
\frac{1}{2} m_s u_s^{2} {\bf u}_s  f_s({\bf r}, {\bf v},t) d^3{\bf v}.$">|; 

$key = q/displaystyle{bfq}_{Te};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1308.png"
 ALT="$\displaystyle {\bf q}_{Te}$">|; 

$key = q/displaystyle{bfq}_{Ue};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1310.png"
 ALT="$\displaystyle {\bf q}_{Ue}$">|; 

$key = q/displaystyle{bfr}(t)={bfR}(t)+;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img229.png"
 ALT="$\displaystyle {\bf r}(t) = {\bf R}(t) +$">|; 

$key = q/displaystyle{bfr};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img279.png"
 ALT="$\displaystyle {\bf r}$">|; 

$key = q/displaystyle{bfr}_s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img673.png"
 ALT="$\displaystyle {\bf r}_s$">|; 

$key = q/displaystyle{bfr}_{s'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img675.png"
 ALT="$\displaystyle {\bf r}_{s'}$">|; 

$key = q/displaystyle{bfs}_s=s_s,{bfV}_s+frac{{bfq}_s}{T_s}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.46ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img1092.png"
 ALT="$\displaystyle {\bf s}_s = s_s {\bf V}_s + \frac{{\bf q}_s}{T_s}.$">|; 

$key = q/displaystyle{bfu};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.12ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img290.png"
 ALT="$\displaystyle {\bf u}$">|; 

$key = q/displaystyle{bfu}=left(frac{1}{2},rho,V^{2}+frac{mitGamma}{{mitGamma}-1},pright){bfV}+frac{{bfB}times({bfV}times{bfB})}{mu_0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3055.png"
 ALT="$\displaystyle {\bf u} = \left(\frac{1}{2} \rho V^{2}+ \frac{\mit\Gamma}{{\mit\Gamma}-1} p\right){\bf V}
+ \frac{{\bf B}\times ({\bf V}\times {\bf B})}{\mu_0}$">|; 

$key = q/displaystyle{bfu}=u_perpleft(singamma,{bfe}_1+cosgamma,{bfe}_2right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img307.png"
 ALT="$\displaystyle {\bf u} = u_\perp \left(\sin\gamma  {\bf e}_1+ \cos\gamma {\bf e}_2\right),$">|; 

$key = q/displaystyle{bfu}={bfc}+u_perpleft[sin,({mitOmega},gammaslashomega),{bfe}_1+cos,({mitOmega},gammaslashomega),{bfe}_2right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.60ex; " SRC="|."$dir".q|img302.png"
 ALT="$\displaystyle {\bf u} = {\bf c} + u_\perp \left[\sin  ({\mit\Omega} \gamma/\omega)  {\bf e}_1
+\cos ({\mit\Omega} \gamma/\omega) {\bf e}_2\right],$">|; 

$key = q/displaystyle{bfu}={mitOmega},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img313.png"
 ALT="$\displaystyle {\bf u} = {\mit\Omega} $">|; 

$key = q/displaystyle{bfu}_sequiv{bfv}-{bfV}_s,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1026.png"
 ALT="$\displaystyle {\bf u}_s\equiv {\bf v} - {\bf V}_s,$">|; 

$key = q/displaystyle{bfu}_{ss'}={bfv}_s-{bfv}_{s'}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img593.png"
 ALT="$\displaystyle {\bf u}_{ss'} = {\bf v}_s-{\bf v}_{s'}.$">|; 

$key = q/displaystyle{bfv}'=left(v_perpcosleft[{mitOmega},(t-t')+theta,right],,v_perpsinleft[{mitOmega},(t-t')+theta,right],,v_parallelright),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img2369.png"
 ALT="$\displaystyle {\bf v}' = \left( v_\perp\cos\left[{\mit\Omega} (t-t')+\theta \...
... 
v_\perp\sin\left[{\mit\Omega} (t-t')+\theta \right],  v_\parallel\right),$">|; 

$key = q/displaystyle{bfv};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.12ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img282.png"
 ALT="$\displaystyle {\bf v}$">|; 

$key = q/displaystyle{bfv}=left(v_perpcostheta,,v_perpsintheta,,v_parallelright).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img2368.png"
 ALT="$\displaystyle {\bf v} =
\left(v_\perp\cos\theta,  v_\perp\sin\theta,  v_\parallel\right).$">|; 

$key = q/displaystyle{bfv}_E=frac{{bfE}times{bfB}}{B^{2}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img226.png"
 ALT="$\displaystyle {\bf v}_E = \frac{{\bf E}\times{\bf B}}{B^{2}}.$">|; 

$key = q/displaystyle{bfv}_g=frac{partialomega}{partial{bfk}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1794.png"
 ALT="$\displaystyle {\bf v}_g = \frac{\partial\omega}{\partial {\bf k}},$">|; 

$key = q/displaystyle{bfv}_g=frac{partial{mitOmega}}{partial{bfk}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2115.png"
 ALT="$\displaystyle {\bf v}_g = \frac{\partial{\mit\Omega}}{\partial {\bf k}}$">|; 

$key = q/displaystyle{bfv}_s';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img735.png"
 ALT="$\displaystyle {\bf v}_s'$">|; 

$key = q/displaystyle{bfv}_s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img595.png"
 ALT="$\displaystyle {\bf v}_s$">|; 

$key = q/displaystyle{bfv}_{1perp}=frac{left(v_perp^{2}slash2+v_parallel^{2}right)}{{mitOmega},B},{bfb}timesnablaB.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.74ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img480.png"
 ALT="$\displaystyle {\bf v}_{1\perp} = \frac{\left(v_\perp^{2}/2+v_\parallel^{2}\right)}{{\mit\Omega} B} 
{\bf b}\times\nabla B.$">|; 

$key = q/displaystyle{bfv}_{rmph}=frac{omega}{k},skew{-3}hat{bfk},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img1667.png"
 ALT="$\displaystyle {\bf v}_{\rm ph} = \frac{\omega}{k} \skew{-3}\hat{\bf k},$">|; 

$key = q/displaystyle{bfv}_{s'}';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img737.png"
 ALT="$\displaystyle {\bf v}_{s'}'$">|; 

$key = q/displaystyle{bfv}_{s'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img597.png"
 ALT="$\displaystyle {\bf v}_{s'}$">|; 

$key = q/displaystyle{bfv}cdotnablaf=C(f).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1634.png"
 ALT="$\displaystyle {\bf v}\cdot \nabla f = C(f).
$">|; 

$key = q/displaystyle{bfw}_{ss'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img995.png"
 ALT="$\displaystyle {\bf w}_{ss'}$">|; 

$key = q/displaystyle{bfw}_{ss'}=frac{{bfI}-{bfl}{bfl}}{u_{ss'}}=frac{u_{ss'}^2,{bfI}-{bfu}_{ss'}{bfu}_{ss'}}{u_{ss'}^3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.44ex; " SRC="|."$dir".q|img774.png"
 ALT="$\displaystyle {\bf w}_{ss'} = \frac{{\bf I}-{\bf l}{\bf l}}{u_{ss'}} = \frac{u_{ss'}^2 {\bf I}-{\bf u}_{ss'}{\bf u}_{ss'}}{u_{ss'}^3}$">|; 

$key = q/displaystyle{bfz}(t,tau)={bfZ}(t)+epsilon,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img246.png"
 ALT="$\displaystyle {\bf z}(t,\tau) = {\bf Z}(t) +\epsilon $">|; 

$key = q/displaystyle{calE}(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img548.png"
 ALT="$\displaystyle {\cal E}(t)$">|; 

$key = q/displaystyle{calE}=K+e,{mitPhi}=frac{m}{2},(U_parallel^{2}+{bfv}_E^{2})+mu,B+e,{mitPhi};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.01ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img413.png"
 ALT="$\displaystyle {\cal E} = K + e {\mit\Phi} = \frac{m}{2} (U_\parallel^{2} + {\bf v}_E^{2}) +\mu B
+ e {\mit\Phi}$">|; 

$key = q/displaystyle{calE}=mu,B.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img421.png"
 ALT="$\displaystyle {\cal E} = \mu B.$">|; 

$key = q/displaystyle{calI}=oint_{C(t)}{bfp}cdotd{bfq},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.30ex; vertical-align: -2.31ex; " SRC="|."$dir".q|img385.png"
 ALT="$\displaystyle {\cal I} = \oint_{C(t)} {\bf p}\cdot d{\bf q},$">|; 

$key = q/displaystyle{calI}simeqI=oint{bfp}cdotfrac{partial{bfq}}{partialgamma},dgamma.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img396.png"
 ALT="$\displaystyle {\cal I} \simeq I = \oint {\bf p}\cdot \frac{\partial{\bf q}}{\partial\gamma} 
d\gamma.$">|; 

$key = q/displaystyle{calJ}=oint_C{bfp}cdotd{bfq}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img488.png"
 ALT="$\displaystyle {\cal J} = \oint_C {\bf p}\cdot d{\bf q}.$">|; 

$key = q/displaystyle{calJ}simeqJ=ointp_parallel,ds,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img489.png"
 ALT="$\displaystyle {\cal J} \simeq J = \oint p_\parallel ds,$">|; 

$key = q/displaystyle{calM}(omega,{bfk})equivA,n^4-B,n^2+C=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1743.png"
 ALT="$\displaystyle {\cal M}(\omega,{\bf k}) \equiv A n^4- B n^2 + C = 0,$">|; 

$key = q/displaystyle{calM}(omega,{bfk})equiv{rmdet}({bfM})=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1683.png"
 ALT="$\displaystyle {\cal M} (\omega, {\bf k}) \equiv {\rm det}({\bf M}) = 0,$">|; 

$key = q/displaystyle{calM}(omega,{bfk},{bfr},t)=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2103.png"
 ALT="$\displaystyle {\cal M}(\omega,{\bf k}, {\bf r}, t) = 0,$">|; 

$key = q/displaystyle{calM}=omega^2-k^2c^2-{mitPi}_e^{2}=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.51ex; vertical-align: -0.65ex; " SRC="|."$dir".q|img2130.png"
 ALT="$\displaystyle {\cal M} = \omega^2 - k^2 c^2 - {\mit\Pi}_e^{2} = 0,$">|; 

$key = q/displaystyle{calS}>(3,epsilon^{1slash4})^8sim10^4,epsilon^2.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3724.png"
 ALT="$\displaystyle {\cal S} &gt; (3 \epsilon^{1/4})^8 \sim 10^4 \epsilon^2.$">|; 

$key = q/displaystyle{hat{J},hat{psi}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3500.png"
 ALT="$\displaystyle \{\hat{J},\hat{\psi}\}$">|; 

$key = q/displaystyle{mbox{boldmathpsi}}({bfr},t)=intF({bfk}),{mbox{boldmathpsi}},{rme}^{,{rmi},phi},d^3{bfk},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img2109.png"
 ALT="$\displaystyle {\mbox{\boldmath$\psi$}}({\bf r}, t) = \int F({\bf k}) {\mbox{\boldmath$\psi$}} {\rm e}^{ {\rm i} 
\phi} d^3{\bf k},$">|; 

$key = q/displaystyle{mitDelta}'(hat{W})={mitDelta}'(0)-alpha,hat{W}+{calO}(hat{W}^2),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3601.png"
 ALT="$\displaystyle {\mit\Delta}'(\hat{W}) = {\mit\Delta}'(0) - \alpha \hat{W} + {\cal O}(\hat{W}^2),$">|; 

$key = q/displaystyle{mitDelta}',hat{W}ll1.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3532.png"
 ALT="$\displaystyle {\mit\Delta}' \hat{W}\ll 1.$">|; 

$key = q/displaystyle{mitDelta}';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img3523.png"
 ALT="$\displaystyle {\mit\Delta}'$">|; 

$key = q/displaystyle{mitDelta}'=frac{2,(1-hat{k}^2)}{hat{k}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -1.96ex; " SRC="|."$dir".q|img3362.png"
 ALT="$\displaystyle {\mit\Delta}' =\frac{2 (1-\hat{k}^2)}{\hat{k}},$">|; 

$key = q/displaystyle{mitDelta}'=frac{2,hat{k}}{tanhhat{k}}left[frac{hat{k}+hat{k},tanhhat{k}-1}{1-hat{k}slashtanhhat{k}-hat{k}}right].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.74ex; vertical-align: -2.30ex; " SRC="|."$dir".q|img3729.png"
 ALT="$\displaystyle {\mit\Delta}' = \frac{2 \hat{k}}{\tanh\hat{k}}\left[\frac{\hat{k} + \hat{k} \tanh\hat{k}-1}{1-\hat{k}/\tanh\hat{k}-\hat{k}}\right].
$">|; 

$key = q/displaystyle{mitDelta}'=left[frac{1}{hat{psi}},frac{dhat{psi}}{dhat{x}}right]_{hat{x}=0_-}^{hat{x}=0_+}:;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.13ex; vertical-align: -2.40ex; " SRC="|."$dir".q|img3350.png"
 ALT="$\displaystyle {\mit\Delta}' =\left[\frac{1}{\hat{\psi}} \frac{d\hat{\psi}}{d\hat{x}}\right]_{\hat{x}=0_-}^{\hat{x}=0_+}:$">|; 

$key = q/displaystyle{mitDelta}'llS^{1slash3}:;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3417.png"
 ALT="$\displaystyle {\mit\Delta}' \ll S^{1/3}:$">|; 

$key = q/displaystyle{mitDelta}'rightarrow-2,hat{k}+2left[1+frac{1}{2,hat{k}}+{calO}left(frac{1}{hat{k}^{2}}right)right]exp(-2,hat{k});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3731.png"
 ALT="$\displaystyle {\mit\Delta}'\rightarrow -2 \hat{k} + 2\left[1+\frac{1}{2 \hat{k}}+{\cal O}\left(\frac{1}{\hat{k}^{2}}\right)\right]\exp(-2 \hat{k})
$">|; 

$key = q/displaystyle{mitDelta}'rightarrowfrac{2}{hat{k}}-frac{8}{3}+{calO}(hat{k});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.96ex; " SRC="|."$dir".q|img3730.png"
 ALT="$\displaystyle {\mit\Delta}' \rightarrow \frac{2}{\hat{k}} -\frac{8}{3}+{\cal O}(\hat{k})
$">|; 

$key = q/displaystyle{mitDelta}(hat{gamma},S)={mitDelta}'.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3380.png"
 ALT="$\displaystyle {\mit\Delta}(\hat{\gamma},S)={\mit\Delta}'.$">|; 

$key = q/displaystyle{mitDelta}=-frac{pi}{8},frac{{Gamma}(Q^{3slash2}slash4-1slash4)}{{Gamma}(Q^{3slash2}slash4+5slash4)},S^{1slash3},Q^{5slash4},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.30ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img3443.png"
 ALT="$\displaystyle {\mit\Delta} =- \frac{\pi}{8} \frac{{\Gamma}(Q^{3/2}/4-1/4)}{{\Gamma}(Q^{3/2}/4+5/4)} S^{1/3} Q^{5/4},$">|; 

$key = q/displaystyle{mitDelta}=2pi,frac{Gamma(3slash4)}{Gamma(1slash4)},S^{1slash3},Q^{5slash4},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img3747.png"
 ALT="$\displaystyle {\mit\Delta} = 2\pi \frac{\Gamma(3/4)}{\Gamma(1/4)} S^{1/3} Q^{5/4},
$">|; 

$key = q/displaystyle{mitDelta}=6^{2slash3}pi,frac{Gamma(5slash6)}{Gamma(1slash6)},S^{1slash3},Q,P^{1slash6}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img3749.png"
 ALT="$\displaystyle {\mit\Delta} = 6^{2/3}\pi \frac{\Gamma(5/6)}{\Gamma(1/6)} S^{1/3} Q P^{1/6}.
$">|; 

$key = q/displaystyle{mitDelta}=frac{2pi,Gamma(3slash4)}{Gamma(1slash4)},S^{1slash3},Q^{5slash4}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img3410.png"
 ALT="$\displaystyle {\mit\Delta} =\frac{2\pi \Gamma(3/4)}{\Gamma(1/4)} S^{1/3} 
Q^{5/4}.$">|; 

$key = q/displaystyle{mitDelta}=pi,frac{a_{-1}}{a_0},S^{1slash3}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.41ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img3393.png"
 ALT="$\displaystyle {\mit\Delta} = \pi \frac{a_{-1}}{a_0} S^{1/3}.$">|; 

$key = q/displaystyle{mitDelta}l_parallelsimfrac{v_t,L}{V}simfrac{L}{delta};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1550.png"
 ALT="$\displaystyle {\mit\Delta} l_\parallel \sim \frac{v_t L}{V} \sim \frac{L}{\delta}$">|; 

$key = q/displaystyle{mitDelta}l_parallelsimfrac{v_t,L}{V}simfrac{v_t}{delta,{mitOmega}}simL;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1540.png"
 ALT="$\displaystyle {\mit\Delta} l_\parallel \sim \frac{v_t L}{V} \sim \frac{v_t}{\delta {\mit\Omega}}\sim L$">|; 

$key = q/displaystyle{mitDelta}l_parallelsimfrac{v_t,L}{V}simfrac{v_t}{mitOmega}simrho.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1538.png"
 ALT="$\displaystyle {\mit\Delta} l_\parallel \sim \frac{v_t L}{V} \sim \frac{v_t}{\mit\Omega}\sim \rho.$">|; 

$key = q/displaystyle{mitDelta}l_perpsimfrac{v_d,L}{V}simL;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1552.png"
 ALT="$\displaystyle {\mit\Delta} l_\perp \sim \frac{v_d L}{V} \sim L$">|; 

$key = q/displaystyle{mitDelta}simeqfrac{2pi,{Gamma}(3slash4)}{{Gamma}(1slash4)},S^{1slash3},Q^{5slash4},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img3444.png"
 ALT="$\displaystyle {\mit\Delta} \simeq\frac{2\pi {\Gamma}(3/4)}{{\Gamma}(1/4)} S^{1/3} Q^{5/4},$">|; 

$key = q/displaystyle{mitGamma}_{ss'}=frac{2,gamma_{ss'}}{m_s^{2}}=left(frac{e_s,e_{s'}}{4pi,epsilon_0,m_s}right)^2,4pi,ln{mitLambda}_c.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img819.png"
 ALT="$\displaystyle {\mit\Gamma}_{ss'} = \frac{2 \gamma_{ss'}}{m_s^{2}}= \left(\frac{e_s e_{s'}}{4\pi \epsilon_0 m_s}\right)^2 4\pi \ln{\mit\Lambda}_c.$">|; 

$key = q/displaystyle{mitLambda}=frac{4pi}{3},n,lambda_D^{3}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img76.png"
 ALT="$\displaystyle {\mit\Lambda} = \frac{4\pi}{3}  n  \lambda_D^{3}.$">|; 

$key = q/displaystyle{mitOmega}(X,xi)=frac{X^2}{2}+cosxi.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3509.png"
 ALT="$\displaystyle {\mit\Omega}(X,\xi) = \frac{X^2}{2} + \cos\xi.$">|; 

$key = q/displaystyle{mitOmega},frac{partialmbox{boldmathrho}}{partialgamma}={bfu}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img310.png"
 ALT="$\displaystyle {\mit\Omega} \frac{\partial\mbox{\boldmath$\rho$}}{\partial \gamma} = {\bf u}.$">|; 

$key = q/displaystyle{mitOmega},tau_R>frac{2^{5slash2},(k,a)^{3}}{m}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img3035.png"
 ALT="$\displaystyle {\mit\Omega} \tau_R &gt; \frac{2^{5/2} (k a)^{3}}{m}.$">|; 

$key = q/displaystyle{mitOmega}=frac{eB}{m};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img135.png"
 ALT="$\displaystyle {\mit\Omega} = \frac{e B}{m}$">|; 

$key = q/displaystyle{mitOmega}>frac{2pi,R}{M},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img2917.png"
 ALT="$\displaystyle {\mit\Omega} &gt; \frac{ 2\pi R}{M},$">|; 

$key = q/displaystyle{mitOmega}>frac{2pi,R}{M}:;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img2899.png"
 ALT="$\displaystyle {\mit\Omega} &gt; \frac{2\pi R}{M}:$">|; 

$key = q/displaystyle{mitOmega}_esim{mitOmega}_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1431.png"
 ALT="$\displaystyle {\mit\Omega}_e \sim {\mit\Omega}_i$">|; 

$key = q/displaystyle{mitOmega}_i,tau_i,,,,{mitOmega}_e,tau_egg1,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1222.png"
 ALT="$\displaystyle {\mit\Omega}_i \tau_i,    {\mit\Omega}_e  \tau_e \gg 1,$">|; 

$key = q/displaystyle{mitOmega}_i,tau_i,,,,{mitOmega}_e,tau_ell1,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1156.png"
 ALT="$\displaystyle {\mit\Omega}_i \tau_i,    {\mit\Omega}_e \tau_e \ll 1,$">|; 

$key = q/displaystyle{mitOmega}_p=frac{e,B}{m_p}=2.98,L^{-3},,{rmkHz},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.13ex; vertical-align: -2.26ex; " SRC="|."$dir".q|img447.png"
 ALT="$\displaystyle {\mit\Omega}_p = \frac{e B}{m_p} = 2.98 L^{-3}  {\rm kHz},$">|; 

$key = q/displaystyle{mitPhi}(x)=frac{sigma,lambda_D}{2,epsilon_0},{rme}^{-|x|slashlambda_D},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.85ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img192.png"
 ALT="$\displaystyle {\mit\Phi}(x) = \frac{\sigma \lambda_D}{2 \epsilon_0} {\rm e}^{-\vert x\vert/\lambda_D},
$">|; 

$key = q/displaystyle{mitPhi}_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img2903.png"
 ALT="$\displaystyle {\mit\Phi}_1$">|; 

$key = q/displaystyle{mitPhi}_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img2905.png"
 ALT="$\displaystyle {\mit\Phi}_2$">|; 

$key = q/displaystyle{mitPi}=left(frac{e^2,n_0}{2,epsilon_0,m_e}right)^{1slash2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.91ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img208.png"
 ALT="$\displaystyle {\mit\Pi}=\left(\frac{e^2 n_0}{2 \epsilon_0 m_e}\right)^{1/2},
$">|; 

$key = q/displaystyle{mitPi}=left(frac{e^2,n_0}{3,epsilon_0,m_e}right)^{1slash2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.91ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img210.png"
 ALT="$\displaystyle {\mit\Pi}=\left(\frac{e^2 n_0}{3 \epsilon_0 m_e}\right)^{1/2},
$">|; 

$key = q/displaystyle{mitPi}=left(frac{n,e^2}{epsilon_0,m}right)^{1slash2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.91ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img42.png"
 ALT="$\displaystyle {\mit\Pi} = \left(\frac{n e^2}{\epsilon_0 m}\right)^{1/2},$">|; 

$key = q/displaystyle{mitPi}=left({mitPi}_e^{2}+{mitPi}_i^{2}right)^{1slash2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.68ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img163.png"
 ALT="$\displaystyle {\mit\Pi} = \left({\mit\Pi}_e^{2} + {\mit\Pi}_i^{2}\right)^{1/2},
$">|; 

$key = q/displaystyle{mitPi}=left[frac{e^2,n_0}{2,epsilon_0}left(frac{1}{m_e}+frac{1}{m_i}right)right]^{1slash2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.91ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img209.png"
 ALT="$\displaystyle {\mit\Pi}=\left[\frac{e^2 n_0}{2 \epsilon_0}\left(\frac{1}{m_e}+\frac{1}{m_i}\right)\right]^{1/2}.
$">|; 

$key = q/displaystyle{mitPi}_e=sqrt{frac{N,e^2}{epsilon_0,m_e}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.75ex; vertical-align: -2.57ex; " SRC="|."$dir".q|img2131.png"
 ALT="$\displaystyle {\mit\Pi}_e = \sqrt{\frac{N e^2}{\epsilon_0 m_e}}.$">|; 

$key = q/displaystyle{mitPsi}=int_{bfS}{bfB}cdotd{bfS}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img2690.png"
 ALT="$\displaystyle {\mit\Psi} = \int_{\bf S} {\bf B}\cdot d{\bf S}.$">|; 

$key = q/displaystyle{mitTheta}=frac{pi}{2}-sin^{-1}left(frac{alpha}{sqrt{4+alpha^{2}}}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.52ex; vertical-align: -2.30ex; " SRC="|."$dir".q|img715.png"
 ALT="$\displaystyle {\mit\Theta} = \frac{\pi}{2}-\sin^{-1}\left(\frac{\alpha}{\sqrt{4+\alpha^{2}}}\right).$">|; 

$key = q/displaystyle{mitTheta}=int_0^{z_{rmmax}}frac{dtheta}{dz},dz.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.13ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img707.png"
 ALT="$\displaystyle {\mit\Theta} = \int_0^{z_{\rm max}} \frac{d\theta}{dz} dz.$">|; 

$key = q/displaystyle{mitTheta}_s=frac{w_s}{T_s}-frac{mbox{boldmathpi}_s:nabla{bfV}_s}{T_s}-frac{{bfq}_s}{T_s}cdotfrac{nablaT_s}{T_s}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img1094.png"
 ALT="$\displaystyle {\mit\Theta}_s = \frac{w_s}{T_s} - \frac{\mbox{\boldmath$\pi$}_s : \nabla {\bf V}_s}{T_s}
- \frac{{\bf q}_s}{T_s} \cdot \frac{\nabla T_s}{T_s}.$">|; 

$key = q/displaystyle{mitchi}_t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1126.png"
 ALT="$\displaystyle {\mit\chi}_t$">|; 

$key = q/displaystyle{mitchi}_v;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1124.png"
 ALT="$\displaystyle {\mit\chi}_v$">|; 

$key = q/displaystyle{rmAi}(-hat{z})simeqfrac{1}{2sqrt{pi}},|hat{z}|^{-1slash4},expleft(-frac{2}{3},|hat{z}|^{3slash2}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.52ex; vertical-align: -2.30ex; " SRC="|."$dir".q|img1957.png"
 ALT="$\displaystyle {\rm Ai}(-\hat{z})\simeq \frac{1}{2\sqrt{\pi}}  \vert\hat{z}\vert^{-1/4} \exp
\left(-\frac{2}{3} \vert\hat{z}\vert^{3/2}\right)$">|; 

$key = q/displaystyle{rmAi}(-hat{z})simeqfrac{1}{sqrt{pi}},hat{z}^{-1slash4},sinleft(frac{2}{3},hat{z}^{3slash2}+frac{pi}{4}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.52ex; vertical-align: -2.30ex; " SRC="|."$dir".q|img1958.png"
 ALT="$\displaystyle {\rm Ai}(-\hat{z})\simeq \frac{1}{\sqrt{\pi}}  \hat{z}^{-1/4} \sin
\left(\frac{2}{3} \hat{z}^{3/2}+\frac{\pi}{4}\right)$">|; 

$key = q/displaystyle{rmerf}(zeta)=frac{2}{sqrt{pi}}int_0^zeta{rme}^{-t^{2}},dt;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.69ex; vertical-align: -2.30ex; " SRC="|."$dir".q|img906.png"
 ALT="$\displaystyle {\rm erf}(\zeta) = \frac{2}{\sqrt{\pi}}\int_0^\zeta {\rm e}^{-t^{2}} dt$">|; 

$key = q/displaystyle{rme}^{,{rmi},a,sinx}equivsum_{n=-infty,infty}J_n(a),{rme}^{,{rmi},n,x},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -2.80ex; " SRC="|."$dir".q|img2388.png"
 ALT="$\displaystyle {\rm e}^{ {\rm i} a \sin x} \equiv \sum_{n=-\infty,\infty}
J_n(a) {\rm e}^{ {\rm i} n x},$">|; 

$key = q/displaystyle{rmi},k,E=-frac{e}{epsilon_0}int_{-infty}^{infty}F_1(u),du,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.05ex; " SRC="|."$dir".q|img2246.png"
 ALT="$\displaystyle {\rm i} k E =-\frac{e}{\epsilon_0} \int_{-\infty}^{\infty} F_1(u) du,$">|; 

$key = q/displaystyle{rmi},k,bar{E}=-frac{e}{epsilon_0}int_{-infty}^{infty}!bar{F}_1(u),du,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.05ex; " SRC="|."$dir".q|img2254.png"
 ALT="$\displaystyle {\rm i} k \bar{E} =-\frac{e}{\epsilon_0}\int_{-\infty}^{\infty}\!\bar{F}_1(u) 
du,$">|; 

$key = q/displaystyle{rmi},omega,B_x=-frac{dE_y}{dz}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.80ex; " SRC="|."$dir".q|img2038.png"
 ALT="$\displaystyle {\rm i} \omega B_x = -\frac{d E_y}{dz}.$">|; 

$key = q/displaystyle{{mitOmega}}_e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1694.png"
 ALT="$\displaystyle {{\mit\Omega}}_e$">|; 

$key = q/displaystyle{{mitOmega}}_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1696.png"
 ALT="$\displaystyle {{\mit\Omega}}_i$">|; 

$key = q/displaystyle{{mitPi}}_e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1690.png"
 ALT="$\displaystyle { {\mit\Pi}}_e$">|; 

$key = q/displaystyle{{mitPi}}_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1692.png"
 ALT="$\displaystyle { {\mit\Pi}}_i$">|; 

$key = q/displaystyle|{mitOmega}_e|=frac{e,B}{m_e}=5.46,L^{-3},,{rmMHz},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.85ex; vertical-align: -1.96ex; " SRC="|."$dir".q|img448.png"
 ALT="$\displaystyle \vert{\mit\Omega}_e\vert = \frac{e B}{m_e} = 5.46 L^{-3}  {\rm MHz},$">|; 

$key = q/displaystyle|{mitOmega}_e|=omega+|{mitOmega}_e|',z,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img2052.png"
 ALT="$\displaystyle \vert{\mit\Omega}_e\vert = \omega + \vert{\mit\Omega}_e\vert' z,$">|; 

$key = q/dll!sqrt{A};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.34ex; " SRC="|."$dir".q|img180.png"
 ALT="$d\ll \!\sqrt{A}$">|; 

$key = q/dot{phantom{r}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 0.28ex; vertical-align: 1.04ex; " SRC="|."$dir".q|img669.png"
 ALT="$\dot{\phantom{r}}$">|; 

$key = q/ds;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img471.png"
 ALT="$ds$">|; 

$key = q/dsigmaslashd{mitOmega};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img643.png"
 ALT="$d\sigma/d{\mit\Omega}$">|; 

$key = q/dskew{3}hat{mitPhi}slashdy;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1584.png"
 ALT="$d\skew{3}\hat{\mit\Phi}/dy$">|; 

$key = q/dslashdt=partialslashpartialt+{bfU}cdotnabla;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img411.png"
 ALT="$d/dt = \partial/\partial t+{\bf U}\cdot\nabla$">|; 

$key = q/dslashdtequivpartialslashpartialt+{bfV}cdotnabla;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1479.png"
 ALT="$d/dt \equiv \partial/\partial t + {\bf V} \cdot\nabla$">|; 

$key = q/dt=-dzslashu_z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2082.png"
 ALT="$dt = -dz/u_z$">|; 

$key = q/duslashdr;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2789.png"
 ALT="$du/dr$">|; 

$key = q/d{bfr};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img2694.png"
 ALT="$d{\bf r}$">|; 

$key = q/d{mitOmega}=2pi,sinchi,dchi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img722.png"
 ALT="$d{\mit\Omega}=2\pi \sin\chi d\chi$">|; 

$key = q/d{mitOmega}=sinchi,dchi,dphi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img733.png"
 ALT="$d{\mit\Omega}= \sin\chi d\chi d\phi$">|; 

$key = q/d{mitOmega}slashdb;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img727.png"
 ALT="$d{\mit\Omega}/db$">|; 

$key = q/d{mitOmega}slashdr;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2986.png"
 ALT="$d{\mit\Omega}/dr$">|; 

$key = q/e,({mitPhi}_p-{mitPhi}_s)=T_eslash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1624.png"
 ALT="$e ({\mit\Phi}_p-{\mit\Phi}_s) =T_e/2$">|; 

$key = q/e,VslashT;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img204.png"
 ALT="$e V/T$">|; 

$key = q/e,n_e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2549.png"
 ALT="$e n_e$">|; 

$key = q/e,{mitOmega}slash2pi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img340.png"
 ALT="$e {\mit\Omega}/2\pi$">|; 

$key = q/e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img28.png"
 ALT="$e$">|; 

$key = q/e_i=-e_e=e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img62.png"
 ALT="$e_i = - e_e = e$">|; 

$key = q/e_s,e_{s'}slash(4pi,epsilon_0,mu_{ss'},u_{ss'}^{2});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.51ex; vertical-align: -0.76ex; " SRC="|."$dir".q|img834.png"
 ALT="$e_s e_{s'}/(4\pi \epsilon_0 \mu_{ss'} u_{ss'}^{2})$">|; 

$key = q/e_s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img576.png"
 ALT="$e_s$">|; 

$key = q/e_{s'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img663.png"
 ALT="$e_{s'}$">|; 

$key = q/epsilon(k,p);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2258.png"
 ALT="$\epsilon(k,p)$">|; 

$key = q/epsilon(k,p)=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2276.png"
 ALT="$\epsilon(k,p)=0$">|; 

$key = q/epsilon;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img240.png"
 ALT="$\epsilon$">|; 

$key = q/epsilon<0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1977.png"
 ALT="$\epsilon&lt;0$">|; 

$key = q/epsilon=aslashL;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3703.png"
 ALT="$\epsilon = a/L$">|; 

$key = q/epsilon>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1976.png"
 ALT="$\epsilon&gt;0$">|; 

$key = q/epsilon_i(k,omega_r);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2605.png"
 ALT="$\epsilon_i(k,\omega_r)$">|; 

$key = q/epsilon_r(k,omega_r);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2603.png"
 ALT="$\epsilon_r(k,\omega_r)$">|; 

$key = q/epsilonll1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2655.png"
 ALT="$\epsilon \ll 1$">|; 

$key = q/epsilonrightarrow0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1985.png"
 ALT="$\epsilon\rightarrow 0$">|; 

$key = q/epsilonsim1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3725.png"
 ALT="$\epsilon\sim 1$">|; 

$key = q/eta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1116.png"
 ALT="$\eta$">|; 

$key = q/eta=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2930.png"
 ALT="$\eta=0$">|; 

$key = q/eta_0^e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.81ex; " SRC="|."$dir".q|img1274.png"
 ALT="$\eta_0^e$">|; 

$key = q/eta_0^i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.57ex; vertical-align: -0.81ex; " SRC="|."$dir".q|img1275.png"
 ALT="$\eta_0^i$">|; 

$key = q/eta_0^islasheta_0^esimsqrt{m_islashm_e};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.62ex; vertical-align: -0.81ex; " SRC="|."$dir".q|img1221.png"
 ALT="$\eta_0^i/\eta_0^e\sim\sqrt{m_i/m_e}$">|; 

$key = q/etarightarrow0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2925.png"
 ALT="$\eta\rightarrow 0$">|; 

$key = q/etasimn,m,chi_v;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1220.png"
 ALT="$\eta\sim n m \chi_v$">|; 

$key = q/exp(,{rmi},phi);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.58ex; " SRC="|."$dir".q|img2069.png"
 ALT="$\exp( {\rm i} \phi)$">|; 

$key = q/exp(-{rmi},omega,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.58ex; " SRC="|."$dir".q|img2172.png"
 ALT="$\exp(-{\rm i} \omega t)$">|; 

$key = q/exp(zeta^{2});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.58ex; " SRC="|."$dir".q|img2326.png"
 ALT="$\exp(\zeta^{2})$">|; 

$key = q/exp[,{rmi},({bfk}cdot{bfr}-omega,t)];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.58ex; " SRC="|."$dir".q|img1871.png"
 ALT="$\exp[ {\rm i} ({\bf k}\cdot{\bf r}-\omega t)]$">|; 

$key = q/f(U)-k^{2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2526.png"
 ALT="$f(U)-k^{2}$">|; 

$key = q/f(U);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2528.png"
 ALT="$f(U)$">|; 

$key = q/f(U)rightarrow0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2529.png"
 ALT="$f(U)\rightarrow 0$">|; 

$key = q/f(u);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2541.png"
 ALT="$f(u)$">|; 

$key = q/f;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img370.png"
 ALT="$f$">|; 

$key = q/f_0({bfv}')=f_0({bfv});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2377.png"
 ALT="$f_0({\bf v}') = f_0({\bf v})$">|; 

$key = q/f_0({bfv});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2243.png"
 ALT="$f_0({\bf v})$">|; 

$key = q/f_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1109.png"
 ALT="$f_0$">|; 

$key = q/f_1({bfv},t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2244.png"
 ALT="$f_1({\bf v},t)$">|; 

$key = q/f_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1110.png"
 ALT="$f_1$">|; 

$key = q/f_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1111.png"
 ALT="$f_2$">|; 

$key = q/f_e({bfr},{bfv},t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2226.png"
 ALT="$f_e({\bf r},{\bf v}, t)$">|; 

$key = q/f_e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1649.png"
 ALT="$f_e$">|; 

$key = q/f_s',f_{s'}'-f_s,f_{s'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.76ex; " SRC="|."$dir".q|img859.png"
 ALT="$f_s' f_{s'}'-f_s f_{s'}$">|; 

$key = q/f_s';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img633.png"
 ALT="$f_s'$">|; 

$key = q/f_s'equivf_s({bfr},{bfv}_s',t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img740.png"
 ALT="$f_s'\equiv f_s({\bf r},{\bf v}_s', t)$">|; 

$key = q/f_s({bfr},{bfv},t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1011.png"
 ALT="$f_s({\bf r}, {\bf v}, t)$">|; 

$key = q/f_s({bfr},{bfv}_s',t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img635.png"
 ALT="$f_s({\bf r}, {\bf v}_s',t)$">|; 

$key = q/f_s({bfr},{bfv}_s,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img621.png"
 ALT="$f_s({\bf r}, {\bf v}_s,t)$">|; 

$key = q/f_s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img623.png"
 ALT="$f_s$">|; 

$key = q/f_{1,s};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2397.png"
 ALT="$f_{1 s}$">|; 

$key = q/f_{s'}';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.76ex; " SRC="|."$dir".q|img634.png"
 ALT="$f_{s'}'$">|; 

$key = q/f_{s'}'equivf_{s'}({bfr},{bfv}_{s'}',t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.76ex; " SRC="|."$dir".q|img743.png"
 ALT="$f_{s'}'\equiv f_{s'}({\bf r},{\bf v}_{s'}', t)$">|; 

$key = q/f_{s'}({bfr},{bfv}_{s'}',t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.76ex; " SRC="|."$dir".q|img636.png"
 ALT="$f_{s'}({\bf r}, {\bf v}_{s'}',t)$">|; 

$key = q/f_{s'}({bfr},{bfv}_{s'},t),d^3{bfr},d^3{bfv}_{s'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img616.png"
 ALT="$f_{s'}({\bf r},{\bf v}_{s'},t) d^3{\bf r} d^3{\bf v}_{s'}$">|; 

$key = q/f_{s'}({bfr},{bfv}_{s'},t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img622.png"
 ALT="$f_{s'}({\bf r}, {\bf v}_{s'},t)$">|; 

$key = q/f_{s'}({bfv});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img893.png"
 ALT="$f_{s'}({\bf v})$">|; 

$key = q/f_{s'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img624.png"
 ALT="$f_{s'}$">|; 

$key = q/g({bfr},t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1063.png"
 ALT="$g({\bf r}, t)$">|; 

$key = q/g;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1065.png"
 ALT="$g$">|; 

$key = q/gamma,tau_A=0.6235,{calS}^{-1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3700.png"
 ALT="$\gamma \tau_A = 0.6235 {\cal S}^{-1/2}$">|; 

$key = q/gamma,tau_A=tilde{gamma},{calS}^{-1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3693.png"
 ALT="$\gamma \tau_A =\tilde{\gamma}
  {\cal S}^{-1/2}$">|; 

$key = q/gamma,tau_Asim{calS}^{-1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3687.png"
 ALT="$\gamma \tau_A\sim {\cal S}^{-1/2}$">|; 

$key = q/gamma;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img285.png"
 ALT="$\gamma$">|; 

$key = q/gamma<0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2640.png"
 ALT="$\gamma&lt;0$">|; 

$key = q/gamma=M,{mitOmega}slash(2pi,L);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2901.png"
 ALT="$\gamma= M {\mit\Omega}/(2\pi L)$">|; 

$key = q/gamma=hat{gamma}slashtau_H;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3312.png"
 ALT="$\gamma=\hat{\gamma}/\tau_H$">|; 

$key = q/gamma>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2916.png"
 ALT="$\gamma&gt;0$">|; 

$key = q/gamma_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img225.png"
 ALT="$\gamma_0$">|; 

$key = q/gammaequiv-{rmi},omegasimeqk,(V-v_e);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2556.png"
 ALT="$\gamma \equiv -{\rm i} \omega \simeq k (V-v_e)$">|; 

$key = q/gammarightarrow0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2918.png"
 ALT="$\gamma\rightarrow 0$">|; 

$key = q/gammasimS^{-1slash3}slashtau_H=S^{2slash3}slashtau_R;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3620.png"
 ALT="$\gamma\sim S^{-1/3}/\tau_H=S^{2/3}/\tau_R$">|; 

$key = q/gammaslashomega_r;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2643.png"
 ALT="$\gamma/\omega_r$">|; 

$key = q/h(omega)=c,tau(omega)slash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2201.png"
 ALT="$h(\omega)=c \tau(\omega)/2$">|; 

$key = q/h;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img150.png"
 ALT="$h$">|; 

$key = q/h_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2209.png"
 ALT="$h_0$">|; 

$key = q/hat{J}({mitOmega});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3527.png"
 ALT="$\hat{J}({\mit\Omega})$">|; 

$key = q/hat{J};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3499.png"
 ALT="$\hat{J}$">|; 

$key = q/hat{J}geq1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.22ex; " SRC="|."$dir".q|img3624.png"
 ALT="$\hat{J}\geq 1$">|; 

$key = q/hat{J}simhat{W};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3493.png"
 ALT="$\hat{J}\sim \hat{W}$">|; 

$key = q/hat{U};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3497.png"
 ALT="$\hat{U}$">|; 

$key = q/hat{U}sim1slashhat{W}^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3496.png"
 ALT="$\hat{U}\sim 1/\hat{W}^{ 2}$">|; 

$key = q/hat{W};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3465.png"
 ALT="$\hat{W}$">|; 

$key = q/hat{W}=skew{3}hat{mitPsi}_1^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.73ex; vertical-align: -0.80ex; " SRC="|."$dir".q|img3554.png"
 ALT="$\hat{W}= \skew{3}\hat{\mit\Psi}_1^{1/2}$">|; 

$key = q/hat{W}_sll1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3607.png"
 ALT="$\hat{W}_s\ll 1$">|; 

$key = q/hat{W}sim1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3609.png"
 ALT="$\hat{W}\sim 1$">|; 

$key = q/hat{W}simepsilon;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3707.png"
 ALT="$\hat{W}\sim \epsilon$">|; 

$key = q/hat{delta};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3470.png"
 ALT="$\hat{\delta}$">|; 

$key = q/hat{delta}=S^{-1slash3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3668.png"
 ALT="$\hat{\delta}= S^{-1/3}$">|; 

$key = q/hat{delta}=S^{-2slash5};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3475.png"
 ALT="$\hat{\delta} = S^{-2/5}$">|; 

$key = q/hat{delta}_{rmSP}=delta_{rmSP}slasha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3709.png"
 ALT="$\hat{\delta}_{\rm SP} =\delta_{\rm SP}/a$">|; 

$key = q/hat{delta}gghat{W};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3615.png"
 ALT="$\hat{\delta}\gg\hat{W}$">|; 

$key = q/hat{delta}llhat{W};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3616.png"
 ALT="$\hat{\delta}\ll \hat{W}$">|; 

$key = q/hat{delta}simS^{-1slash3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3619.png"
 ALT="$\hat{\delta}\sim S^{-1/3}$">|; 

$key = q/hat{delta}simS^{-2slash5};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3473.png"
 ALT="$\hat{\delta}\sim S^{-2/5}$">|; 

$key = q/hat{gamma};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3413.png"
 ALT="$\hat{\gamma}$">|; 

$key = q/hat{gamma}^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3323.png"
 ALT="$\hat{\gamma}^{ 2}$">|; 

$key = q/hat{gamma}rightarrow0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3416.png"
 ALT="$\hat{\gamma}\rightarrow 0$">|; 

$key = q/hat{gamma}simS^{-3slash5};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3421.png"
 ALT="$\hat{\gamma}\sim S^{-3/5}$">|; 

$key = q/hat{k};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img3370.png"
 ALT="$\hat{k}$">|; 

$key = q/hat{k}<1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img3366.png"
 ALT="$\hat{k}&lt; 1$">|; 

$key = q/hat{k}<hat{k}_c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img3733.png"
 ALT="$\hat{k}&lt;\hat{k}_c$">|; 

$key = q/hat{k}=0.5;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3352.png"
 ALT="$\hat{k}=0.5$">|; 

$key = q/hat{k}=1.5;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3353.png"
 ALT="$\hat{k}=1.5$">|; 

$key = q/hat{k}=k,a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img3645.png"
 ALT="$\hat{k}=k a$">|; 

$key = q/hat{k}>1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img3364.png"
 ALT="$\hat{k}&gt;1$">|; 

$key = q/hat{k}_c=0.639;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img3735.png"
 ALT="$\hat{k}_c=0.639$">|; 

$key = q/hat{k}rightarrow0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3368.png"
 ALT="$\hat{k}\rightarrow 0$">|; 

$key = q/hat{k}rightarrowinfty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img3732.png"
 ALT="$\hat{k}\rightarrow\infty$">|; 

$key = q/hat{mitPsi}(0)=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3662.png"
 ALT="$\hat{\mit\Psi}(0) = 0$">|; 

$key = q/hat{mitPsi}^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img3622.png"
 ALT="$\hat{\mit\Psi}^{1/2}$">|; 

$key = q/hat{mitPsi}^{1slash2}simhat{delta};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3670.png"
 ALT="$\hat{\mit\Psi}^{1/2}\sim \hat{\delta}$">|; 

$key = q/hat{mitPsi}sim1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img3664.png"
 ALT="$\hat{\mit\Psi}\sim 1$">|; 

$key = q/hat{psi}(-hat{x})=hat{psi}(hat{x});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3374.png"
 ALT="$\hat{\psi}(-\hat{x})=\hat{\psi}(\hat{x})$">|; 

$key = q/hat{psi}(hat{x});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3342.png"
 ALT="$\hat{\psi}(\hat{x})$">|; 

$key = q/hat{psi}(hat{x})rightarrow0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3727.png"
 ALT="$\hat{\psi}(\hat{x})\rightarrow 0$">|; 

$key = q/hat{psi}(hat{x},xi);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3452.png"
 ALT="$\hat{\psi}(\hat{x},\xi)$">|; 

$key = q/hat{psi}(hat{x},xi)=skew{3}hat{mitPsi};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3464.png"
 ALT="$\hat{\psi}(\hat{x},\xi) = \skew{3}\hat{\mit\Psi}$">|; 

$key = q/hat{psi}(hat{x},xi,hat{t})=skew{3}hat{mitPsi}(hat{t}),{mitOmega}(X,xi);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3508.png"
 ALT="$\hat{\psi}(\hat{x},\xi,\hat{t}) = \skew{3}\hat{\mit\Psi}(\hat{t}) {\mit\Omega}(X,\xi)$">|; 

$key = q/hat{psi}(|hat{x}|rightarrowinfty)rightarrow0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3354.png"
 ALT="$\hat{\psi}(\vert\hat{x}\vert\rightarrow\infty)\rightarrow 0$">|; 

$key = q/hat{psi};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3348.png"
 ALT="$\hat{\psi}$">|; 

$key = q/hat{psi}=hat{x},skew{3}hat{phi}_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3372.png"
 ALT="$\hat{\psi}=\hat{x} \skew{3}\hat{\phi}_0$">|; 

$key = q/hat{psi}simhat{W}^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3492.png"
 ALT="$\hat{\psi}\sim \hat{W}^{ 2}$">|; 

$key = q/hat{psi}simskew{3}hat{phi};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3321.png"
 ALT="$\hat{\psi}\sim \skew{3}\hat{\phi}$">|; 

$key = q/hat{t}simhat{W};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3494.png"
 ALT="$\hat{t}\sim \hat{W}$">|; 

$key = q/hat{x};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img3343.png"
 ALT="$\hat{x}$">|; 

$key = q/hat{x}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3334.png"
 ALT="$\hat{x}=0$">|; 

$key = q/hat{x}=0_+;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3345.png"
 ALT="$\hat{x}=0_+$">|; 

$key = q/hat{x}=0_-;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3347.png"
 ALT="$\hat{x}=0_-$">|; 

$key = q/hat{x}rightarrow-infty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img3346.png"
 ALT="$\hat{x}\rightarrow-\infty$">|; 

$key = q/hat{x}rightarrowinfty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img3344.png"
 ALT="$\hat{x}\rightarrow\infty$">|; 

$key = q/hat{x}simhat{W};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3490.png"
 ALT="$\hat{x}\sim \hat{W}$">|; 

$key = q/hat{z};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.73ex; vertical-align: -0.27ex; " SRC="|."$dir".q|img1962.png"
 ALT="$\hat{z}$">|; 

$key = q/hat{z}=-{rmi},skew{3}hat{epsilon};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.27ex; " SRC="|."$dir".q|img1974.png"
 ALT="$\hat{z} = -{\rm i} \skew{3}\hat{\epsilon}$">|; 

$key = q/hat{z}>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.73ex; vertical-align: -0.27ex; " SRC="|."$dir".q|img2026.png"
 ALT="$\hat{z}&gt; 0$">|; 

$key = q/hat{z}rightarrow+infty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.73ex; vertical-align: -0.27ex; " SRC="|."$dir".q|img1959.png"
 ALT="$\hat{z}\rightarrow +\infty$">|; 

$key = q/hat{z}rightarrow-infty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.73ex; vertical-align: -0.27ex; " SRC="|."$dir".q|img1956.png"
 ALT="$\hat{z}\rightarrow-\infty$">|; 

$key = q/hbarslash(2,mu_{ss'},u_{ss'});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img835.png"
 ALT="$\hbar/(2 \mu_{ss'} u_{ss'})$">|; 

$key = q/i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img34.png"
 ALT="$i$">|; 

$key = q/includegraphics[height=1.5in]{Chapter08slashfig8_6.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="528" HEIGHT="169" STYLE=""
 SRC="|."$dir".q|img2932.png"
 ALT="\includegraphics[height=1.5in]{Chapter08/fig8_6.eps}">;WIDTH="528" HEIGHT="169"|; 

$key = q/includegraphics[height=1.8in]{Chapter02slashfig2_4.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="522" HEIGHT="204" STYLE=""
 SRC="|."$dir".q|img496.png"
 ALT="\includegraphics[height=1.8in]{Chapter02/fig2_4.eps}">;WIDTH="522" HEIGHT="204"|; 

$key = q/includegraphics[height=2.5in]{Chapter02slashfig2_2.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="314" HEIGHT="286" STYLE=""
 SRC="|."$dir".q|img433.png"
 ALT="\includegraphics[height=2.5in]{Chapter02/fig2_2.eps}">;WIDTH="314" HEIGHT="286"|; 

$key = q/includegraphics[height=2.5in]{Chapter03slashfig3_1.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="496" HEIGHT="279" STYLE=""
 SRC="|."$dir".q|img700.png"
 ALT="\includegraphics[height=2.5in]{Chapter03/fig3_1.eps}">;WIDTH="496" HEIGHT="279"|; 

$key = q/includegraphics[height=2.5in]{Chapter07slashfig7_3.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="364" HEIGHT="285" STYLE=""
 SRC="|."$dir".q|img2273.png"
 ALT="\includegraphics[height=2.5in]{Chapter07/fig7_3.eps}">;WIDTH="364" HEIGHT="285"|; 

$key = q/includegraphics[height=2.5in]{Chapter07slashfig7_5.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="403" HEIGHT="284" STYLE=""
 SRC="|."$dir".q|img2313.png"
 ALT="\includegraphics[height=2.5in]{Chapter07/fig7_5.eps}">;WIDTH="403" HEIGHT="284"|; 

$key = q/includegraphics[height=2.5in]{Chapter07slashfig7_6.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="455" HEIGHT="284" STYLE=""
 SRC="|."$dir".q|img2317.png"
 ALT="\includegraphics[height=2.5in]{Chapter07/fig7_6.eps}">;WIDTH="455" HEIGHT="284"|; 

$key = q/includegraphics[height=2.5in]{Chapter07slashfig7_7.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="511" HEIGHT="284" STYLE=""
 SRC="|."$dir".q|img2348.png"
 ALT="\includegraphics[height=2.5in]{Chapter07/fig7_7.eps}">;WIDTH="511" HEIGHT="284"|; 

$key = q/includegraphics[height=2.5in]{Chapter08slashfig8_5.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="219" HEIGHT="284" STYLE=""
 SRC="|."$dir".q|img2896.png"
 ALT="\includegraphics[height=2.5in]{Chapter08/fig8_5.eps}">;WIDTH="219" HEIGHT="284"|; 

$key = q/includegraphics[height=2.5in]{Chapter08slashfig8_7.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="353" HEIGHT="279" STYLE=""
 SRC="|."$dir".q|img3056.png"
 ALT="\includegraphics[height=2.5in]{Chapter08/fig8_7.eps}">;WIDTH="353" HEIGHT="279"|; 

$key = q/includegraphics[height=2.5in]{Chapter08slashfig8_8.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="461" HEIGHT="283" STYLE=""
 SRC="|."$dir".q|img3180.png"
 ALT="\includegraphics[height=2.5in]{Chapter08/fig8_8.eps}">;WIDTH="461" HEIGHT="283"|; 

$key = q/includegraphics[height=2.5in]{Chapter08slashfig8_9.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="360" HEIGHT="283" STYLE=""
 SRC="|."$dir".q|img3198.png"
 ALT="\includegraphics[height=2.5in]{Chapter08/fig8_9.eps}">;WIDTH="360" HEIGHT="283"|; 

$key = q/includegraphics[height=2.75in]{Chapter07slashfig7_11.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="497" HEIGHT="312" STYLE=""
 SRC="|."$dir".q|img2638.png"
 ALT="\includegraphics[height=2.75in]{Chapter07/fig7_11.eps}">;WIDTH="497" HEIGHT="312"|; 

$key = q/includegraphics[height=2.9in]{Chapter09slashfig9_1.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="497" HEIGHT="331" STYLE=""
 SRC="|."$dir".q|img3285.png"
 ALT="\includegraphics[height=2.9in]{Chapter09/fig9_1.eps}">;WIDTH="497" HEIGHT="331"|; 

$key = q/includegraphics[height=2in]{Chapter07slashfig7_4.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="512" HEIGHT="225" STYLE=""
 SRC="|."$dir".q|img2289.png"
 ALT="\includegraphics[height=2in]{Chapter07/fig7_4.eps}">;WIDTH="512" HEIGHT="225"|; 

$key = q/includegraphics[height=2in]{Chapter09slashfig9_10.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="528" HEIGHT="223" STYLE=""
 SRC="|."$dir".q|img3629.png"
 ALT="\includegraphics[height=2in]{Chapter09/fig9_10.eps}">;WIDTH="528" HEIGHT="223"|; 

$key = q/includegraphics[height=3.1in]{Chapter05slashfig5_3.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="412" HEIGHT="344" STYLE=""
 SRC="|."$dir".q|img1868.png"
 ALT="\includegraphics[height=3.1in]{Chapter05/fig5_3.eps}">;WIDTH="412" HEIGHT="344"|; 

$key = q/includegraphics[height=3.26in]{Chapter06slashfig6_1.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="300" HEIGHT="368" STYLE=""
 SRC="|."$dir".q|img1980.png"
 ALT="\includegraphics[height=3.26in]{Chapter06/fig6_1.eps}">;WIDTH="300" HEIGHT="368"|; 

$key = q/includegraphics[height=3.2in]{Chapter02slashfig2_3.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="527" HEIGHT="366" STYLE=""
 SRC="|."$dir".q|img482.png"
 ALT="\includegraphics[height=3.2in]{Chapter02/fig2_3.eps}">;WIDTH="527" HEIGHT="366"|; 

$key = q/includegraphics[height=3.5in]{Chapter04slashfig4_4.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="485" HEIGHT="360" STYLE=""
 SRC="|."$dir".q|img1605.png"
 ALT="\includegraphics[height=3.5in]{Chapter04/fig4_4.eps}">;WIDTH="485" HEIGHT="360"|; 

$key = q/includegraphics[height=3.5in]{Chapter04slashfig4_5.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="520" HEIGHT="360" STYLE=""
 SRC="|."$dir".q|img1619.png"
 ALT="\includegraphics[height=3.5in]{Chapter04/fig4_5.eps}">;WIDTH="520" HEIGHT="360"|; 

$key = q/includegraphics[height=3.5in]{Chapter07slashfig7_10.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="368" HEIGHT="398" STYLE=""
 SRC="|."$dir".q|img2525.png"
 ALT="\includegraphics[height=3.5in]{Chapter07/fig7_10.eps}">;WIDTH="368" HEIGHT="398"|; 

$key = q/includegraphics[height=3.5in]{Chapter07slashfig7_8.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="527" HEIGHT="401" STYLE=""
 SRC="|."$dir".q|img2476.png"
 ALT="\includegraphics[height=3.5in]{Chapter07/fig7_8.eps}">;WIDTH="527" HEIGHT="401"|; 

$key = q/includegraphics[height=3.5in]{Chapter07slashfig7_9.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="527" HEIGHT="401" STYLE=""
 SRC="|."$dir".q|img2497.png"
 ALT="\includegraphics[height=3.5in]{Chapter07/fig7_9.eps}">;WIDTH="527" HEIGHT="401"|; 

$key = q/includegraphics[height=3.5in]{Chapter08slashfig8_2.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="527" HEIGHT="401" STYLE=""
 SRC="|."$dir".q|img2794.png"
 ALT="\includegraphics[height=3.5in]{Chapter08/fig8_2.eps}">;WIDTH="527" HEIGHT="401"|; 

$key = q/includegraphics[height=3.5in]{Chapter08slashfig8_3.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="527" HEIGHT="396" STYLE=""
 SRC="|."$dir".q|img2812.png"
 ALT="\includegraphics[height=3.5in]{Chapter08/fig8_3.eps}">;WIDTH="527" HEIGHT="396"|; 

$key = q/includegraphics[height=3.5in]{Chapter08slashfig8_4.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="466" HEIGHT="400" STYLE=""
 SRC="|."$dir".q|img2833.png"
 ALT="\includegraphics[height=3.5in]{Chapter08/fig8_4.eps}">;WIDTH="466" HEIGHT="400"|; 

$key = q/includegraphics[height=3.5in]{Chapter09slashfig9_11.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="527" HEIGHT="396" STYLE=""
 SRC="|."$dir".q|img3690.png"
 ALT="\includegraphics[height=3.5in]{Chapter09/fig9_11.eps}">;WIDTH="527" HEIGHT="396"|; 

$key = q/includegraphics[height=3.75in]{Chapter09slashfig9_5.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="512" HEIGHT="376" STYLE=""
 SRC="|."$dir".q|img3451.png"
 ALT="\includegraphics[height=3.75in]{Chapter09/fig9_5.eps}">;WIDTH="512" HEIGHT="376"|; 

$key = q/includegraphics[height=3.75in]{Chapter09slashfig9_7.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="490" HEIGHT="373" STYLE=""
 SRC="|."$dir".q|img3559.png"
 ALT="\includegraphics[height=3.75in]{Chapter09/fig9_7.eps}">;WIDTH="490" HEIGHT="373"|; 

$key = q/includegraphics[height=3.8in]{Chapter09slashfig9_6.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="512" HEIGHT="381" STYLE=""
 SRC="|."$dir".q|img3537.png"
 ALT="\includegraphics[height=3.8in]{Chapter09/fig9_6.eps}">;WIDTH="512" HEIGHT="381"|; 

$key = q/includegraphics[height=3.8in]{Chapter09slashfig9_8.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="512" HEIGHT="381" STYLE=""
 SRC="|."$dir".q|img3591.png"
 ALT="\includegraphics[height=3.8in]{Chapter09/fig9_8.eps}">;WIDTH="512" HEIGHT="381"|; 

$key = q/includegraphics[height=3.8in]{Chapter09slashfig9_9.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="495" HEIGHT="381" STYLE=""
 SRC="|."$dir".q|img3618.png"
 ALT="\includegraphics[height=3.8in]{Chapter09/fig9_9.eps}">;WIDTH="495" HEIGHT="381"|; 

$key = q/includegraphics[height=3.in]{Chapter09slashfig9_2.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="514" HEIGHT="344" STYLE=""
 SRC="|."$dir".q|img3351.png"
 ALT="\includegraphics[height=3.in]{Chapter09/fig9_2.eps}">;WIDTH="514" HEIGHT="344"|; 

$key = q/includegraphics[height=3.in]{Chapter09slashfig9_3.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="511" HEIGHT="339" STYLE=""
 SRC="|."$dir".q|img3369.png"
 ALT="\includegraphics[height=3.in]{Chapter09/fig9_3.eps}">;WIDTH="511" HEIGHT="339"|; 

$key = q/includegraphics[height=3.in]{Chapter09slashfig9_4.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="514" HEIGHT="342" STYLE=""
 SRC="|."$dir".q|img3437.png"
 ALT="\includegraphics[height=3.in]{Chapter09/fig9_4.eps}">;WIDTH="514" HEIGHT="342"|; 

$key = q/includegraphics[height=3in]{Chapter02slashfig2_1.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="469" HEIGHT="342" STYLE=""
 SRC="|."$dir".q|img422.png"
 ALT="\includegraphics[height=3in]{Chapter02/fig2_1.eps}">;WIDTH="469" HEIGHT="342"|; 

$key = q/includegraphics[height=3in]{Chapter04slashfig4_1.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="447" HEIGHT="334" STYLE=""
 SRC="|."$dir".q|img1238.png"
 ALT="\includegraphics[height=3in]{Chapter04/fig4_1.eps}">;WIDTH="447" HEIGHT="334"|; 

$key = q/includegraphics[height=3in]{Chapter04slashfig4_2.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="442" HEIGHT="334" STYLE=""
 SRC="|."$dir".q|img1260.png"
 ALT="\includegraphics[height=3in]{Chapter04/fig4_2.eps}">;WIDTH="442" HEIGHT="334"|; 

$key = q/includegraphics[height=3in]{Chapter04slashfig4_3.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="445" HEIGHT="334" STYLE=""
 SRC="|."$dir".q|img1533.png"
 ALT="\includegraphics[height=3in]{Chapter04/fig4_3.eps}">;WIDTH="445" HEIGHT="334"|; 

$key = q/includegraphics[height=3in]{Chapter05slashfig5_1.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="396" HEIGHT="333" STYLE=""
 SRC="|."$dir".q|img1844.png"
 ALT="\includegraphics[height=3in]{Chapter05/fig5_1.eps}">;WIDTH="396" HEIGHT="333"|; 

$key = q/includegraphics[height=3in]{Chapter05slashfig5_2.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="429" HEIGHT="333" STYLE=""
 SRC="|."$dir".q|img1854.png"
 ALT="\includegraphics[height=3in]{Chapter05/fig5_2.eps}">;WIDTH="429" HEIGHT="333"|; 

$key = q/includegraphics[height=3in]{Chapter07slashfig7_1.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="313" HEIGHT="340" STYLE=""
 SRC="|."$dir".q|img2260.png"
 ALT="\includegraphics[height=3in]{Chapter07/fig7_1.eps}">;WIDTH="313" HEIGHT="340"|; 

$key = q/includegraphics[height=3in]{Chapter07slashfig7_2.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="344" HEIGHT="337" STYLE=""
 SRC="|."$dir".q|img2269.png"
 ALT="\includegraphics[height=3in]{Chapter07/fig7_2.eps}">;WIDTH="344" HEIGHT="337"|; 

$key = q/includegraphics[height=3in]{Chapter08slashfig8_1.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="430" HEIGHT="340" STYLE=""
 SRC="|."$dir".q|img2748.png"
 ALT="\includegraphics[height=3in]{Chapter08/fig8_1.eps}">;WIDTH="430" HEIGHT="340"|; 

$key = q/infty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 0.89ex; vertical-align: 0.04ex; " SRC="|."$dir".q|img3529.png"
 ALT="$\infty$">|; 

$key = q/intf_0,d^3{bfv}=n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.84ex; vertical-align: -0.92ex; " SRC="|."$dir".q|img2230.png"
 ALT="$\int f_0 d^3{\bf v}
=n$">|; 

$key = q/j=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1603.png"
 ALT="$j=0$">|; 

$key = q/j_e=(1slash4),e,n_e(0),bar{V}_e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1595.png"
 ALT="$j_e=(1/4) e n_e(0) \bar{V}_e$">|; 

$key = q/j_parallelequiv{bfj}cdot{bfb};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img1701.png"
 ALT="$j_\parallel \equiv {\bf j}\cdot{\bf b}$">|; 

$key = q/j_pm={bfj}cdot{bfe}_pm;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1713.png"
 ALT="$j_\pm = {\bf j}\cdot {\bf e}_\pm$">|; 

$key = q/j_{0,z}slash(B_0slashmu_0,a);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3287.png"
 ALT="$j_{0 z}/(B_0/\mu_0 a)$">|; 

$key = q/j_{0tmspace+thinmuskip{.1667em}z}slash(B_0slashmu_0tmspace+thinmuskip{.1667em}a);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img7.png"
 ALT="$j_{0\tmspace +\thinmuskip {.1667em}z}/(B_0/\mu _0\tmspace +\thinmuskip {.1667em}a)$">|; 

$key = q/k(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img541.png"
 ALT="$k(t)$">|; 

$key = q/k,Lgg1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img1910.png"
 ALT="$k L\gg 1$">|; 

$key = q/k,Lrightarrowinfty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img1659.png"
 ALT="$k L\rightarrow \infty$">|; 

$key = q/k,a,{calS}^{1slash4}geq1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.22ex; " SRC="|."$dir".q|img3686.png"
 ALT="$k a {\cal S}^{1/4}\geq 1$">|; 

$key = q/k,a,{calS}^{1slash4}ll1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.15ex; " SRC="|."$dir".q|img3683.png"
 ALT="$k a {\cal S}^{1/4}\ll 1$">|; 

$key = q/k,a=0.39;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.14ex; " SRC="|."$dir".q|img3045.png"
 ALT="$k a=0.39$">|; 

$key = q/k,a=1.359,{calS}^{-1slash4};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.15ex; " SRC="|."$dir".q|img3701.png"
 ALT="$k a=1.359 {\cal S}^{-1/4}$">|; 

$key = q/k,a=tilde{k},{calS}^{-1slash4};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.15ex; " SRC="|."$dir".q|img3694.png"
 ALT="$k a = \tilde{k} {\cal S}^{-1/4}$">|; 

$key = q/k,agg1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img3020.png"
 ALT="$k a\gg 1$">|; 

$key = q/k,all1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img3677.png"
 ALT="$k a\ll 1$">|; 

$key = q/k,asim{calS}^{-1slash4};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.15ex; " SRC="|."$dir".q|img3688.png"
 ALT="$k a\sim {\cal S}^{-1/4}$">|; 

$key = q/k,lambda_Dll1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img2297.png"
 ALT="$k \lambda_D\ll 1$">|; 

$key = q/k,lambda_{D,e}ll1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2564.png"
 ALT="$k \lambda_{D e}\ll 1$">|; 

$key = q/k,u_0-omegarightarrow0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2309.png"
 ALT="$k u_0-\omega\rightarrow 0$">|; 

$key = q/k;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img1010.png"
 ALT="$k$">|; 

$key = q/k=0,1,2,cdots;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img1014.png"
 ALT="$k=0,1,2,\cdots$">|; 

$key = q/k=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3561.png"
 ALT="$k=0$">|; 

$key = q/k=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img3562.png"
 ALT="$k=1$">|; 

$key = q/k=2pislashL;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3704.png"
 ALT="$k=2\pi/L$">|; 

$key = q/k=hat{k}slasha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3311.png"
 ALT="$k=\hat{k}/a$">|; 

$key = q/k=k_0,n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1918.png"
 ALT="$k=k_0 n$">|; 

$key = q/k=k_m;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img3546.png"
 ALT="$k=k_m$">|; 

$key = q/k=sqrt{(1+{mitOmega})slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.51ex; " SRC="|."$dir".q|img3560.png"
 ALT="$k =\sqrt{(1+{\mit\Omega})/2}$">|; 

$key = q/k>1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img3563.png"
 ALT="$k&gt;1$">|; 

$key = q/k^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img2160.png"
 ALT="$k^2$">|; 

$key = q/k^{2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img2531.png"
 ALT="$k^{2}$">|; 

$key = q/k_0=omegaslashc;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1917.png"
 ALT="$k_0=\omega/c$">|; 

$key = q/k_0^{2},n^2,E_y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.57ex; vertical-align: -0.79ex; " SRC="|."$dir".q|img1938.png"
 ALT="$k_0^{2} n^2 E_y$">|; 

$key = q/k_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3549.png"
 ALT="$k_1$">|; 

$key = q/k_m;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img3556.png"
 ALT="$k_m$">|; 

$key = q/k_m=m,k_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img3548.png"
 ALT="$k_m=m k_1$">|; 

$key = q/k_parallel;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img2475.png"
 ALT="$k_\parallel$">|; 

$key = q/k_parallelrightarrow0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img2456.png"
 ALT="$k_\parallel\rightarrow 0$">|; 

$key = q/k_perp;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img2496.png"
 ALT="$k_\perp$">|; 

$key = q/k_perprightarrow0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img2439.png"
 ALT="$k_\perp\rightarrow 0$">|; 

$key = q/k_x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2164.png"
 ALT="$k_x$">|; 

$key = q/k_x^{2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.65ex; " SRC="|."$dir".q|img2162.png"
 ALT="$k_x^{2}$">|; 

$key = q/k_y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2165.png"
 ALT="$k_y$">|; 

$key = q/k_y^{2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.68ex; vertical-align: -0.95ex; " SRC="|."$dir".q|img2163.png"
 ALT="$k_y^{2}$">|; 

$key = q/k_z^{2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.51ex; vertical-align: -0.76ex; " SRC="|."$dir".q|img2161.png"
 ALT="$k_z^{2}$">|; 

$key = q/kappa;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1117.png"
 ALT="$\kappa$">|; 

$key = q/kappa=(y_+^{2}-y_-^{2})slash(y_+^{2}+y_-^{2});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.64ex; " SRC="|."$dir".q|img562.png"
 ALT="$\kappa=(y_+^{2}-y_-^{2})/(y_+^{2}+y_-^{2})$">|; 

$key = q/kappa_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2762.png"
 ALT="$\kappa_0$">|; 

$key = q/kappa_parallel^eslashkappa_parallel^isimsqrt{m_islashm_e};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.84ex; vertical-align: -1.05ex; " SRC="|."$dir".q|img1206.png"
 ALT="$\kappa_\parallel^e/\kappa_\parallel^i\sim \sqrt{m_i/m_e}$">|; 

$key = q/kappa_perp^islashkappa_perp^esimsqrt{m_islashm_e};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.64ex; " SRC="|."$dir".q|img1250.png"
 ALT="$\kappa_\perp^i/\kappa_\perp^e\sim \sqrt{m_i/m_e}$">|; 

$key = q/kequiv|{bfk}|;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img1668.png"
 ALT="$k\equiv \vert{\bf k}\vert$">|; 

$key = q/kll{mitPi}_eslashV;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2555.png"
 ALT="$k\ll {\mit\Pi}_e/V$">|; 

$key = q/l;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img1105.png"
 ALT="$l$">|; 

$key = q/l=tau,v_t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1205.png"
 ALT="$l=\tau v_t$">|; 

$key = q/l=v_tslashnu;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1638.png"
 ALT="$l=v_t/\nu$">|; 

$key = q/l_e,partialT_eslashpartialx;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1180.png"
 ALT="$l_e \partial T_e/\partial x$">|; 

$key = q/l_esimv_e,tau_e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1179.png"
 ALT="$l_e\sim v_e \tau_e$">|; 

$key = q/lambda(z)=2pislash[k_0,n(z)];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1944.png"
 ALT="$\lambda(z)= 2\pi/ [k_0 n(z)]$">|; 

$key = q/lambda;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2467.png"
 ALT="$\lambda$">|; 

$key = q/lambda_D({rmm});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img84.png"
 ALT="$\lambda_D({\rm m})$">|; 

$key = q/lambda_D;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img71.png"
 ALT="$\lambda_D$">|; 

$key = q/lambda_D=(T_eslashm_e,{mitPi}_e^{2})^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.65ex; " SRC="|."$dir".q|img2296.png"
 ALT="$\lambda_D =(T_e/m_e {\mit\Pi}_e^{2})^{1/2}$">|; 

$key = q/lambda_D=(epsilon_0,T_eslashe^2,n_s)^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1580.png"
 ALT="$\lambda_D= (\epsilon_0 T_e/e^2 n_s)^{1/2}$">|; 

$key = q/lambda_D=[(epsilon_0slashe^2,n_0),T_i,T_eslash(T_i+T_e)]^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img193.png"
 ALT="$\lambda_D =[(\epsilon_0/e^2 n_0) T_i T_e/(T_i+T_e)]^{1/2}$">|; 

$key = q/lambda_D=sqrt{epsilon_0,Tslash2,e^2,n_0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.73ex; vertical-align: -0.63ex; " SRC="|."$dir".q|img199.png"
 ALT="$\lambda_D = \sqrt{\epsilon_0 T/2 e^2 n_0}$">|; 

$key = q/lambda_Drightarrow0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img175.png"
 ALT="$\lambda_D\rightarrow 0$">|; 

$key = q/lambda_e,bar{v}_e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1320.png"
 ALT="$\lambda_e \bar{v}_e$">|; 

$key = q/lambda_e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1375.png"
 ALT="$\lambda_e$">|; 

$key = q/lambda_erightarrow0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2486.png"
 ALT="$\lambda_e\rightarrow 0$">|; 

$key = q/lambda_erightarrowinfty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2492.png"
 ALT="$\lambda_e\rightarrow\infty$">|; 

$key = q/lambda_i,bar{v}_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1385.png"
 ALT="$\lambda_i \bar{v}_i$">|; 

$key = q/lambda_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1417.png"
 ALT="$\lambda_i$">|; 

$key = q/lambda_s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2417.png"
 ALT="$\lambda_s$">|; 

$key = q/lambda_s=k_perp^{2},v_s^{2}slash(2,{mitOmega}_s^{2});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img2514.png"
 ALT="$\lambda_s=k_\perp^{2} v_s^{2}/(2 {\mit\Omega}_s^{2})$">|; 

$key = q/lambda_sll1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2480.png"
 ALT="$\lambda_s\ll 1$">|; 

$key = q/lambda_srightarrow0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2423.png"
 ALT="$\lambda_s\rightarrow 0$">|; 

$key = q/lambda_{D,e}=(epsilon_0,T_eslashn_e,e^2)^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img168.png"
 ALT="$\lambda_{D e} = (\epsilon_0 T_e/n_e e^2)^{1/2}$">|; 

$key = q/lambda_{D,e}=v_eslash{mitPi}_e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2565.png"
 ALT="$\lambda_{D e} = v_e/{\mit\Pi}_e$">|; 

$key = q/lambda_{D,i}=(epsilon_0,T_islashn_i,Z^{2},e^2)^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img169.png"
 ALT="$\lambda_{D i} = (\epsilon_0 T_i/n_i Z^{2} e^2)^{1/2}$">|; 

$key = q/lambda_{D,s}=(T_sslashm_s,{mitPi}_s^{2})^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img2576.png"
 ALT="$\lambda_{D s}=(T_s/m_s {\mit\Pi}_s^{2})^{1/2}$">|; 

$key = q/lambdalesssimrho_s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2473.png"
 ALT="$\lambda\lesssim \rho_s$">|; 

$key = q/lambdarightarrowrho_s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2472.png"
 ALT="$\lambda\rightarrow
\rho_s$">|; 

$key = q/langlecdotsrangleequivoint(cdots),dgammaslash2pi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.84ex; vertical-align: -0.92ex; " SRC="|."$dir".q|img511.png"
 ALT="$\langle\cdots\rangle\equiv \oint(\cdots) d\gamma/2\pi$">|; 

$key = q/langlecosxirangleslashlangle1rangle;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3538.png"
 ALT="$\langle\cos\xi\rangle/\langle 1\rangle$">|; 

$key = q/langlewidetilde{cosxi}rangle=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.62ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3520.png"
 ALT="$\langle\widetilde{\cos\xi}\rangle = 0$">|; 

$key = q/ln(IslashI_s+1);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1623.png"
 ALT="$\ln (I/I_s+1)$">|; 

$key = q/ln(f_s,f_{s'}slashf_s',f_{s'}');MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.76ex; " SRC="|."$dir".q|img858.png"
 ALT="$\ln(f_s f_{s'}/f_s' f_{s'}')$">|; 

$key = q/ln(m_islash2pi,m_e)^{1slash2}simeq2.8;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1606.png"
 ALT="$\ln(m_i/2\pi m_e)^{1/2}\simeq 2.8$">|; 

$key = q/ln{mitLambda}_c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img828.png"
 ALT="$\ln{\mit\Lambda}_c$">|; 

$key = q/ln{mitLambda}_c=ln(b_{rmmax}slashb_{rmmin});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img833.png"
 ALT="$\ln{\mit\Lambda}_c= \ln(b_{\rm max}/b_{\rm min})$">|; 

$key = q/ln{mitLambda}_csimln{mitLambda};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img976.png"
 ALT="$\ln{\mit\Lambda}_c\sim \ln {\mit\Lambda}$">|; 

$key = q/ln{rme}=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img202.png"
 ALT="$\ln{\rm e}=1$">|; 

$key = q/m,u_perp^{2}slash(2,B);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.64ex; " SRC="|."$dir".q|img384.png"
 ALT="$m u_\perp^{2}/(2 B)$">|; 

$key = q/m;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img44.png"
 ALT="$m$">|; 

$key = q/m=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3037.png"
 ALT="$m=0$">|; 

$key = q/m=1,infty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img3547.png"
 ALT="$m=1,\infty$">|; 

$key = q/m=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img21.png"
 ALT="$m=1$">|; 

$key = q/m>1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img3542.png"
 ALT="$m&gt;1$">|; 

$key = q/m_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img1192.png"
 ALT="$m_1$">|; 

$key = q/m_1slashm_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1191.png"
 ALT="$m_1/m_2$">|; 

$key = q/m_e,n,v_eslashtau_e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1176.png"
 ALT="$m_e n v_e/\tau_e$">|; 

$key = q/m_e,{bfU};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1168.png"
 ALT="$m_e {\bf U}$">|; 

$key = q/m_e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img26.png"
 ALT="$m_e$">|; 

$key = q/m_ellm_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img971.png"
 ALT="$m_e\ll m_i$">|; 

$key = q/m_eslashm_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1185.png"
 ALT="$m_e/m_i$">|; 

$key = q/m_eslashm_ill1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1725.png"
 ALT="$m_e/m_i\ll 1$">|; 

$key = q/m_eslashm_irightarrow0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1729.png"
 ALT="$m_e/m_i\rightarrow 0$">|; 

$key = q/m_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img29.png"
 ALT="$m_i$">|; 

$key = q/m_islashm_e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1187.png"
 ALT="$m_i/m_e$">|; 

$key = q/m_s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img577.png"
 ALT="$m_s$">|; 

$key = q/m_s^{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img2628.png"
 ALT="$m_s^{-1}$">|; 

$key = q/m_{s'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img589.png"
 ALT="$m_{s'}$">|; 

$key = q/mathaccentV{hat}05E{k};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img12.png"
 ALT="$\mathaccentV {hat}05E{k}$">|; 

$key = q/mathaccentV{hat}05E{k}=0.5;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img9.png"
 ALT="$\mathaccentV {hat}05E{k}=0.5$">|; 

$key = q/mathaccentV{hat}05E{k}=1.5;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img10.png"
 ALT="$\mathaccentV {hat}05E{k}=1.5$">|; 

$key = q/mathaccentV{hat}05E{psi}(mathaccentV{hat}05E{x},xi);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img16.png"
 ALT="$\mathaccentV {hat}05E{\psi }(\mathaccentV {hat}05E{x},\xi )$">|; 

$key = q/mathaccentV{tilde}07E{gamma}=0.6235;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img24.png"
 ALT="$\mathaccentV {tilde}07E{\gamma }=0.6235$">|; 

$key = q/mathaccentV{tilde}07E{k}=1.359;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.14ex; " SRC="|."$dir".q|img25.png"
 ALT="$\mathaccentV {tilde}07E{k}=1.359$">|; 

$key = q/mpm1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img3003.png"
 ALT="$m\pm 1$">|; 

$key = q/mu,nabla^2{bfV};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3200.png"
 ALT="$\mu \nabla^2 {\bf V}$">|; 

$key = q/mu;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img342.png"
 ALT="$\mu$">|; 

$key = q/mu=m,u_perp^2slash(2,B);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.64ex; " SRC="|."$dir".q|img363.png"
 ALT="$\mu=m  u_\perp^2 /(2 B)$">|; 

$key = q/mu=m,u_perp^{2}slash(2,B);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.64ex; " SRC="|."$dir".q|img350.png"
 ALT="$\mu=m u_\perp^{2}/(2 B)$">|; 

$key = q/mu=m,v_perp^{2}slash(2,B_{rmmin});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.64ex; " SRC="|."$dir".q|img429.png"
 ALT="$\mu = m  v_\perp^{2}/(2  B_{\rm min})$">|; 

$key = q/mu_{ss'}=m_s,m_{s'}slash(m_s+m_{s'});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img836.png"
 ALT="$\mu_{ss'}=m_s m_{s'}/(m_s+m_{s'})$">|; 

$key = q/murightarrow0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3030.png"
 ALT="$\mu\rightarrow 0$">|; 

$key = q/musim{calO}(1);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1422.png"
 ALT="$\mu\sim {\cal O}(1)$">|; 

$key = q/n(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1926.png"
 ALT="$n(z)$">|; 

$key = q/n({rmm}^{-3});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img81.png"
 ALT="$n({\rm m}^{-3})$">|; 

$key = q/n,T;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img142.png"
 ALT="$n T$">|; 

$key = q/n,T_e,U;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1210.png"
 ALT="$n T_e U$">|; 

$key = q/n,T_i,v_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1255.png"
 ALT="$n T_i v_i$">|; 

$key = q/n,v_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1254.png"
 ALT="$n v_i$">|; 

$key = q/n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img41.png"
 ALT="$n$">|; 

$key = q/n=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2159.png"
 ALT="$n=0$">|; 

$key = q/n=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img1960.png"
 ALT="$n=1$">|; 

$key = q/n=n(x);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1647.png"
 ALT="$n=n(x)$">|; 

$key = q/n=n(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1925.png"
 ALT="$n=n(z)$">|; 

$key = q/n=n_0+n_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1906.png"
 ALT="$n=n_0+n_1$">|; 

$key = q/n=n_e=n_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1138.png"
 ALT="$n=n_e=n_i$">|; 

$key = q/n=pm1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img2431.png"
 ALT="$n=\pm 1$">|; 

$key = q/n^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img1750.png"
 ALT="$n^2$">|; 

$key = q/n^2=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1840.png"
 ALT="$n^2=0$">|; 

$key = q/n^2=1-alpha,(z-h_0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2216.png"
 ALT="$n^2=1-\alpha (z-h_0)$">|; 

$key = q/n^2=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img1839.png"
 ALT="$n^2=1$">|; 

$key = q/n^2=L;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img1770.png"
 ALT="$n^2 = L$">|; 

$key = q/n^2=R;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img1768.png"
 ALT="$n^2 = R$">|; 

$key = q/n^2rightarrowinfty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img1834.png"
 ALT="$n^2\rightarrow\infty$">|; 

$key = q/n^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img1945.png"
 ALT="$n^{1/2}$">|; 

$key = q/n_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img61.png"
 ALT="$n_0$">|; 

$key = q/n_e(0)=n_s,exp[,e,({mitPhi}_w-{mitPhi}_s)slashT_e)];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.58ex; " SRC="|."$dir".q|img1593.png"
 ALT="$n_e(0) = n_s \exp[ e ({\mit\Phi}_w-{\mit\Phi}_s)/T_e)]$">|; 

$key = q/n_e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img159.png"
 ALT="$n_e$">|; 

$key = q/n_e=n_s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1574.png"
 ALT="$n_e=n_s$">|; 

$key = q/n_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1559.png"
 ALT="$n_i$">|; 

$key = q/n_i=n_e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img839.png"
 ALT="$n_i=n_e$">|; 

$key = q/n_i=n_eslashZ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img162.png"
 ALT="$n_i=n_e/Z$">|; 

$key = q/n_p;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1626.png"
 ALT="$n_p$">|; 

$key = q/n_perp;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img2465.png"
 ALT="$n_\perp$">|; 

$key = q/n_s({bfr},t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img580.png"
 ALT="$n_s({\bf r},t)$">|; 

$key = q/n_s,{bfV}_s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1069.png"
 ALT="$n_s {\bf V}_s$">|; 

$key = q/n_s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img37.png"
 ALT="$n_s$">|; 

$key = q/n_{s'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img718.png"
 ALT="$n_{s'}$">|; 

$key = q/nablaB;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img334.png"
 ALT="$\nabla B$">|; 

$key = q/nabla^{2}_v(1slashv)=-4pi,delta({bfv});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.66ex; " SRC="|."$dir".q|img815.png"
 ALT="$\nabla^{2}_v(1/v)=-4\pi \delta ({\bf v})$">|; 

$key = q/nabla^{2}_v(v)=2slashv;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.66ex; " SRC="|."$dir".q|img816.png"
 ALT="$\nabla^{2}_v(v)=2/v$">|; 

$key = q/nabla^{2}_v;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.66ex; " SRC="|."$dir".q|img814.png"
 ALT="$\nabla^{2}_v$">|; 

$key = q/nabla_parallel(cdots)equiv[{bfb}cdotnabla(cdots)],{bfb};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img1227.png"
 ALT="$\nabla_\parallel(\cdots) \equiv [{\bf b}\cdot\nabla
(\cdots)] {\bf b}$">|; 

$key = q/nabla_perpequivnabla-nabla_parallel;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img1228.png"
 ALT="$\nabla_\perp \equiv
\nabla-\nabla_\parallel$">|; 

$key = q/nabla_vequivpartialslashpartial{bfv};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1007.png"
 ALT="$\nabla_v\equiv\partial/\partial{\bf v}$">|; 

$key = q/nabla_{bfk};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img2113.png"
 ALT="$\nabla_{\bf k}$">|; 

$key = q/nabla_{bfk}phi=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2112.png"
 ALT="$\nabla_{\bf k} \phi=0$">|; 

$key = q/nablacdot{bfB}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1873.png"
 ALT="$\nabla\cdot{\bf B}=0$">|; 

$key = q/nablacdot{bfB}=nablacdot{bfV}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img2978.png"
 ALT="$\nabla\cdot{\bf B}=\nabla\cdot{\bf V}=0$">|; 

$key = q/nablacdot{bfE}=rho_cslashepsilon_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1872.png"
 ALT="$\nabla\cdot{\bf E}=\rho_c/\epsilon_0$">|; 

$key = q/nablacdot{bfV};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3245.png"
 ALT="$\nabla\cdot{\bf V}$">|; 

$key = q/nablacdot{bfV}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img2931.png"
 ALT="$\nabla\cdot{\bf V} = 0$">|; 

$key = q/nablacdot{bfV}={rmi},{bfk}cdot{bfV}={rmi},k,V_x,sintheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1824.png"
 ALT="$\nabla\cdot{\bf V} =
{\rm i} {\bf k}\cdot{\bf V} = {\rm i} k V_x \sin\theta$">|; 

$key = q/nablacdot{bfj}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.54ex; " SRC="|."$dir".q|img1480.png"
 ALT="$\nabla\cdot{\bf j} =0$">|; 

$key = q/nablaequivpartialslashpartial{bfr};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1006.png"
 ALT="$\nabla\equiv\partial/\partial{\bf r}$">|; 

$key = q/nablantimes{bfb};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1531.png"
 ALT="$\nabla n \times{\bf b}$">|; 

$key = q/nablatimes({bfj}times{bfB}+nablap)=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3502.png"
 ALT="$\nabla\times({\bf j}\times {\bf B} +\nabla p)=0$">|; 

$key = q/nablatimes({bfj}times{bfB}+nablap)={bf0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3330.png"
 ALT="$\nabla\times({\bf j}\times{\bf B}+\nabla p)={\bf0}$">|; 

$key = q/nablatimes{bfB}simeq{bf0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img478.png"
 ALT="$\nabla\times{\bf B} \simeq {\bf0}$">|; 

$key = q/nsim2times10^{14},{rmm}^{-3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2768.png"
 ALT="$n\sim
2\times 10^{14} {\rm m}^{-3}$">|; 

$key = q/nsim{calO}(1);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2470.png"
 ALT="$n\sim {\cal O}(1)$">|; 

$key = q/ntimesn;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.23ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img2096.png"
 ALT="$n\times n$">|; 

$key = q/nu,l^{2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1133.png"
 ALT="$\nu l^{2}$">|; 

$key = q/nu;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img121.png"
 ALT="$\nu$">|; 

$key = q/nu=tau^{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1204.png"
 ALT="$\nu=\tau^{-1}$">|; 

$key = q/nu_e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1652.png"
 ALT="$\nu_e$">|; 

$key = q/nu_eequivtau_e^{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.65ex; " SRC="|."$dir".q|img2048.png"
 ALT="$\nu_e \equiv\tau_e^{-1}$">|; 

$key = q/nu_s,m_s,{bfV}_s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1885.png"
 ALT="$\nu_s m_s {\bf V}_s$">|; 

$key = q/nu_s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1886.png"
 ALT="$\nu_s$">|; 

$key = q/nu_sllomega;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1889.png"
 ALT="$\nu_s\ll \omega$">|; 

$key = q/nu_{ss'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img117.png"
 ALT="$\nu_{ss'}$">|; 

$key = q/nugg{mitPi};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img127.png"
 ALT="$\nu\gg {\mit\Pi}$">|; 

$key = q/null{mitOmega};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img212.png"
 ALT="$\nu\ll {\mit\Omega}$">|; 

$key = q/null{mitPi};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img126.png"
 ALT="$\nu\ll {\mit\Pi}$">|; 

$key = q/oint;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.84ex; vertical-align: -0.92ex; " SRC="|."$dir".q|img253.png"
 ALT="$\oint$">|; 

$key = q/omega;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img176.png"
 ALT="$\omega$">|; 

$key = q/omega=(T_eslashm_i)^{1slash2},k;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2343.png"
 ALT="$\omega=(T_e/m_i)^{1/2} k$">|; 

$key = q/omega=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3247.png"
 ALT="$\omega=0$">|; 

$key = q/omega=omega_0+deltaomega;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2298.png"
 ALT="$\omega=\omega_0+\delta\omega$">|; 

$key = q/omega=omega_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img1842.png"
 ALT="$\omega=\omega_1$">|; 

$key = q/omega=omega_r+{rmi},gamma;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2584.png"
 ALT="$\omega=\omega_r + {\rm i} \gamma$">|; 

$key = q/omega=omega_s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2071.png"
 ALT="$\omega=\omega_s$">|; 

$key = q/omega=omega_{n,s};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2481.png"
 ALT="$\omega=\omega_{n s}$">|; 

$key = q/omega=omega_{rmLH};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img1865.png"
 ALT="$\omega= \omega_{\rm LH}$">|; 

$key = q/omega=omega_{rmUH};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1861.png"
 ALT="$\omega=\omega_{\rm UH}$">|; 

$key = q/omega=pmomega_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2064.png"
 ALT="$\omega=\pm
\omega_0$">|; 

$key = q/omega={bfk}cdot{bfB}slash!sqrt{mu_0,rho};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.80ex; " SRC="|."$dir".q|img3246.png"
 ALT="$\omega={\bf k}\cdot{\bf B}/\!\sqrt{\mu_0 \rho}$">|; 

$key = q/omega={bfk}cdot{bfv};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2237.png"
 ALT="$\omega={\bf k}\cdot{\bf v}$">|; 

$key = q/omega={mitOmega}({bfR},t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img305.png"
 ALT="$\omega={\mit\Omega}({\bf R}, t)$">|; 

$key = q/omega={mitPi}_e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1896.png"
 ALT="$\omega={\mit \Pi}_e$">|; 

$key = q/omega={{mitPi}}_e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1792.png"
 ALT="$\omega = {{\mit\Pi}}_e$">|; 

$key = q/omega^2=k^2c^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1796.png"
 ALT="$\omega^2=k^2 c^2$">|; 

$key = q/omega^2={mitPi}_e^{2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.65ex; " SRC="|."$dir".q|img2302.png"
 ALT="$\omega^2={\mit\Pi}_e^{2}$">|; 

$key = q/omega^2slashk^2=T_eslashm_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2346.png"
 ALT="$\omega^2/k^2 = T_e/m_i$">|; 

$key = q/omega^{2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3204.png"
 ALT="$\omega^{2}$">|; 

$key = q/omega_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2061.png"
 ALT="$\omega_0$">|; 

$key = q/omega_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img1845.png"
 ALT="$\omega_1$">|; 

$key = q/omega_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img1859.png"
 ALT="$\omega_2$">|; 

$key = q/omega_r;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img2599.png"
 ALT="$\omega_r$">|; 

$key = q/omega_r>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img2641.png"
 ALT="$\omega_r&gt;0$">|; 

$key = q/omega_rslashk;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2601.png"
 ALT="$\omega_r/k$">|; 

$key = q/omega_{UH}slash|{mitOmega}_e|=2.5;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img3.png"
 ALT="$\omega _{UH}/\vert{\mit \Omega }_e\vert=2.5$">|; 

$key = q/omega_{rmLH};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img1867.png"
 ALT="$\omega_{\rm LH}$">|; 

$key = q/omega_{rmUH};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1863.png"
 ALT="$\omega_{\rm UH}$">|; 

$key = q/omegageq{{mitPi}}_e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1797.png"
 ALT="$\omega\geq {{\mit\Pi}}_e$">|; 

$key = q/omegaggk,u;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2290.png"
 ALT="$\omega\gg k u$">|; 

$key = q/omegagg{mitOmega}_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2049.png"
 ALT="$\omega\gg {\mit\Omega}_i$">|; 

$key = q/omegalesssimk_parallel,v_s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img2451.png"
 ALT="$\omega\lesssim k_\parallel v_s$">|; 

$key = q/omegallk,u;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2338.png"
 ALT="$\omega\ll k u$">|; 

$key = q/omegall{{mitOmega}}_i,{{mitPi}}_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1798.png"
 ALT="$\omega\ll {{\mit\Omega}}_i, {{\mit\Pi}}_i$">|; 

$key = q/omegall{{mitOmega}}_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1832.png"
 ALT="$\omega\ll {{\mit\Omega}}_i$">|; 

$key = q/omeganeq0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.21ex; " SRC="|."$dir".q|img2713.png"
 ALT="$\omega\neq 0$">|; 

$key = q/omeganeqn,{mitOmega}_e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2487.png"
 ALT="$\omega\neq n {\mit\Omega}_e$">|; 

$key = q/omegarightarrow0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1877.png"
 ALT="$\omega\rightarrow 0$">|; 

$key = q/omegarightarrown,{mitOmega}_e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2491.png"
 ALT="$\omega\rightarrow n {\mit\Omega}_e$">|; 

$key = q/omegarightarrow|{{mitOmega}}_e|;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img1835.png"
 ALT="$\omega\rightarrow\vert{{\mit\Omega}}_e\vert$">|; 

$key = q/omegaslashk;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2311.png"
 ALT="$\omega/k$">|; 

$key = q/p,bar{F}_1-F_1(u,t=0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2252.png"
 ALT="$p \bar{F}_1-F_1(u,t=0)$">|; 

$key = q/p;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1103.png"
 ALT="$p$">|; 

$key = q/p=n,(T_e+T_i);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1514.png"
 ALT="$p=n (T_e+T_i)$">|; 

$key = q/p=n,T;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1032.png"
 ALT="$p=n T$">|; 

$key = q/p=p_0+p_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1907.png"
 ALT="$p=p_0+p_1$">|; 

$key = q/p=p_e+p_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1491.png"
 ALT="$p=p_e+p_i$">|; 

$key = q/p>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3390.png"
 ALT="$p&gt;0$">|; 

$key = q/p_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1904.png"
 ALT="$p_0$">|; 

$key = q/p_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3060.png"
 ALT="$p_1$">|; 

$key = q/p_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3064.png"
 ALT="$p_2$">|; 

$key = q/p_e=n,T_e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1516.png"
 ALT="$p_e=n T_e$">|; 

$key = q/p_i=n,T_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1517.png"
 ALT="$p_i=n T_i$">|; 

$key = q/p_i=p_i(s,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img390.png"
 ALT="$p_i=p_i(s,t)$">|; 

$key = q/p_parallelequiv{bfp}cdot{bfb};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img490.png"
 ALT="$p_\parallel\equiv {\bf p}\cdot{\bf b}$">|; 

$key = q/p_phi=m,v_phi+e,A_phi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img500.png"
 ALT="$p_\phi = m v_\phi + e A_\phi$">|; 

$key = q/p_s({mitOmega}),d{mitOmega};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img719.png"
 ALT="$p_s({\mit\Omega}) d{\mit\Omega}$">|; 

$key = q/p_s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1090.png"
 ALT="$p_s$">|; 

$key = q/partialF_0slashpartialu;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2291.png"
 ALT="$\partial F_0/\partial u$">|; 

$key = q/partialF_1slashpartialt;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2251.png"
 ALT="$\partial F_1/\partial t$">|; 

$key = q/partialepsilon_r(k,omega_r)slashpartialomega;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2604.png"
 ALT="$\partial\epsilon_r(k,\omega_r)/\partial\omega$">|; 

$key = q/partialf_0slashpartialtheta=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2353.png"
 ALT="$\partial f_0/\partial \theta =0$">|; 

$key = q/partialslashpartialt=partialslashpartialy=partialslashpartialz=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3057.png"
 ALT="$\partial/\partial t = \partial/\partial y =\partial/\partial z=0$">|; 

$key = q/partialslashpartialthetaequiv0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2934.png"
 ALT="$\partial/\partial\theta
\equiv 0$">|; 

$key = q/partialslashpartialx=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3058.png"
 ALT="$\partial/\partial x=0$">|; 

$key = q/partialslashpartialz=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3250.png"
 ALT="$\partial/\partial z=0$">|; 

$key = q/pggQ^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3397.png"
 ALT="$p\gg Q^{1/2}$">|; 

$key = q/phi(omega);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2070.png"
 ALT="$\phi(\omega)$">|; 

$key = q/phi(x,y);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3256.png"
 ALT="$\phi(x,y)$">|; 

$key = q/phi(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1921.png"
 ALT="$\phi(z)$">|; 

$key = q/phi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img642.png"
 ALT="$\phi$">|; 

$key = q/phi=(aslashk,tau_R),skew{3}hat{phi};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3478.png"
 ALT="$\phi=(a/k \tau_R) \skew{3}\hat{\phi}$">|; 

$key = q/phi=phi(varpi,z,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2944.png"
 ALT="$\phi=\phi(\varpi,z,t)$">|; 

$key = q/phi=phi(x,y);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3227.png"
 ALT="$\phi=\phi(x,y)$">|; 

$key = q/phi_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3300.png"
 ALT="$\phi_1$">|; 

$key = q/phi_1={rmi},(gamma,aslashk),skew{3}hat{phi};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3314.png"
 ALT="$\phi_1={\rm i} (\gamma a/k) \skew{3}\hat{\phi}$">|; 

$key = q/phirightarrowphi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img648.png"
 ALT="$\phi\rightarrow\phi$">|; 

$key = q/pi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1080.png"
 ALT="$\pi$">|; 

$key = q/pllQ^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3408.png"
 ALT="$p\ll Q^{1/2}$">|; 

$key = q/pmV;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img2547.png"
 ALT="$\pm V$">|; 

$key = q/prightarrow0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2805.png"
 ALT="$p\rightarrow 0$">|; 

$key = q/prightarrowinfty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3399.png"
 ALT="$p\rightarrow \infty$">|; 

$key = q/psi(x,y);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3257.png"
 ALT="$\psi(x,y)$">|; 

$key = q/psi(x,y,t)=-B_0,a,hat{psi}(x,y,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3454.png"
 ALT="$\psi(x,y,t)=-B_0 a \hat{\psi}(x,y,t)$">|; 

$key = q/psi(x_1,y_1)-psi(x_2,y_2);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3262.png"
 ALT="$\psi(x_1,y_1)-\psi(x_2,y_2)$">|; 

$key = q/psi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img17.png"
 ALT="$\psi $">|; 

$key = q/psi=-B_0,a,hat{psi};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3476.png"
 ALT="$\psi = -B_0 a \hat{\psi}$">|; 

$key = q/psi=psi(varpi,z,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2943.png"
 ALT="$\psi=\psi(\varpi,z,t)$">|; 

$key = q/psi=psi(x,y);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3226.png"
 ALT="$\psi=\psi(x,y)$">|; 

$key = q/psi_1(x),{rme}^{,gamma,t}=-B_0,a,skew{3}hat{mitPsi}(t),{rme}^{-{rmi},varphi};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3455.png"
 ALT="$\psi_1(x) {\rm e}^{ \gamma t}= -B_0 a \skew{3}\hat{\mit\Psi}(t) {\rm
e}^{-{\rm i} \varphi}$">|; 

$key = q/psi_1(x);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3453.png"
 ALT="$\psi_1(x)$">|; 

$key = q/psi_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3298.png"
 ALT="$\psi_1$">|; 

$key = q/psi_1=-a,B_0,hat{psi};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3313.png"
 ALT="$\psi_1=-a B_0 \hat{\psi}$">|; 

$key = q/q;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.56ex; " SRC="|."$dir".q|img68.png"
 ALT="$q$">|; 

$key = q/q_i=q_i(s,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.56ex; " SRC="|."$dir".q|img389.png"
 ALT="$q_i = q_i(s,t)$">|; 

$key = q/r;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.00ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img173.png"
 ALT="$r$">|; 

$key = q/r<1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img3115.png"
 ALT="$r&lt;1$">|; 

$key = q/r<r_A;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img2843.png"
 ALT="$r&lt;r_A$">|; 

$key = q/r=(varpi^{2}+z^{2})^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2953.png"
 ALT="$r=(\varpi^{2}+z^{2})^{1/2}$">|; 

$key = q/r=(x^2+y^2)^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img520.png"
 ALT="$r=(x^2+y^2)^{1/2}$">|; 

$key = q/r=(x^{2}+y^{2})^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img688.png"
 ALT="$r=(x^{2}+y^{2})^{1/2}$">|; 

$key = q/r=({mitGamma}+1)slash({mitGamma}-1);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3147.png"
 ALT="$r=({\mit\Gamma}+1)/({\mit\Gamma}-1)$">|; 

$key = q/r=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3146.png"
 ALT="$r=0$">|; 

$key = q/r=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img3121.png"
 ALT="$r=1$">|; 

$key = q/r=R=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img3107.png"
 ALT="$r=R=1$">|; 

$key = q/r=a-delta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3013.png"
 ALT="$r=a-\delta$">|; 

$key = q/r=a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img2766.png"
 ALT="$r=a$">|; 

$key = q/r=r_A;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img2867.png"
 ALT="$r=r_A$">|; 

$key = q/r=r_c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2785.png"
 ALT="$r=r_c$">|; 

$key = q/r=r_{rmeq}ggdslash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.75ex; " SRC="|."$dir".q|img526.png"
 ALT="$r=r_{\rm eq}\gg d/2$">|; 

$key = q/r=z^{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.27ex; " SRC="|."$dir".q|img692.png"
 ALT="$r=z^{-1}$">|; 

$key = q/r>1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img3114.png"
 ALT="$r&gt;1$">|; 

$key = q/r>r_A;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img2844.png"
 ALT="$r&gt;r_A$">|; 

$key = q/r^{2},rho,u_r;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2871.png"
 ALT="$r^{2} \rho u_r$">|; 

$key = q/r_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3140.png"
 ALT="$r_1$">|; 

$key = q/r_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3141.png"
 ALT="$r_2$">|; 

$key = q/r_A;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img2839.png"
 ALT="$r_A$">|; 

$key = q/r_c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img155.png"
 ALT="$r_c$">|; 

$key = q/r_c<r<infty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2784.png"
 ALT="$r_c&lt;r&lt;\infty$">|; 

$key = q/r_cgglambdabar;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img154.png"
 ALT="$r_c\gg\lambdabar$">|; 

$key = q/r_csim5,R_odot;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2810.png"
 ALT="$r_c\sim 5 R_\odot$">|; 

$key = q/r_csimr_dslash{mitLambda}^{2slash3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img156.png"
 ALT="$r_c\sim r_d/{\mit\Lambda}^{2/3}$">|; 

$key = q/r_d;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img148.png"
 ALT="$r_d$">|; 

$key = q/r_dgglambdabar;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img153.png"
 ALT="$r_d\gg\lambdabar$">|; 

$key = q/r_dgg{mitLambda}^{2slash3},lambdabar;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img157.png"
 ALT="$r_d\gg {\mit\Lambda}^{2/3} \lambdabar$">|; 

$key = q/r_dlllambdabar;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img151.png"
 ALT="$r_d\ll \lambdabar$">|; 

$key = q/r_dslashr_c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img75.png"
 ALT="$r_d/r_c$">|; 

$key = q/r_{rmeq};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.75ex; " SRC="|."$dir".q|img440.png"
 ALT="$r_{\rm eq}$">|; 

$key = q/r_{rmmin};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img709.png"
 ALT="$r_{\rm min}$">|; 

$key = q/requivrho_2slashrho_1rightarrow({mitGamma}+1)slash({mitGamma}-1);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3129.png"
 ALT="$r\equiv \rho_2/\rho_1\rightarrow ({\mit\Gamma}+1)/({\mit\Gamma}-1)$">|; 

$key = q/rggd;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img522.png"
 ALT="$r\gg d$">|; 

$key = q/rggr_A;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img2841.png"
 ALT="$r\gg r_A$">|; 

$key = q/rggr_c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2822.png"
 ALT="$r\gg r_c$">|; 

$key = q/rho,u^2slash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2835.png"
 ALT="$\rho  u^2/2$">|; 

$key = q/rho;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img213.png"
 ALT="$\rho$">|; 

$key = q/rho=u_perpslash{mitOmega};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img312.png"
 ALT="$\rho = u_\perp/{\mit\Omega}$">|; 

$key = q/rho_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2708.png"
 ALT="$\rho_0$">|; 

$key = q/rho_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3059.png"
 ALT="$\rho_1$">|; 

$key = q/rho_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3063.png"
 ALT="$\rho_2$">|; 

$key = q/rho_c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img568.png"
 ALT="$\rho_c$">|; 

$key = q/rho_e,partialT_eslashpartialx;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1233.png"
 ALT="$\rho_e \partial T_e/\partial x$">|; 

$key = q/rho_e,partialnslashpartialx;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1530.png"
 ALT="$\rho_e \partial n/\partial x$">|; 

$key = q/rho_e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1232.png"
 ALT="$\rho_e$">|; 

$key = q/rho_esimv_eslash|{mitOmega}_e|;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1231.png"
 ALT="$\rho_e\sim v_e/\vert{\mit\Omega}_e\vert$">|; 

$key = q/rho_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1253.png"
 ALT="$\rho_i$">|; 

$key = q/rho_infty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2800.png"
 ALT="$\rho_\infty$">|; 

$key = q/rho_isimv_islash{mitOmega}_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1251.png"
 ALT="$\rho_i\sim v_i/{\mit\Omega}_i$">|; 

$key = q/rho_s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2468.png"
 ALT="$\rho_s$">|; 

$key = q/rho_s=v_sslash|{mitOmega}_s|;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2463.png"
 ALT="$\rho_s=v_s/\vert{\mit\Omega}_s\vert$">|; 

$key = q/rhoggL;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img137.png"
 ALT="$\rho\gg L$">|; 

$key = q/rhorightarrow0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2804.png"
 ALT="$\rho\rightarrow 0$">|; 

$key = q/rhorightarrowepsilon,rho;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img273.png"
 ALT="$\rho\rightarrow \epsilon \rho$">|; 

$key = q/rhosimeqn_e,m_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1811.png"
 ALT="$\rho\simeq n_e m_i$">|; 

$key = q/rhoslashL;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img216.png"
 ALT="$\rho/L$">|; 

$key = q/rhoslashLrightarrow0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img499.png"
 ALT="$\rho/L\rightarrow 0$">|; 

$key = q/rlessgtrr_c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.73ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img3218.png"
 ALT="$r\lessgtr r_c$">|; 

$key = q/rllr_A;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img2842.png"
 ALT="$r\ll r_A$">|; 

$key = q/rneq1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.21ex; " SRC="|."$dir".q|img3109.png"
 ALT="$r\neq 1$">|; 

$key = q/rrightarrow1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img3171.png"
 ALT="$r\rightarrow 1$">|; 

$key = q/rrightarrowinfty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img2771.png"
 ALT="$r\rightarrow\infty$">|; 

$key = q/rrightarrowr_m=({mitGamma}+1)slash({mitGamma}-1);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3185.png"
 ALT="$r\rightarrow r_m=({\mit\Gamma}+1)/({\mit\Gamma}-1)$">|; 

$key = q/rslashr_c=1+x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3212.png"
 ALT="$r/r_c =1 +x$">|; 

$key = q/s';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img118.png"
 ALT="$s'$">|; 

$key = q/s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img33.png"
 ALT="$s$">|; 

$key = q/sequiv{rmsgn}(X);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.58ex; " SRC="|."$dir".q|img3513.png"
 ALT="$s\equiv{\rm sgn}(X)$">|; 

$key = q/sigma'({bfv}_s,{bfv}_{s'};{bfv}_s',{bfv}_{s'}'),d^3{bfv}_s',d^{3}{bfv}_{s'}';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.51ex; vertical-align: -0.76ex; " SRC="|."$dir".q|img603.png"
 ALT="$\sigma'({\bf v}_s, {\bf v}_{s'}; {\bf v}_s',{\bf v}_{s'}') d^3{\bf v}_s' d^{3}{\bf v}_{s'}'$">|; 

$key = q/sigma'({bfv}_s,{bfv}_{s'};{bfv}_s',{bfv}_{s'}');MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.76ex; " SRC="|."$dir".q|img638.png"
 ALT="$\sigma'({\bf v}_s, {\bf v}_{s'};{\bf v}_s',{\bf v}_{s'}')$">|; 

$key = q/sigma;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img189.png"
 ALT="$\sigma$">|; 

$key = q/sigma=e,n,deltax;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img46.png"
 ALT="$\sigma=e n \delta x$">|; 

$key = q/sigma^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1140.png"
 ALT="$\sigma^2$">|; 

$key = q/sigma_parallel;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img1164.png"
 ALT="$\sigma_\parallel$">|; 

$key = q/sigma_parallelsimtau_e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img1171.png"
 ALT="$\sigma_\parallel \sim \tau_e$">|; 

$key = q/sigma_perp;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img1225.png"
 ALT="$\sigma_\perp$">|; 

$key = q/sigma_{ss'}';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.76ex; " SRC="|."$dir".q|img853.png"
 ALT="$\sigma_{ss'}'$">|; 

$key = q/sigmarightarrowinfty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.12ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3208.png"
 ALT="$\sigma\rightarrow\infty$">|; 

$key = q/sigmasim4times10^5,{rmS},{rmm}^{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2884.png"
 ALT="$\sigma\sim 4\times 10^5 
{\rm S} {\rm m}^{-1}$">|; 

$key = q/sintheta=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2863.png"
 ALT="$\sin\theta=1$">|; 

$key = q/skew{-3}hat{bfk};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img1669.png"
 ALT="$\skew{-3}\hat{\bf k}$">|; 

$key = q/skew{3}bar{phi}(-p)=-skew{3}bar{phi}(p);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3383.png"
 ALT="$\skew{3}\bar{\phi}(-p)=-\skew{3}\bar{\phi}(p)$">|; 

$key = q/skew{3}hat{delta};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3423.png"
 ALT="$\skew{3}\hat{\delta}$">|; 

$key = q/skew{3}hat{delta}simS^{-2slash5};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3422.png"
 ALT="$\skew{3}\hat{\delta}\sim S^{-2/5}$">|; 

$key = q/skew{3}hat{epsilon}=(k_0^{2},b),epsilon;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.57ex; vertical-align: -0.79ex; " SRC="|."$dir".q|img1973.png"
 ALT="$\skew{3}\hat{\epsilon} = (k_0^{2} b) \epsilon$">|; 

$key = q/skew{3}hat{mitPhi};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img1587.png"
 ALT="$\skew{3}\hat{\mit\Phi}$">|; 

$key = q/skew{3}hat{mitPhi}=-e,({mitPhi}-{mitPhi}_s)slashT_e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1577.png"
 ALT="$\skew{3}\hat{\mit\Phi}=-e ({\mit\Phi}-{\mit\Phi}_s)/T_e$">|; 

$key = q/skew{3}hat{mitPhi}rightarrow0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1582.png"
 ALT="$\skew{3}\hat{\mit\Phi}\rightarrow 0$">|; 

$key = q/skew{3}hat{mitPsi};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img3456.png"
 ALT="$\skew{3}\hat{\mit\Psi}$">|; 

$key = q/skew{3}hat{mitPsi}_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3553.png"
 ALT="$\skew{3}\hat{\mit\Psi}_1$">|; 

$key = q/skew{3}hat{mitPsi}_m(hat{t});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3544.png"
 ALT="$\skew{3}\hat{\mit\Psi}_m(\hat{t})$">|; 

$key = q/skew{3}hat{mitPsi}_m;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img3545.png"
 ALT="$\skew{3}\hat{\mit\Psi}_m$">|; 

$key = q/skew{3}hat{mitPsi}proptohat{W}^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3471.png"
 ALT="$\skew{3}\hat{\mit\Psi}\propto \hat{W}^{ 2}$">|; 

$key = q/skew{3}hat{phi}(-hat{x})=-skew{3}hat{phi}(hat{x});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3375.png"
 ALT="$\skew{3}\hat{\phi}(-\hat{x})=-\skew{3}\hat{\phi}(\hat{x})$">|; 

$key = q/skew{3}hat{phi};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3391.png"
 ALT="$\skew{3}\hat{\phi}$">|; 

$key = q/skew{3}hat{phi}=skew{3}hat{phi}_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3371.png"
 ALT="$\skew{3}\hat{\phi}=\skew{3}\hat{\phi}_0$">|; 

$key = q/skew{3}hat{phi}_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3373.png"
 ALT="$\skew{3}\hat{\phi}_0$">|; 

$key = q/skew{3}hat{phi}sim1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3495.png"
 ALT="$\skew{3}\hat{\phi}\sim 1$">|; 

$key = q/t'=t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img2367.png"
 ALT="$t'=t$">|; 

$key = q/t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.28ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img242.png"
 ALT="$t$">|; 

$key = q/t=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img554.png"
 ALT="$t=0$">|; 

$key = q/t=tau_R,hat{t};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3480.png"
 ALT="$t=\tau_R \hat{t}$">|; 

$key = q/t={rmi},x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img2328.png"
 ALT="$t={\rm i} x$">|; 

$key = q/tau(omega);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2200.png"
 ALT="$\tau(\omega)$">|; 

$key = q/tau;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img50.png"
 ALT="$\tau$">|; 

$key = q/tau_A=aslash(B_0^{,2}slashmu_0,rho)^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.57ex; vertical-align: -0.79ex; " SRC="|."$dir".q|img3674.png"
 ALT="$\tau_A=a/(B_0^{ 2}/\mu_0 \rho)^{1/2}$">|; 

$key = q/tau_Arightarrowhat{delta}_{rmSP},a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3711.png"
 ALT="$\tau_A\rightarrow \hat{\delta}_{\rm SP} a$">|; 

$key = q/tau_H;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3325.png"
 ALT="$\tau_H$">|; 

$key = q/tau_H^{1slash2},tau_R^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.68ex; vertical-align: -0.77ex; " SRC="|."$dir".q|img3671.png"
 ALT="$\tau_H^{1/2} \tau_R^{1/2}$">|; 

$key = q/tau_H^{2slash5},tau_R^{3slash5};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.73ex; vertical-align: -0.77ex; " SRC="|."$dir".q|img3414.png"
 ALT="$\tau_H^{2/5} \tau_R^{3/5}$">|; 

$key = q/tau_R;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img2998.png"
 ALT="$\tau_R$">|; 

$key = q/tau_Rggtau_A;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3719.png"
 ALT="$\tau_R\gg\tau_A$">|; 

$key = q/tau_Rggtau_H;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3666.png"
 ALT="$\tau_R\gg \tau_H$">|; 

$key = q/tau_b(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img543.png"
 ALT="$\tau_b(t)$">|; 

$key = q/tau_b;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img469.png"
 ALT="$\tau_b$">|; 

$key = q/tau_d;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img497.png"
 ALT="$\tau_d$">|; 

$key = q/tau_e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1167.png"
 ALT="$\tau_e$">|; 

$key = q/tau_esimT_e^{3slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.47ex; " SRC="|."$dir".q|img1170.png"
 ALT="$\tau_e\sim T_e^{3/2}$">|; 

$key = q/tau_p;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img54.png"
 ALT="$\tau_p$">|; 

$key = q/tau_pequiv2pislash{mitPi};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img51.png"
 ALT="$\tau_p\equiv 2\pi/{\mit\Pi}$">|; 

$key = q/tau_{rmSP};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3665.png"
 ALT="$\tau_{\rm SP}$">|; 

$key = q/tau_{rmohm}sim2times10^5;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2885.png"
 ALT="$\tau_{\rm ohm}\sim 2\times 10^5$">|; 

$key = q/tau_{ss'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img965.png"
 ALT="$\tau_{ss'}$">|; 

$key = q/theta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img438.png"
 ALT="$\theta$">|; 

$key = q/theta=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img706.png"
 ALT="$\theta=0$">|; 

$key = q/theta=pislash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1758.png"
 ALT="$\theta=\pi/2$">|; 

$key = q/theta=pislash3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2220.png"
 ALT="$\theta=\pi/3$">|; 

$key = q/theta=tan^{-1}(yslashx);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img521.png"
 ALT="$\theta=\tan^{-1}(y/x)$">|; 

$key = q/theta=theta(r);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img694.png"
 ALT="$\theta=\theta(r)$">|; 

$key = q/theta_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3167.png"
 ALT="$\theta_1$">|; 

$key = q/theta_1=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3187.png"
 ALT="$\theta_1=0$">|; 

$key = q/tilde{gamma};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3697.png"
 ALT="$\tilde{\gamma}$">|; 

$key = q/tilde{gamma}=0.6235;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3691.png"
 ALT="$\tilde{\gamma}=0.6235$">|; 

$key = q/tilde{gamma}=tilde{k}^{2slash3},Q;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3696.png"
 ALT="$\tilde{\gamma} =\tilde{k}^{2/3} Q$">|; 

$key = q/tilde{k};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img3698.png"
 ALT="$\tilde{k}$">|; 

$key = q/tilde{k}=1.359;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.14ex; " SRC="|."$dir".q|img3692.png"
 ALT="$\tilde{k}=1.359$">|; 

$key = q/times{bfb};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img319.png"
 ALT="$\times {\bf b}$">|; 

$key = q/trightarrow-infty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.28ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img2361.png"
 ALT="$t\rightarrow -\infty$">|; 

$key = q/u(r);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2790.png"
 ALT="$u(r)$">|; 

$key = q/u(r)=u_s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2823.png"
 ALT="$u(r) = u_s$">|; 

$key = q/u(r_c)=u_c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2793.png"
 ALT="$u(r_c) = u_c$">|; 

$key = q/u;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img2239.png"
 ALT="$u$">|; 

$key = q/u<u_c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img3221.png"
 ALT="$u&lt;u_c$">|; 

$key = q/u=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2551.png"
 ALT="$u=0$">|; 

$key = q/u=U_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2542.png"
 ALT="$u=U_0$">|; 

$key = q/u=omegaslashk;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2287.png"
 ALT="$u=\omega/k$">|; 

$key = q/u=u_c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2807.png"
 ALT="$u=u_c$">|; 

$key = q/u={bfk}cdot{bfv}slashk;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2240.png"
 ALT="$u= {\bf k}\cdot{\bf v}/k$">|; 

$key = q/u>u_c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img3223.png"
 ALT="$u&gt;u_c$">|; 

$key = q/u^2-u_c^{2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.65ex; " SRC="|."$dir".q|img2791.png"
 ALT="$u^2-u_c^{2}$">|; 

$key = q/u_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2305.png"
 ALT="$u_0$">|; 

$key = q/u_0<u_c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3220.png"
 ALT="$u_0 &lt; u_c$">|; 

$key = q/u_0>u_c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3222.png"
 ALT="$u_0&gt;u_c$">|; 

$key = q/u_0nequ_c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3216.png"
 ALT="$u_0\neq u_c$">|; 

$key = q/u_c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2788.png"
 ALT="$u_c$">|; 

$key = q/u_e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2559.png"
 ALT="$u_e$">|; 

$key = q/u_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2560.png"
 ALT="$u_i$">|; 

$key = q/u_perp;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img309.png"
 ALT="$u_\perp$">|; 

$key = q/u_phi(r);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2845.png"
 ALT="$u_\phi(r)$">|; 

$key = q/u_phi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2820.png"
 ALT="$u_\phi$">|; 

$key = q/u_s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2824.png"
 ALT="$u_s$">|; 

$key = q/u_z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2085.png"
 ALT="$u_z$">|; 

$key = q/u_{r,A}equivu_r(r_A);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2873.png"
 ALT="$u_{r A} \equiv u_r(r_A)$">|; 

$key = q/u_{ss'}'=u_{ss'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.76ex; " SRC="|."$dir".q|img629.png"
 ALT="$u_{ss'}'=u_{ss'}$">|; 

$key = q/u_{ss'},f_s({bfr},{bfv}_s,t),d^3{bfv}_s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img615.png"
 ALT="$u_{ss'} f_s({\bf r}, {\bf v}_s,t) d^3{\bf v}_s$">|; 

$key = q/u_{ss'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img602.png"
 ALT="$u_{ss'}$">|; 

$key = q/u_{ss'}=|{bfv}_s-{bfv}_{s'}|;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img620.png"
 ALT="$u_{ss'}= \vert{\bf v}_s-{\bf v}_{s'}\vert$">|; 

$key = q/u_{ss'}rightarrowu_{ss'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img646.png"
 ALT="$u_{ss'}\rightarrow u_{ss'}$">|; 

$key = q/ugtrlessu_c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.73ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img3219.png"
 ALT="$u\gtrless u_c$">|; 

$key = q/ulessgtru_c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.73ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img3217.png"
 ALT="$u\lessgtr u_c$">|; 

$key = q/ullV_A;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img2838.png"
 ALT="$u\ll V_A$">|; 

$key = q/usim10,V_A;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img2837.png"
 ALT="$u\sim 10 V_A$">|; 

$key = q/uslashu_c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2797.png"
 ALT="$u/u_c$">|; 

$key = q/v;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img32.png"
 ALT="$v$">|; 

$key = q/v_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3630.png"
 ALT="$v_0$">|; 

$key = q/v_0=(aslashtau_R),hat{v}_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3640.png"
 ALT="$v_0= (a/\tau_R) \hat{v}_0$">|; 

$key = q/v_1=V_{x,1}=V_1,costheta_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img3166.png"
 ALT="$v_1= V_{x 1} = V_1 \cos\theta_1$">|; 

$key = q/v_1=costheta_1,V_{A,1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3197.png"
 ALT="$v_1=\cos\theta_1 V_{A 1}$">|; 

$key = q/v_1=sqrt{r},V_{A,1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.57ex; " SRC="|."$dir".q|img3193.png"
 ALT="$v_1 =\sqrt{r}  V_{A 1}$">|; 

$key = q/v_1>V_{+,1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3183.png"
 ALT="$v_1&gt; V_{+ 1}$">|; 

$key = q/v_1>V_{-,1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3181.png"
 ALT="$v_1&gt; V_{- 1}$">|; 

$key = q/v_1>costheta_1,V_{A,1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3182.png"
 ALT="$v_1&gt; \cos\theta_1 V_{A 1}$">|; 

$key = q/v_1^{2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.77ex; " SRC="|."$dir".q|img3168.png"
 ALT="$v_1^{2}$">|; 

$key = q/v_1^{2}rightarrowinfty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.77ex; " SRC="|."$dir".q|img3184.png"
 ALT="$v_1^{2}\rightarrow \infty$">|; 

$key = q/v_ast;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.28ex; vertical-align: -0.35ex; " SRC="|."$dir".q|img3631.png"
 ALT="$v_\ast$">|; 

$key = q/v_ast=(aslashtau_R),hat{v}_ast;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3641.png"
 ALT="$v_\ast = (a/\tau_R) \hat{v}_\ast$">|; 

$key = q/v_d;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1455.png"
 ALT="$v_d$">|; 

$key = q/v_e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1177.png"
 ALT="$v_e$">|; 

$key = q/v_e<V;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2554.png"
 ALT="$v_e &lt; V$">|; 

$key = q/v_e<sqrt{3},V;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2550.png"
 ALT="$v_e &lt; \sqrt{3} V$">|; 

$key = q/v_e=(T_eslashm_e)^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2568.png"
 ALT="$v_e=(T_e/m_e)^{1/2}$">|; 

$key = q/v_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1252.png"
 ALT="$v_i$">|; 

$key = q/v_i=(T_islashm_i)^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2569.png"
 ALT="$v_i=(T_i/m_i)^{1/2}$">|; 

$key = q/v_parallel;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img2355.png"
 ALT="$v_\parallel$">|; 

$key = q/v_parallel=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img457.png"
 ALT="$v_\parallel=0$">|; 

$key = q/v_perp;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img2354.png"
 ALT="$v_\perp$">|; 

$key = q/v_perp=(v_x'^{2}+v_y'^{2})^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.68ex; vertical-align: -0.95ex; " SRC="|."$dir".q|img2378.png"
 ALT="$v_\perp = (v_x'^{2} + v_y'^{2})^{1/2}$">|; 

$key = q/v_phi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img501.png"
 ALT="$v_\phi$">|; 

$key = q/v_s=(2,T_sslashm_s)^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2415.png"
 ALT="$v_s=(2 T_s/m_s)^{1/2}$">|; 

$key = q/v_srightarrow0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2422.png"
 ALT="$v_s\rightarrow 0$">|; 

$key = q/v_t,tau_p;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img53.png"
 ALT="$v_t \tau_p$">|; 

$key = q/v_t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2676.png"
 ALT="$v_t$">|; 

$key = q/v_t=sqrt{2,Tslashm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1637.png"
 ALT="$v_t=\sqrt{2 T/m}$">|; 

$key = q/v_x=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img566.png"
 ALT="$v_x=0$">|; 

$key = q/v_{parallel,e}rightarrow0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img2637.png"
 ALT="$v_{\parallel e}\rightarrow 0$">|; 

$key = q/v_{parallel,s}=(2,T_{parallel,s}slashm_s)^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img2617.png"
 ALT="$v_{\parallel s} = (2 T_{\parallel s}/m_s)^{1/2}$">|; 

$key = q/v_{perp,s},,v_{parallel,s}rightarrow0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img2626.png"
 ALT="$v_{\perp s}, v_{\parallel s}\rightarrow 0$">|; 

$key = q/v_{perp,s}=(2,T_{perp,s}slashm_s)^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2616.png"
 ALT="$v_{\perp s} = (2 T_{\perp s}/m_s)^{1/2}$">|; 

$key = q/v_{t,e}=sqrt{2,T_eslashm_e};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1654.png"
 ALT="$v_{t e}=\sqrt{2 T_e/m_e}$">|; 

$key = q/v_{t,e}slashc=0.2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2498.png"
 ALT="$v_{t e}/c=0.2$">|; 

$key = q/v_{t,s};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img921.png"
 ALT="$v_{t s}$">|; 

$key = q/v_{t,s}=sqrt{2,T_sslashm_s};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img889.png"
 ALT="$v_{t s}=\sqrt{2 T_s/m_s}$">|; 

$key = q/v_{t,{s'}}=sqrt{2,T_{s'}slashm_{s'}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img890.png"
 ALT="$v_{t {s'}}=\sqrt{2 T_{s'}/m_{s'}}$">|; 

$key = q/v_{ttmspace+thinmuskip{.1667em}e}slashc=0.2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img4.png"
 ALT="$v_{t\tmspace +\thinmuskip {.1667em}e}/c=0.2$">|; 

$key = q/varphi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3457.png"
 ALT="$\varphi$">|; 

$key = q/varpi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2938.png"
 ALT="$\varpi$">|; 

$key = q/vartheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img529.png"
 ALT="$\vartheta$">|; 

$key = q/vartheta=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img525.png"
 ALT="$\vartheta=0$">|; 

$key = q/vartheta=0^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img441.png"
 ALT="$\vartheta=0^\circ$">|; 

$key = q/vartheta=pislash2-theta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img437.png"
 ALT="$\vartheta
= \pi/2 - \theta$">|; 

$key = q/vartheta=pmvartheta_m;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img528.png"
 ALT="$\vartheta=\pm\vartheta_m$">|; 

$key = q/vartheta_E;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img462.png"
 ALT="$\vartheta_E$">|; 

$key = q/vartheta_m;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img460.png"
 ALT="$\vartheta_m$">|; 

$key = q/w_T;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img1298.png"
 ALT="$w_T$">|; 

$key = q/w_U;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1297.png"
 ALT="$w_U$">|; 

$key = q/w_e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1195.png"
 ALT="$w_e$">|; 

$key = q/w_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1184.png"
 ALT="$w_i$">|; 

$key = q/w_s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1072.png"
 ALT="$w_s$">|; 

$key = q/widehat{bfq}_{Te};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1367.png"
 ALT="$\widehat{\bf q}_{Te}$">|; 

$key = q/widehat{bfq}_{i};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1409.png"
 ALT="$\widehat{\bf q}_{i}$">|; 

$key = q/widehat{mbox{boldmathpi}}_e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1364.png"
 ALT="$\widehat{\mbox{\boldmath $\pi$}}_e$">|; 

$key = q/widehat{mbox{boldmathpi}}_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1406.png"
 ALT="$\widehat{\mbox{\boldmath $\pi$}}_i$">|; 

$key = q/x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img5.png"
 ALT="$x$">|; 

$key = q/x=(omegaslash{mitPi}_e)^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2652.png"
 ALT="$x=(\omega/{\mit\Pi}_e)^2$">|; 

$key = q/x=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img516.png"
 ALT="$x=0$">|; 

$key = q/x=a,hat{x};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img3310.png"
 ALT="$x= a \hat{x}$">|; 

$key = q/x=pmx_m(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img542.png"
 ALT="$x=\pm x_m(t)$">|; 

$key = q/x=x_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1236.png"
 ALT="$x=x_0$">|; 

$key = q/x>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1553.png"
 ALT="$x&gt;0$">|; 

$key = q/x_0+u_0,t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2306.png"
 ALT="$x_0+u_0 t$">|; 

$key = q/x_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1173.png"
 ALT="$x_0$">|; 

$key = q/x_0=6sqrt{3},h_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2221.png"
 ALT="$x_0=6\sqrt{3} h_0$">|; 

$key = q/x_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3258.png"
 ALT="$x_1$">|; 

$key = q/x_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3260.png"
 ALT="$x_2$">|; 

$key = q/x_s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img200.png"
 ALT="$x_s$">|; 

$key = q/x_sslashlambda_D;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img203.png"
 ALT="$x_s/\lambda_D$">|; 

$key = q/xgg+a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.23ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img3283.png"
 ALT="$x\gg +a$">|; 

$key = q/xi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3463.png"
 ALT="$\xi$">|; 

$key = q/xi=k,y+varphi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3648.png"
 ALT="$\xi=k y +\varphi$">|; 

$key = q/xi=k,y-varphi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3459.png"
 ALT="$\xi= k y-\varphi$">|; 

$key = q/xi=n,2pi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3462.png"
 ALT="$\xi=n 2\pi$">|; 

$key = q/xi=v_{t,{s'}}^{2}slashv_{t,s}^{2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.51ex; vertical-align: -0.76ex; " SRC="|."$dir".q|img945.png"
 ALT="$\xi = v_{t {s'}}^{2}/v_{t s}^{2}$">|; 

$key = q/xi_0=cos^{-1}({mitOmega});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3517.png"
 ALT="$\xi_0=\cos^{-1}({\mit\Omega})$">|; 

$key = q/xi_n=(omega-n,{mitOmega}_s)slash(k_parallel,v_s);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img2515.png"
 ALT="$\xi_n = (\omega-n {\mit\Omega}_s)/(k_\parallel v_s)$">|; 

$key = q/xi_nrightarrowinfty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2424.png"
 ALT="$\xi_n\rightarrow \infty$">|; 

$key = q/xisim1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3491.png"
 ALT="$\xi\sim 1$">|; 

$key = q/xll-a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.23ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img3281.png"
 ALT="$x\ll -a$">|; 

$key = q/xrightarrowinfty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.12ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img1566.png"
 ALT="$x\rightarrow\infty$">|; 

$key = q/y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img190.png"
 ALT="$y$">|; 

$key = q/y=-dslash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img518.png"
 ALT="$y=-d/2$">|; 

$key = q/y=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img556.png"
 ALT="$y=0$">|; 

$key = q/y=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3010.png"
 ALT="$y=1$">|; 

$key = q/y=dslash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img517.png"
 ALT="$y=d/2$">|; 

$key = q/y=k,lambda_D;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2653.png"
 ALT="$y=k \lambda_D$">|; 

$key = q/y=sqrt{2},xslashlambda_D;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1578.png"
 ALT="$y = \sqrt{2} x/\lambda_D$">|; 

$key = q/y>1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3002.png"
 ALT="$y&gt;1$">|; 

$key = q/y_+geqygeqy_-;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img557.png"
 ALT="$y_+\geq y\geq y_-$">|; 

$key = q/y_0geqygeq-y_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img564.png"
 ALT="$y_0\geq y\geq -y_0$">|; 

$key = q/y_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3259.png"
 ALT="$y_1$">|; 

$key = q/y_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3261.png"
 ALT="$y_2$">|; 

$key = q/ygeq0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1586.png"
 ALT="$y\geq 0$">|; 

$key = q/yleq1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3000.png"
 ALT="$y\leq 1$">|; 

$key = q/yrightarrow0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3004.png"
 ALT="$y\rightarrow 0$">|; 

$key = q/yrightarrowinfty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1583.png"
 ALT="$y\rightarrow \infty$">|; 

$key = q/z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.17ex; vertical-align: -0.27ex; " SRC="|."$dir".q|img1.png"
 ALT="$z$">|; 

$key = q/z<0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.73ex; vertical-align: -0.27ex; " SRC="|."$dir".q|img1951.png"
 ALT="$z&lt;0$">|; 

$key = q/z<a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.27ex; " SRC="|."$dir".q|img2065.png"
 ALT="$z&lt;a$">|; 

$key = q/z<h_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2212.png"
 ALT="$z&lt;h_0$">|; 

$key = q/z=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.73ex; vertical-align: -0.27ex; " SRC="|."$dir".q|img183.png"
 ALT="$z=0$">|; 

$key = q/z=a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.23ex; vertical-align: -0.27ex; " SRC="|."$dir".q|img2060.png"
 ALT="$z=a$">|; 

$key = q/z=z(theta);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img693.png"
 ALT="$z=z(\theta)$">|; 

$key = q/z=z_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2155.png"
 ALT="$z=z_0$">|; 

$key = q/z>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.73ex; vertical-align: -0.27ex; " SRC="|."$dir".q|img185.png"
 ALT="$z&gt;0$">|; 

$key = q/z_0(omega);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2205.png"
 ALT="$z_0(\omega)$">|; 

$key = q/z_{rmmax}=1slashr_{rmmin};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img708.png"
 ALT="$z_{\rm max} =1/r_{\rm min}$">|; 

$key = q/zeta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img249.png"
 ALT="$\zeta$">|; 

$key = q/zeta=(omegaslash{mitPi}_e)slash(k,lambda_D)slash!sqrt{2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2658.png"
 ALT="$\zeta = (\omega/{\mit\Pi}_e)/(k \lambda_D)/\!\sqrt{2}$">|; 

$key = q/zeta=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img904.png"
 ALT="$\zeta=0$">|; 

$key = q/zeta=omega+{rmi},k,v_e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2670.png"
 ALT="$\zeta= \omega+{\rm i} k v_e$">|; 

$key = q/zeta=vslashv_{t,s'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img926.png"
 ALT="$\zeta=v/v_{t s'}$">|; 

$key = q/zeta=vslashv_{t,{s'}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img902.png"
 ALT="$\zeta=v/v_{t {s'}}$">|; 

$key = q/zeta=x+{rmi},y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2332.png"
 ALT="$\zeta=x+{\rm i} y$">|; 

$key = q/zeta_e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1377.png"
 ALT="$\zeta_e$">|; 

$key = q/zeta_e=(m_eslash2,T_e)^{1slash2},(omegaslashk-U_e);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2577.png"
 ALT="$\zeta_e = (m_e/2 T_e)^{1/2} (\omega/k-U_e)$">|; 

$key = q/zeta_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1419.png"
 ALT="$\zeta_i$">|; 

$key = q/zeta_i=(m_islash2,T_i),(omegaslashk);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2578.png"
 ALT="$\zeta_i=(m_i/2 T_i) (\omega/k)$">|; 

$key = q/zeta_s=(m_sslash2,T_s)^{1slash2},omegaslashk;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2663.png"
 ALT="$\zeta_s= (m_s/2 T_s)^{1/2} \omega/k$">|; 

$key = q/zetarightarrow0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1534.png"
 ALT="$\zeta\rightarrow 0$">|; 

$key = q/zgeqh_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2214.png"
 ALT="$z\geq h_0$">|; 

$key = q/zrightarrowinfty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.28ex; vertical-align: -0.27ex; " SRC="|."$dir".q|img184.png"
 ALT="$z\rightarrow\infty$">|; 

$key = q/{Gamma}(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2215.png"
 ALT="${\Gamma}(z)$">|; 

$key = q/{align*}=left{{array}{lll}K(pislash2,k)slashpi&~~~~&0leqk<1[2ex]K(pislash2,1slashk)slashk,pi&&k>1{array}right.,{align*};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="297" HEIGHT="66" STYLE=""
 SRC="|."$dir".q|img3565.png"
 ALT="\begin{align*}= \left\{
\begin{array}{lll}
K(\pi/2,k)/\pi&amp;&nbsp;&nbsp;&nbsp;&nbsp;&amp;0\leq k &lt; 1\ [2ex]
K(\pi/2,1/k)/k \pi&amp;&amp;k&gt;1
\end{array}\right.,\end{align*}">;WIDTH="297" HEIGHT="66"|; 

$key = q/{bf0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img892.png"
 ALT="${\bf0}$">|; 

$key = q/{bfA};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img398.png"
 ALT="${\bf A}$">|; 

$key = q/{bfB}({bfr},t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1663.png"
 ALT="${\bf B}({\bf r},t)$">|; 

$key = q/{bfB};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img130.png"
 ALT="${\bf B}$">|; 

$key = q/{bfB}={bf0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1793.png"
 ALT="${\bf B} = {\bf0}$">|; 

$key = q/{bfB}_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1740.png"
 ALT="${\bf B}_0$">|; 

$key = q/{bfB}_0=(0,,0,,B_0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2508.png"
 ALT="${\bf B}_0=(0, 0, B_0)$">|; 

$key = q/{bfB}_0cdot{bfB}slashmu_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2739.png"
 ALT="${\bf B}_0\cdot {\bf B}/\mu_0$">|; 

$key = q/{bfB}_0equivB_0,{bfe}_z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2349.png"
 ALT="${\bf B}_0\equiv B_0 {\bf e}_z$">|; 

$key = q/{bfB}_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3062.png"
 ALT="${\bf B}_1$">|; 

$key = q/{bfB}_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3066.png"
 ALT="${\bf B}_2$">|; 

$key = q/{bfB}_p;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2965.png"
 ALT="${\bf B}_p$">|; 

$key = q/{bfB}_p=nablapsitimes{bfe}_z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3229.png"
 ALT="${\bf B}_p=\nabla\psi\times {\bf e}_z$">|; 

$key = q/{bfB}_p={bf0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3230.png"
 ALT="${\bf B}_p={\bf0}$">|; 

$key = q/{bfB}_t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2973.png"
 ALT="${\bf B}_t$">|; 

$key = q/{bfB}_t=B_z,{bfe}_z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3232.png"
 ALT="${\bf B}_t=B_z {\bf e}_z$">|; 

$key = q/{bfB}cdotnablapsi=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2949.png"
 ALT="${\bf B}\cdot\nabla\psi=0$">|; 

$key = q/{bfB}cdot{bfV}timesd{bfr};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img2696.png"
 ALT="${\bf B} \cdot{\bf V}\times d{\bf r}$">|; 

$key = q/{bfB}proptoexp(gamma,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.58ex; " SRC="|."$dir".q|img2924.png"
 ALT="${\bf B}\propto \exp(\gamma t)$">|; 

$key = q/{bfE}({bfr},t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2231.png"
 ALT="${\bf E}({\bf r}, t)$">|; 

$key = q/{bfE};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img214.png"
 ALT="${\bf E}$">|; 

$key = q/{bfE}=-nabla{mitPhi};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img408.png"
 ALT="${\bf E}= -\nabla{\mit\Phi}$">|; 

$key = q/{bfE}=-{bfV}times{bfB};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img132.png"
 ALT="${\bf E} = - {\bf V}\times {\bf B}$">|; 

$key = q/{bfE}=E,{bfk}slashk;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2247.png"
 ALT="${\bf E}= E {\bf k}/k$">|; 

$key = q/{bfE}=E_z,{bfe}_z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img186.png"
 ALT="${\bf E}=E_z {\bf e}_z$">|; 

$key = q/{bfE}={bfE}_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img1909.png"
 ALT="${\bf E}={\bf E}_1$">|; 

$key = q/{bfE}_0={bf0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1660.png"
 ALT="${\bf E}_0 = {\bf0}$">|; 

$key = q/{bfE}_perp={bf0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img227.png"
 ALT="${\bf E}_\perp= {\bf0}$">|; 

$key = q/{bfE}propto{bfk};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img2224.png"
 ALT="${\bf E}\propto {\bf k}$">|; 

$key = q/{bfE}times{bfB};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.10ex; " SRC="|."$dir".q|img348.png"
 ALT="${\bf E}\times{\bf B}$">|; 

$key = q/{bfF};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img1288.png"
 ALT="${\bf F}$">|; 

$key = q/{bfF}_+-{bfF}_-;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img1182.png"
 ALT="${\bf F}_+ - {\bf F}_-$">|; 

$key = q/{bfF}_+;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img1175.png"
 ALT="${\bf F}_+$">|; 

$key = q/{bfF}_-;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.07ex; " SRC="|."$dir".q|img1174.png"
 ALT="${\bf F}_-$">|; 

$key = q/{bfF}_T;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img1290.png"
 ALT="${\bf F}_T$">|; 

$key = q/{bfF}_U;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1289.png"
 ALT="${\bf F}_U$">|; 

$key = q/{bfF}_s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1096.png"
 ALT="${\bf F}_s$">|; 

$key = q/{bfF}_{ss'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img933.png"
 ALT="${\bf F}_{ss'}$">|; 

$key = q/{bfF}_{ss}={bf0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img957.png"
 ALT="${\bf F}_{ss}={\bf0}$">|; 

$key = q/{bfI}:nabla{bfB}=nablacdot{bfB}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img331.png"
 ALT="${\bf I}:\nabla{\bf B} = \nabla \cdot {\bf B} = 0$">|; 

$key = q/{bfI};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img330.png"
 ALT="${\bf I}$">|; 

$key = q/{bfI}_perp={bfI}-{bfb}{bfb};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img1272.png"
 ALT="${\bf I}_\perp = {\bf I} - {\bf b}{\bf b}$">|; 

$key = q/{bfK};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img2395.png"
 ALT="${\bf K}$">|; 

$key = q/{bfM};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img2095.png"
 ALT="${\bf M}$">|; 

$key = q/{bfM}_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img1016.png"
 ALT="${\bf M}_1$">|; 

$key = q/{bfM}_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img1017.png"
 ALT="${\bf M}_2$">|; 

$key = q/{bfM}_k;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1013.png"
 ALT="${\bf M}_k$">|; 

$key = q/{bfP};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img2168.png"
 ALT="${\bf P}$">|; 

$key = q/{bfP}_s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1070.png"
 ALT="${\bf P}_s$">|; 

$key = q/{bfQ}_s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.48ex; " SRC="|."$dir".q|img1071.png"
 ALT="${\bf Q}_s$">|; 

$key = q/{bfR};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img235.png"
 ALT="${\bf R}$">|; 

$key = q/{bfS};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img2691.png"
 ALT="${\bf S}$">|; 

$key = q/{bfU};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img284.png"
 ALT="${\bf U}$">|; 

$key = q/{bfU}={bfV}_e-{bfV_i};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1474.png"
 ALT="${\bf U} = {\bf V}_e-{\bf V_i}$">|; 

$key = q/{bfU}={bfV}_e-{bfV}_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1166.png"
 ALT="${\bf U} = {\bf V}_e - {\bf V}_i$">|; 

$key = q/{bfU}_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img299.png"
 ALT="${\bf U}_0$">|; 

$key = q/{bfU}_1={bfU}_{1,perp};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img349.png"
 ALT="${\bf U}_1={\bf U}_{1 \perp}$">|; 

$key = q/{bfU}_{1,perp}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img351.png"
 ALT="${\bf U}_{1 \perp}.$">|; 

$key = q/{bfU}_{ss'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img592.png"
 ALT="${\bf U}_{ss'}$">|; 

$key = q/{bfV}({bfr});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2922.png"
 ALT="${\bf V}({\bf r})$">|; 

$key = q/{bfV}({bfr},t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1664.png"
 ALT="${\bf V}({\bf r},t)$">|; 

$key = q/{bfV};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img131.png"
 ALT="${\bf V}$">|; 

$key = q/{bfV}=V_y(x),{bfe}_y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1640.png"
 ALT="${\bf V} = V_y(x) {\bf e}_y$">|; 

$key = q/{bfV}={bf0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img1643.png"
 ALT="${\bf V}={\bf0}$">|; 

$key = q/{bfV}={bfV}_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img1908.png"
 ALT="${\bf V} = {\bf V}_1$">|; 

$key = q/{bfV}_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3061.png"
 ALT="${\bf V}_1$">|; 

$key = q/{bfV}_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3065.png"
 ALT="${\bf V}_2$">|; 

$key = q/{bfV}_Eequiv{bfE}times{bfB}slashB^{2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1523.png"
 ALT="${\bf V}_E\equiv {\bf E}\times{\bf B}/B^{2}$">|; 

$key = q/{bfV}_s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img891.png"
 ALT="${\bf V}_s$">|; 

$key = q/{bfV}_{s'}={bf0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img954.png"
 ALT="${\bf V}_{s'}={\bf0}$">|; 

$key = q/{bfV}_{ss'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img956.png"
 ALT="${\bf V}_{ss'}$">|; 

$key = q/{bfV}_{ss'}={bfV}_s-{bfV}_{s'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img952.png"
 ALT="${\bf V}_{ss'}= {\bf V}_s-{\bf V}_{s'}$">|; 

$key = q/{bfV}_{ss'}={bfV}_s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img953.png"
 ALT="${\bf V}_{ss'}= {\bf V}_s$">|; 

$key = q/{bfV}cdot({bfj}times{bfB});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.54ex; " SRC="|."$dir".q|img2886.png"
 ALT="${\bf V}\cdot
({\bf j}\times{\bf B})$">|; 

$key = q/{bfV}cdotnablaphi=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2950.png"
 ALT="${\bf V}\cdot\nabla\phi=0$">|; 

$key = q/{bfV}cdotnablaphi={bfB}cdotnablapsi=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3255.png"
 ALT="${\bf V}\cdot\nabla\phi=
{\bf B}\cdot\nabla\psi=0$">|; 

$key = q/{bfV}cdot{bfB}_0=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2728.png"
 ALT="${\bf V}\cdot
{\bf B}_0=0$">|; 

$key = q/{bfV}cdot{bfB}_0neq0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2735.png"
 ALT="${\bf V}\cdot
{\bf B}_0\neq0$">|; 

$key = q/{bfV}timesd{bfr};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img2695.png"
 ALT="${\bf V}\times d{\bf r}$">|; 

$key = q/{bfZ};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img245.png"
 ALT="${\bf Z}$">|; 

$key = q/{bfa};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.12ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1731.png"
 ALT="${\bf a}$">|; 

$key = q/{bfb};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img304.png"
 ALT="${\bf b}$">|; 

$key = q/{bfb}={bfB}_0slashB_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1699.png"
 ALT="${\bf b} = {\bf B}_0/B_0$">|; 

$key = q/{bfb}cdotd{bfb}slashdt=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img346.png"
 ALT="${\bf b}\cdot d{\bf b}/dt=0$">|; 

$key = q/{bfb}equiv{bfB}slashB;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img234.png"
 ALT="${\bf b} \equiv {\bf B}/B$">|; 

$key = q/{bfb}equiv{bfe}_3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1730.png"
 ALT="${\bf b} \equiv {\bf e}_3$">|; 

$key = q/{bfb}timesnablaT_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1258.png"
 ALT="${\bf b}\times\nabla T_i$">|; 

$key = q/{bfc};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.12ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img303.png"
 ALT="${\bf c}$">|; 

$key = q/{bfc}={bf0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img306.png"
 ALT="${\bf c} = {\bf0}$">|; 

$key = q/{bfe}_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img223.png"
 ALT="${\bf e}_1$">|; 

$key = q/{bfe}_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img224.png"
 ALT="${\bf e}_2$">|; 

$key = q/{bfe}_y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.73ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3279.png"
 ALT="${\bf e}_y$">|; 

$key = q/{bfe}_z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3254.png"
 ALT="${\bf e}_z$">|; 

$key = q/{bff};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img237.png"
 ALT="${\bf f}$">|; 

$key = q/{bfg};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1067.png"
 ALT="${\bf g}$">|; 

$key = q/{bfg}=-g,{bfe}_z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img182.png"
 ALT="${\bf g} = -g {\bf e}_z$">|; 

$key = q/{bfg}_{ss'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img741.png"
 ALT="${\bf g}_{ss'}$">|; 

$key = q/{bfg}_{ss'}={bf0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img761.png"
 ALT="${\bf g}_{ss'}={\bf0}$">|; 

$key = q/{bfg}_{ss'}={bfu}_{ss'}'-{bfu}_{ss'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.76ex; " SRC="|."$dir".q|img739.png"
 ALT="${\bf g}_{ss'}= {\bf u}_{ss'}'-{\bf u}_{ss'}$">|; 

$key = q/{bfh}_{ss'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img686.png"
 ALT="${\bf h}_{ss'}$">|; 

$key = q/{bfi};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img1263.png"
 ALT="${\bf i}$">|; 

$key = q/{bfj}({bfr},t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.54ex; " SRC="|."$dir".q|img1675.png"
 ALT="${\bf j}({\bf r},t)$">|; 

$key = q/{bfj};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.54ex; " SRC="|."$dir".q|img569.png"
 ALT="${\bf j}$">|; 

$key = q/{bfj}=-mu_0^{-1},J,{bfe}_z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.57ex; vertical-align: -0.79ex; " SRC="|."$dir".q|img3271.png"
 ALT="${\bf j} = -\mu_0^{-1} J {\bf e}_z$">|; 

$key = q/{bfj}=-n,e,({bfV}_e-{bfV}_i);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.54ex; " SRC="|."$dir".q|img1163.png"
 ALT="${\bf j} = - n e ({\bf V}_e-{\bf V}_i)$">|; 

$key = q/{bfj}_0=nablatimes{bfB}_0slashmu_0={bf0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1661.png"
 ALT="${\bf j}_0 =\nabla\times
{\bf B}_0 /\mu_0= {\bf0}$">|; 

$key = q/{bfj}_parallelequiv({bfb}cdot{bfj}),{bfb};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img1229.png"
 ALT="${\bf j}_\parallel \equiv ({\bf b}\cdot{\bf j}) {\bf b}$">|; 

$key = q/{bfj}_perpequiv{bfj}-j_parallel,{bfb};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img1702.png"
 ALT="${\bf j}_\perp\equiv {\bf j} - j_\parallel {\bf b}$">|; 

$key = q/{bfj}_perpequiv{bfj}-{bfj}_parallel;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img1230.png"
 ALT="${\bf j}_\perp \equiv {\bf j} - {\bf j}_\parallel$">|; 

$key = q/{bfk};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img1666.png"
 ALT="${\bf k}$">|; 

$key = q/{bfk}=(0,,k,,0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3288.png"
 ALT="${\bf k} = (0, k, 0)$">|; 

$key = q/{bfk}cdot{bfB}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3248.png"
 ALT="${\bf k}\cdot{\bf B}=0$">|; 

$key = q/{bfk}cdot{bfB}_0=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3289.png"
 ALT="${\bf k}\cdot{\bf B}_0=0$">|; 

$key = q/{bfk}cdot{bfB}_0equivk,B_0,F=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3324.png"
 ALT="${\bf k}\cdot{\bf B}_0\equiv k B_0 F=0$">|; 

$key = q/{bfk}cdot{bfV}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img2727.png"
 ALT="${\bf k}\cdot{\bf V} =0$">|; 

$key = q/{bfk}cdot{bfV}neq0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.21ex; " SRC="|."$dir".q|img2734.png"
 ALT="${\bf k}\cdot{\bf V} \neq 0$">|; 

$key = q/{bfl};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img751.png"
 ALT="${\bf l}$">|; 

$key = q/{bfm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img752.png"
 ALT="${\bf m}$">|; 

$key = q/{bfn};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img339.png"
 ALT="${\bf n}$">|; 

$key = q/{bfpsi}({bfr},t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2097.png"
 ALT="${\bf\psi}({\bf r}, t)$">|; 

$key = q/{bfp}=m,{bfv}+e,{bfA};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img491.png"
 ALT="${\bf p} = m {\bf v} + e {\bf A}$">|; 

$key = q/{bfp}_s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1024.png"
 ALT="${\bf p}_s$">|; 

$key = q/{bfq};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1104.png"
 ALT="${\bf q}$">|; 

$key = q/{bfq}_e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1304.png"
 ALT="${\bf q}_e$">|; 

$key = q/{bfq}_s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1025.png"
 ALT="${\bf q}_s$">|; 

$key = q/{bfq}_{Te};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1305.png"
 ALT="${\bf q}_{Te}$">|; 

$key = q/{bfq}_{Ue};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1306.png"
 ALT="${\bf q}_{Ue}$">|; 

$key = q/{bfr}(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2356.png"
 ALT="${\bf r}(t)$">|; 

$key = q/{bfr}+d{bfr};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img613.png"
 ALT="${\bf r}+d{\bf r}$">|; 

$key = q/{bfr};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img317.png"
 ALT="${\bf r}$">|; 

$key = q/{bfr}_s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img670.png"
 ALT="${\bf r}_s$">|; 

$key = q/{bfr}_{s'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img671.png"
 ALT="${\bf r}_{s'}$">|; 

$key = q/{bfr}_{ss'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img705.png"
 ALT="${\bf r}_{ss'}$">|; 

$key = q/{bfr}_{ss'}=(x,,y);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img687.png"
 ALT="${\bf r}_{ss'}=(x, y)$">|; 

$key = q/{bfr}_{ss'}={bfr}_s-{bfr}_{s'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img672.png"
 ALT="${\bf r}_{ss'}={\bf r}_s-{\bf r}_{s'}$">|; 

$key = q/{bfr}_{ss'}cdot{bfh}_{ss'}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img685.png"
 ALT="${\bf r}_{ss'}\cdot{\bf h}_{ss'}=0$">|; 

$key = q/{bfu};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.12ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img286.png"
 ALT="${\bf u}$">|; 

$key = q/{bfu}={mitOmega},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img318.png"
 ALT="${\bf u} = {\mit\Omega} $">|; 

$key = q/{bfu}_{ss'}';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.76ex; " SRC="|."$dir".q|img611.png"
 ALT="${\bf u}_{ss'}'$">|; 

$key = q/{bfu}_{ss'}'={bfu}_{ss'}+{bfg}_{ss'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.76ex; " SRC="|."$dir".q|img754.png"
 ALT="${\bf u}_{ss'}'={\bf u}_{ss'}+{\bf g}_{ss'}$">|; 

$key = q/{bfu}_{ss'}'={bfu}_{ss'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.76ex; " SRC="|."$dir".q|img757.png"
 ALT="${\bf u}_{ss'}' = {\bf u}_{ss'}$">|; 

$key = q/{bfu}_{ss'}'={bfv}_s'-{bfv}_{s'}';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.76ex; " SRC="|."$dir".q|img628.png"
 ALT="${\bf u}_{ss'}'={\bf v}_s'-{\bf v}_{s'}'$">|; 

$key = q/{bfu}_{ss'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img594.png"
 ALT="${\bf u}_{ss'}$">|; 

$key = q/{bfu}_{ss'}=u_{ss'},{bfl};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img753.png"
 ALT="${\bf u}_{ss'}= u_{ss'} {\bf l}$">|; 

$key = q/{bfu}_{ss'}={bfv}_s-{bfv}_{s'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img734.png"
 ALT="${\bf u}_{ss'}={\bf v}_s-{\bf v}_{s'}$">|; 

$key = q/{bfu}_{ss'}rightarrow-{bfu}_{ss'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img645.png"
 ALT="${\bf u}_{ss'}\rightarrow-{\bf u}_{ss'}$">|; 

$key = q/{bfv}');MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2364.png"
 ALT="${\bf v}')$">|; 

$key = q/{bfv}(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2357.png"
 ALT="${\bf v}(t)$">|; 

$key = q/{bfv});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2366.png"
 ALT="${\bf v})$">|; 

$key = q/{bfv};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.12ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img364.png"
 ALT="${\bf v}$">|; 

$key = q/{bfv}=v_parallel,{bfb}+{bfv}_perp;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img431.png"
 ALT="${\bf v} = v_\parallel {\bf b} +
{\bf v}_\perp$">|; 

$key = q/{bfv}={bfU}+{bfu};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img366.png"
 ALT="${\bf v} = {\bf U} + {\bf u}$">|; 

$key = q/{bfv}_E;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img228.png"
 ALT="${\bf v}_E$">|; 

$key = q/{bfv}_s'+d{bfv}_{s}';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img605.png"
 ALT="${\bf v}_s'+d{\bf v}_{s}'$">|; 

$key = q/{bfv}_s';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img604.png"
 ALT="${\bf v}_s'$">|; 

$key = q/{bfv}_s+d{bfv}_s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img614.png"
 ALT="${\bf v}_s+d{\bf v}_s$">|; 

$key = q/{bfv}_s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img588.png"
 ALT="${\bf v}_s$">|; 

$key = q/{bfv}_{rmph};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.73ex; vertical-align: -0.75ex; " SRC="|."$dir".q|img1670.png"
 ALT="${\bf v}_{\rm ph}$">|; 

$key = q/{bfv}_{s'}'+d{bfv}_{s'}';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.76ex; " SRC="|."$dir".q|img607.png"
 ALT="${\bf v}_{s'}'+d{\bf v}_{s'}'$">|; 

$key = q/{bfv}_{s'}';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.76ex; " SRC="|."$dir".q|img606.png"
 ALT="${\bf v}_{s'}'$">|; 

$key = q/{bfv}_{s'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img590.png"
 ALT="${\bf v}_{s'}$">|; 

$key = q/{bfw}_{ss'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img782.png"
 ALT="${\bf w}_{ss'}$">|; 

$key = q/{bfz}(t,tau);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img243.png"
 ALT="${\bf z}(t,\tau)$">|; 

$key = q/{bfz};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img241.png"
 ALT="${\bf z}$">|; 

$key = q/{calE};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img414.png"
 ALT="${\cal E}$">|; 

$key = q/{calE}<mu,B+e,{mitPhi}+m,{bfv}_E^{2}slash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.75ex; " SRC="|."$dir".q|img417.png"
 ALT="${\cal E} &lt; \mu B +e {\mit\Phi} + m {\bf v}_E^{2}/2$">|; 

$key = q/{calE}=m,(v_parallel^{2}+v_perp^{2})slash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.79ex; vertical-align: -1.04ex; " SRC="|."$dir".q|img430.png"
 ALT="${\cal E} = m (v_\parallel^{2} + v_\perp^{2})/2$">|; 

$key = q/{calE}=mu,B+e,{mitPhi}+m,{bfv}_E^{2}slash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.75ex; " SRC="|."$dir".q|img418.png"
 ALT="${\cal E} = \mu B +e {\mit\Phi} + m {\bf v}_E^{2}/2$">|; 

$key = q/{calE}>mu,B+e,{mitPhi}+m,{bfv}_E^{2}slash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.75ex; " SRC="|."$dir".q|img416.png"
 ALT="${\cal E} &gt; \mu B +e {\mit\Phi} + m {\bf v}_E^{2}/2$">|; 

$key = q/{calE}_{0,parallel};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img552.png"
 ALT="${\cal E}_{0 \parallel}$">|; 

$key = q/{calE}_{0,perp};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img550.png"
 ALT="${\cal E}_{0 \perp}$">|; 

$key = q/{calF}_s({bfr},{bfv},t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img575.png"
 ALT="${\cal F}_s({\bf r}, {\bf v}, t)$">|; 

$key = q/{calF}_s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img570.png"
 ALT="${\cal F}_s$">|; 

$key = q/{calI};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.15ex; " SRC="|."$dir".q|img387.png"
 ALT="${\cal I}$">|; 

$key = q/{calM}equiv{rmdet}({bfM});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2104.png"
 ALT="${\cal M} \equiv {\rm det}({\bf M})$">|; 

$key = q/{calO}(1);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1363.png"
 ALT="${\cal O}(1)$">|; 

$key = q/{calO}(delta^{-1});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1492.png"
 ALT="${\cal O}(\delta^{-1})$">|; 

$key = q/{calO}(epsilon^0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img315.png"
 ALT="${\cal O}(\epsilon^0)$">|; 

$key = q/{calO}(epsilon^{-1});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img295.png"
 ALT="${\cal O}(\epsilon^{-1})$">|; 

$key = q/{calO}(p^3);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3429.png"
 ALT="${\cal O}(p^3)$">|; 

$key = q/{calO}(zeta);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1537.png"
 ALT="${\cal O}(\zeta)$">|; 

$key = q/{calO}(zeta_e);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1365.png"
 ALT="${\cal O}(\zeta_e)$">|; 

$key = q/{calO}(zeta_e^{2});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.65ex; " SRC="|."$dir".q|img1366.png"
 ALT="${\cal O}(\zeta_e^{2})$">|; 

$key = q/{calO}(zeta_i);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1407.png"
 ALT="${\cal O}(\zeta_i)$">|; 

$key = q/{calO}(zeta_i,mu);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1410.png"
 ALT="${\cal O}(\zeta_i \mu)$">|; 

$key = q/{calO}(zeta_i^{2});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.51ex; vertical-align: -0.76ex; " SRC="|."$dir".q|img1408.png"
 ALT="${\cal O}(\zeta_i^{2})$">|; 

$key = q/{calS};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.15ex; " SRC="|."$dir".q|img3676.png"
 ALT="${\cal S}$">|; 

$key = q/{calS}=tau_Rslashtau_A;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3675.png"
 ALT="${\cal S}= \tau_R/\tau_A$">|; 

$key = q/{calS}rightarrowhat{delta}_{rmSP},{calS};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3712.png"
 ALT="${\cal S}\rightarrow\hat{\delta}_{\rm SP} {\cal S}$">|; 

$key = q/{displaymath}B_z(y)=left{{array}{lll}B_0&mbox{hspace{0.5cm}}&y>a[0.5ex]B_0,(yslasha)&&|y|<a[0.5ex]-B_0&&y<-a{array}right.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 8.70ex; " SRC="|."$dir".q|img555.png"
 ALT="\begin{displaymath}
B_z(y) = \left\{
\begin{array}{lll}
B_0&amp;\mbox{\hspace{0.5cm}...
...a)&amp;&amp;\vert y\vert&lt; a\ [0.5ex]
-B_0 &amp;&amp;y &lt; -a
\end{array}\right.
\end{displaymath}">|; 

$key = q/{displaymath}sigma=left{{array}{lll}0&mbox{hspace{0.5cm}}&y>1slash|x|[0.5ex]1&&|y|<1slash|x|[0.5ex]2&&y<-1slash|x|{array}right..{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 8.70ex; " SRC="|."$dir".q|img2334.png"
 ALT="\begin{displaymath}\sigma = \left\{
\begin{array}{lll}
0&amp;\mbox{\hspace{0.5cm}}&amp; ...
...vert x\vert\ [0.5ex]
2&amp;&amp;y&lt; -1/\vert x\vert
\end{array}\right..\end{displaymath}">|; 

$key = q/{mbox{boldmathpsi}}({bfr},t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2093.png"
 ALT="${\mbox{\boldmath $\psi$}}({\bf r}, t)$">|; 

$key = q/{mbox{boldmathpsi}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2094.png"
 ALT="${\mbox{\boldmath $\psi$}}$">|; 

$key = q/{mitDelta}'(0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3603.png"
 ALT="${\mit\Delta}'(0)$">|; 

$key = q/{mitDelta}',S^{-1slash3}sim1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3621.png"
 ALT="${\mit\Delta}' S^{-1/3}\sim 1$">|; 

$key = q/{mitDelta}',hat{W};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3534.png"
 ALT="${\mit\Delta}' \hat{W}$">|; 

$key = q/{mitDelta}',hat{W}sim1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3705.png"
 ALT="${\mit\Delta}' \hat{W}\sim 1$">|; 

$key = q/{mitDelta}',hat{delta}ll1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3533.png"
 ALT="${\mit\Delta}' \hat{\delta}\ll 1$">|; 

$key = q/{mitDelta}',hat{mitPsi}^{1slash2}geq1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.22ex; " SRC="|."$dir".q|img3623.png"
 ALT="${\mit\Delta}'
 \hat{\mit\Psi}^{1/2}\geq 1$">|; 

$key = q/{mitDelta}';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img11.png"
 ALT="${\mit \Delta }'$">|; 

$key = q/{mitDelta}'<0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3363.png"
 ALT="${\mit\Delta}'&lt;0$">|; 

$key = q/{mitDelta}'>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3365.png"
 ALT="${\mit\Delta}'&gt; 0$">|; 

$key = q/{mitDelta}'ll1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img3608.png"
 ALT="${\mit\Delta}'\ll 1$">|; 

$key = q/{mitDelta}'rightarrowinfty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img3367.png"
 ALT="${\mit\Delta}'\rightarrow\infty$">|; 

$key = q/{mitDelta}'sim1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img3420.png"
 ALT="${\mit\Delta}'\sim 1$">|; 

$key = q/{mitDelta}'sim1slashk;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3706.png"
 ALT="${\mit\Delta}'\sim 1/k$">|; 

$key = q/{mitDelta}'simeq2slash(k,a);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3678.png"
 ALT="${\mit\Delta}'\simeq 2/(k a)$">|; 

$key = q/{mitDelta}'slashS^{1slash3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img14.png"
 ALT="${\mit \Delta }'/S^{1/3}$">|; 

$key = q/{mitDelta}'slashS^{1slash3}gg1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3448.png"
 ALT="${\mit\Delta}'/S^{1/3}\gg 1$">|; 

$key = q/{mitDelta}'slashS^{1slash3}ll1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3447.png"
 ALT="${\mit\Delta}'/S^{1/3}\ll 1$">|; 

$key = q/{mitDelta}'slashS^{1slash3}proptoQ^{5slash4};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img15.png"
 ALT="${\mit \Delta }'/S^{1/3}\propto Q^{5/4}$">|; 

$key = q/{mitDelta}(hat{gamma},S);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3378.png"
 ALT="${\mit\Delta}(\hat{\gamma},S)$">|; 

$key = q/{mitDelta};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img3394.png"
 ALT="${\mit\Delta}$">|; 

$key = q/{mitDelta}_1';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.77ex; " SRC="|."$dir".q|img3557.png"
 ALT="${\mit\Delta}_1'$">|; 

$key = q/{mitDelta}_1'>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.77ex; " SRC="|."$dir".q|img3580.png"
 ALT="${\mit\Delta}_1'&gt;0$">|; 

$key = q/{mitDelta}_m';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.65ex; " SRC="|."$dir".q|img3555.png"
 ALT="${\mit\Delta}_m'$">|; 

$key = q/{mitDelta}g;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1068.png"
 ALT="${\mit\Delta}g$">|; 

$key = q/{mitDelta}tsim{mitOmega}^{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img360.png"
 ALT="${\mit\Delta}t\sim {\mit\Omega}^{-1}$">|; 

$key = q/{mitGamma}<2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img3143.png"
 ALT="${\mit\Gamma} &lt; 2$">|; 

$key = q/{mitGamma}=5slash3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1905.png"
 ALT="${\mit\Gamma}=5/3$">|; 

$key = q/{mitLambda};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img80.png"
 ALT="${\mit\Lambda}$">|; 

$key = q/{mitLambda}=4pi,epsilon_0^{3slash2},T^{3slash2}slash(e^{3},n_e^{1slash2});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.79ex; vertical-align: -0.82ex; " SRC="|."$dir".q|img977.png"
 ALT="${\mit\Lambda} =4\pi \epsilon_0^{3/2} T^{3/2}/(e^{3} n_e^{1/2})$">|; 

$key = q/{mitLambda}gg1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img79.png"
 ALT="${\mit\Lambda}\gg 1$">|; 

$key = q/{mitLambda}ll1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img78.png"
 ALT="${\mit\Lambda}\ll 1$">|; 

$key = q/{mitOmega}(X,xi);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3510.png"
 ALT="${\mit\Omega}(X,\xi)$">|; 

$key = q/{mitOmega}+d{mitOmega};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img720.png"
 ALT="${\mit\Omega}+d{\mit\Omega}$">|; 

$key = q/{mitOmega},R_odot^{2},m;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.71ex; " SRC="|."$dir".q|img2855.png"
 ALT="${\mit\Omega} R_\odot^{2} m$">|; 

$key = q/{mitOmega},r_A^{2},m;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.75ex; " SRC="|."$dir".q|img2854.png"
 ALT="${\mit\Omega} r_A^{2} 
m$">|; 

$key = q/{mitOmega};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img211.png"
 ALT="${\mit\Omega}$">|; 

$key = q/{mitOmega}<0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2900.png"
 ALT="${\mit\Omega}&lt;0$">|; 

$key = q/{mitOmega}=2.7times10^{-6},{rmrad,sec}^{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2819.png"
 ALT="${\mit\Omega}= 2.7\times 10^{-6} {\rm rad sec}^{-1}$">|; 

$key = q/{mitOmega}=e,B_0slashm;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2370.png"
 ALT="${\mit\Omega} = e B_0/m$">|; 

$key = q/{mitOmega}=eBslashm;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img222.png"
 ALT="${\mit\Omega}=eB/m$">|; 

$key = q/{mitOmega}=sinchi,dchi,dphi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img640.png"
 ALT="${\mit\Omega}=\sin\chi d\chi d\phi$">|; 

$key = q/{mitOmega}>1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img3512.png"
 ALT="${\mit\Omega}&gt;1$">|; 

$key = q/{mitOmega}^{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img215.png"
 ALT="${\mit\Omega}^{-1}$">|; 

$key = q/{mitOmega}_0=e,B_0slashm;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img560.png"
 ALT="${\mit\Omega}_0=e B_0/m$">|; 

$key = q/{mitOmega}_e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img446.png"
 ALT="${\mit\Omega}_e$">|; 

$key = q/{mitOmega}_islash(k_parallel,v_{parallel,i});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img2644.png"
 ALT="${\mit\Omega}_i/(k_\parallel v_{\parallel i})$">|; 

$key = q/{mitOmega}_s=e_s,B_0slashm_s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2406.png"
 ALT="${\mit\Omega}_s = e_s B_0/m_s$">|; 

$key = q/{mitOmega}proptom^{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img362.png"
 ALT="${\mit\Omega}\propto m^{-1}$">|; 

$key = q/{mitPhi}(x);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1558.png"
 ALT="${\mit\Phi}(x)$">|; 

$key = q/{mitPhi}({bfr});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img60.png"
 ALT="${\mit\Phi}({\bf r})$">|; 

$key = q/{mitPhi};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img409.png"
 ALT="${\mit\Phi}$">|; 

$key = q/{mitPhi}=M,I;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img2891.png"
 ALT="${\mit\Phi} = M I$">|; 

$key = q/{mitPhi}_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2315.png"
 ALT="${\mit\Phi}_0$">|; 

$key = q/{mitPhi}_p;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1625.png"
 ALT="${\mit\Phi}_p$">|; 

$key = q/{mitPhi}_s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1565.png"
 ALT="${\mit\Phi}_s$">|; 

$key = q/{mitPhi}_w={mitPhi}(0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1594.png"
 ALT="${\mit\Phi}_w={\mit\Phi}(0)$">|; 

$key = q/{mitPi}({rmsec}^{-1});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img83.png"
 ALT="${\mit\Pi}({\rm sec}^{-1})$">|; 

$key = q/{mitPi};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img43.png"
 ALT="${\mit\Pi}$">|; 

$key = q/{mitPi}=(e^2,n_eslashepsilon_0,m_e)^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img178.png"
 ALT="${\mit\Pi} = (e^2 n_e/\epsilon_0 m_e)^{1/2}$">|; 

$key = q/{mitPi}_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2210.png"
 ALT="${\mit\Pi}_0$">|; 

$key = q/{mitPi}_e(0)=omega;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2090.png"
 ALT="${\mit\Pi}_e(0) = \omega$">|; 

$key = q/{mitPi}_e(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2202.png"
 ALT="${\mit\Pi}_e(z)$">|; 

$key = q/{mitPi}_e(z)<omega;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2091.png"
 ALT="${\mit\Pi}_e(z) &lt; \omega$">|; 

$key = q/{mitPi}_e(z)=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2211.png"
 ALT="${\mit\Pi}_e(z)=0$">|; 

$key = q/{mitPi}_e(z_0)=omega;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2204.png"
 ALT="${\mit\Pi}_e(z_0)= \omega$">|; 

$key = q/{mitPi}_e,|{mitOmega}_e|llomega;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img1890.png"
 ALT="${\mit\Pi}_e, \vert{\mit\Omega}_e\vert\ll \omega$">|; 

$key = q/{mitPi}_e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2645.png"
 ALT="${\mit\Pi}_e$">|; 

$key = q/{mitPi}_e=(e^2,n_eslashepsilon_0,m_e)^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img164.png"
 ALT="${\mit\Pi}_e= (e^2 n_e/\epsilon_0 m_e)^{1/2}$">|; 

$key = q/{mitPi}_e=(n,e^2slashepsilon_0,m_e)^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2294.png"
 ALT="${\mit\Pi}_e=(n e^2/\epsilon_0 m_e)^{1/2}$">|; 

$key = q/{mitPi}_e=(n_e,e^2slashepsilon_0,m_e)^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2668.png"
 ALT="${\mit\Pi}_e =(n_e e^2/\epsilon_0 m_e)^{1/2}$">|; 

$key = q/{mitPi}_e=(n_e,e^{2}slashepsilon_0,m_e)^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img979.png"
 ALT="${\mit\Pi}_e=(n_e e^{2}/\epsilon_0 m_e)^{1/2}$">|; 

$key = q/{mitPi}_e={mitPi}_e(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2143.png"
 ALT="${\mit\Pi}_e={\mit\Pi}_e(z)$">|; 

$key = q/{mitPi}_e>n,{mitOmega}_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2646.png"
 ALT="${\mit\Pi}_e&gt; n {\mit\Omega}_i$">|; 

$key = q/{mitPi}_i=(Z^{2},e^2,n_islashepsilon_0,m_i)^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img165.png"
 ALT="${\mit\Pi}_i = (Z^{2} e^2 n_i/\epsilon_0 m_i)^{1/2}$">|; 

$key = q/{mitPi}_i=(n,e^2slashepsilon_0,m_i)^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2337.png"
 ALT="${\mit\Pi}_i = (n e^2/\epsilon_0 m_i)^{1/2}$">|; 

$key = q/{mitPi}_i=(n_i,e^{2}slashepsilon_0,m_i)^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img981.png"
 ALT="${\mit\Pi}_i=(n_i e^{2}/\epsilon_0 m_i)^{1/2}$">|; 

$key = q/{mitPi}_s=(n,e^2slashepsilon_0,m_s)^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2662.png"
 ALT="${\mit\Pi}_s=(n e^2/\epsilon_0 m_s)^{1/2}$">|; 

$key = q/{mitPi}_s=(n_s,e_s^{2}slashepsilon_0,m_s)^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img2414.png"
 ALT="${\mit\Pi}_s = (n_s e_s^{2}/\epsilon_0 m_s)^{1/2}$">|; 

$key = q/{mitPi}_s^{2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img2629.png"
 ALT="${\mit\Pi}_s^{2}$">|; 

$key = q/{mitPsi}';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img3377.png"
 ALT="${\mit\Psi}'$">|; 

$key = q/{mitPsi};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img493.png"
 ALT="${\mit\Psi}$">|; 

$key = q/{mitPsi}=a,B_0,hat{mitPsi};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3638.png"
 ALT="${\mit\Psi} = a B_0 \hat{\mit\Psi}$">|; 

$key = q/{mitPsi}={mitPsi}';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img3379.png"
 ALT="${\mit\Psi}={\mit\Psi}'$">|; 

$key = q/{mitTheta};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img704.png"
 ALT="${\mit\Theta}$">|; 

$key = q/{mitTheta}_s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1095.png"
 ALT="${\mit\Theta}_s$">|; 

$key = q/{mitchi}_t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1123.png"
 ALT="${\mit\chi}_t$">|; 

$key = q/{mitchi}_v;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1122.png"
 ALT="${\mit\chi}_v$">|; 

$key = q/{rmAi}(-hat{z});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1954.png"
 ALT="${\rm Ai}(-\hat{z})$">|; 

$key = q/{rmBi}(-hat{z});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1955.png"
 ALT="${\rm Bi}(-\hat{z})$">|; 

$key = q/{rmIm}(gamma),tau_R=0.41;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3046.png"
 ALT="${\rm Im}(\gamma) \tau_R = 0.41$">|; 

$key = q/{rmIm}(gamma)neq0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3036.png"
 ALT="${\rm Im}(\gamma)\neq 0$">|; 

$key = q/{rmIm}(omega)<0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2278.png"
 ALT="${\rm Im}(\omega)&lt;0$">|; 

$key = q/{rmIm}(omega)>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2277.png"
 ALT="${\rm Im}(\omega)&gt;0$">|; 

$key = q/{rmIm}(omega)leq0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2407.png"
 ALT="${\rm Im}(\omega)\leq 0$">|; 

$key = q/{rmIm}(zeta)>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2320.png"
 ALT="${\rm Im}(\zeta)&gt;0$">|; 

$key = q/{rmIm}(zeta)leq0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2321.png"
 ALT="${\rm Im}(\zeta)\leq 0$">|; 

$key = q/{rmRe}(gamma)>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3034.png"
 ALT="${\rm Re}(\gamma)&gt;0$">|; 

$key = q/{rmRe}(p);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2271.png"
 ALT="${\rm Re}(p)$">|; 

$key = q/{rmRe}(p)>-sigma;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2266.png"
 ALT="${\rm Re}(p)&gt;-\sigma$">|; 

$key = q/{rmcm}^{-3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img847.png"
 ALT="${\rm cm}^{-3}$">|; 

$key = q/{rme}^{-lambda_e},I_n(lambda_e)rightarrow0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2493.png"
 ALT="${\rm e}^{-\lambda_e} I_n(\lambda_e)\rightarrow
0$">|; 

$key = q/{rme}^{-sigma,t};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.73ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2268.png"
 ALT="${\rm e}^{-\sigma t}$">|; 

$key = q/{rme}^{-{rmi},k,u,t};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2275.png"
 ALT="${\rm e}^{-{\rm i} k u t}$">|; 

$key = q/{rme}^{-{rmi},omega,t};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2282.png"
 ALT="${\rm e}^{-{\rm i} \omega t}$">|; 

$key = q/{rme}^{-{rmi},omega_1,t};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2280.png"
 ALT="${\rm e}^{-{\rm i} \omega_1 t}$">|; 

$key = q/{rme}^{-{rmi},omega_2,t};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2281.png"
 ALT="${\rm e}^{-{\rm i} \omega_2 t}$">|; 

$key = q/{rme}^{p_0,t};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.73ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2267.png"
 ALT="${\rm e}^{p_0 t}$">|; 

$key = q/{rmi},E_xslashE_y=-1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1771.png"
 ALT="${\rm i} E_x/E_y = -1$">|; 

$key = q/{rmi},E_xslashE_y=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1769.png"
 ALT="${\rm i} E_x/E_y = 1$">|; 

$key = q/{rmi},Z_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2619.png"
 ALT="${\rm i} Z_i$">|; 

$key = q/{rmkm},{rms}^{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2751.png"
 ALT="${\rm km} {\rm s}^{-1}$">|; 

$key = q/{{mitOmega}}_e,{{mitOmega}}_irightarrow0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1780.png"
 ALT="${{\mit\Omega}}_e, {{\mit\Omega}}_i
\rightarrow 0$">|; 

$key = q/{{mitOmega}}_e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1833.png"
 ALT="${{\mit\Omega}}_e$">|; 

$key = q/{{mitOmega}}_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1849.png"
 ALT="${{\mit\Omega}}_i$">|; 

$key = q/{{mitOmega}}_illomegall|{{mitOmega}}_e|;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img1846.png"
 ALT="${{\mit\Omega}}_i\ll \omega\ll \vert{{\mit\Omega}}_e\vert$">|; 

$key = q/{{mitPi}}_e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1784.png"
 ALT="${{\mit\Pi}}_e$">|; 

$key = q/{{mitPi}}_e^{2}slash({{mitOmega}}_e,{{mitOmega}}_i)=-{{mitPi}}_i^{2}slash{{mitOmega}}_i^{2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.51ex; vertical-align: -0.76ex; " SRC="|."$dir".q|img1804.png"
 ALT="${{\mit\Pi}}_e^{2}/({{\mit\Omega}}_e {{\mit\Omega}}_i)
=-{{\mit\Pi}}_i^{2}/ {{\mit\Omega}}_i^{2}$">|; 

$key = q/{{mitPi}}_e^{2}slashomega^2gg{{mitPi}}_i^{2}slash{{mitOmega}}_i^{2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.51ex; vertical-align: -0.76ex; " SRC="|."$dir".q|img1807.png"
 ALT="${{\mit\Pi}}_e^{2}/\omega^2\gg
{{\mit\Pi}}_i^{2}/{{\mit\Omega}}_i^{2}$">|; 

$key = q/{{mitPi}}_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1783.png"
 ALT="${{\mit\Pi}}_i$">|; 

$key = q/|I_1slashI_m|;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img3579.png"
 ALT="$\vert I_1/I_m\vert$">|; 

$key = q/|R|=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img1967.png"
 ALT="$\vert R\vert=1$">|; 

$key = q/|U|rightarrowinfty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img2530.png"
 ALT="$\vert U\vert\rightarrow \infty$">|; 

$key = q/|alpha_{rmeq}|<alpha_l;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.75ex; " SRC="|."$dir".q|img463.png"
 ALT="$\vert\alpha_{\rm eq}\vert &lt; \alpha_l$">|; 

$key = q/|arg(q)|;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.58ex; " SRC="|."$dir".q|img3028.png"
 ALT="$\vert\arg(q)\vert$">|; 

$key = q/|arg(s)|<pislash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.58ex; " SRC="|."$dir".q|img3029.png"
 ALT="$\vert\arg(s)\vert&lt;\pi/2$">|; 

$key = q/|arg(z)|<pislash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.58ex; " SRC="|."$dir".q|img3025.png"
 ALT="$\vert\arg(z)\vert&lt;\pi/2$">|; 

$key = q/|dslashdhat{x}|gg1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img3336.png"
 ALT="$\vert d/d\hat{x}\vert\gg 1$">|; 

$key = q/|e,{mitPhi}slashT_{i,e}|ll1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.63ex; " SRC="|."$dir".q|img191.png"
 ALT="$\vert e {\mit\Phi}/T_{i,e}\vert\ll 1$">|; 

$key = q/|e,{mitPhi}slashT|;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img195.png"
 ALT="$\vert e {\mit\Phi}/T\vert$">|; 

$key = q/|epsilon_i|ll|epsilon_r|;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img2598.png"
 ALT="$\vert\epsilon_i\vert\ll \vert\epsilon_r\vert$">|; 

$key = q/|epsilon|;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img2046.png"
 ALT="$\vert\epsilon\vert$">|; 

$key = q/|gamma|llomega_r;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2600.png"
 ALT="$\vert\gamma\vert\ll \omega_r$">|; 

$key = q/|gamma|slashomega_rll1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2588.png"
 ALT="$\vert\gamma\vert/\omega_r\ll 1$">|; 

$key = q/|hat{J}|ll1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img3504.png"
 ALT="$\vert\hat{J}\vert\ll 1$">|; 

$key = q/|hat{k},hat{x}|ll1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img3341.png"
 ALT="$\vert\hat{k} \hat{x}\vert\ll 1$">|; 

$key = q/|hat{x}|gghat{W};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img3522.png"
 ALT="$\vert\hat{x}\vert\gg \hat{W}$">|; 

$key = q/|hat{x}|ll1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img3335.png"
 ALT="$\vert\hat{x}\vert\ll 1$">|; 

$key = q/|hat{x}|rightarrow0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img3357.png"
 ALT="$\vert\hat{x}\vert\rightarrow 0$">|; 

$key = q/|hat{x}|rightarrowinfty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img3728.png"
 ALT="$\vert\hat{x}\vert\rightarrow\infty$">|; 

$key = q/|hat{z}|gg1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img2014.png"
 ALT="$\vert\hat{z}\vert\gg 1$">|; 

$key = q/|hat{z}|ll1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img2003.png"
 ALT="$\vert\hat{z}\vert\ll 1$">|; 

$key = q/|n|gg1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img2471.png"
 ALT="$\vert n\vert \gg 1$">|; 

$key = q/|pi-alpha_{rmeq}|<alpha_l;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.75ex; " SRC="|."$dir".q|img464.png"
 ALT="$\vert\pi-\alpha_{\rm eq}\vert &lt; \alpha_l$">|; 

$key = q/|q|,|s|gg1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.56ex; " SRC="|."$dir".q|img3019.png"
 ALT="$\vert q\vert, \vert s\vert \gg 1$">|; 

$key = q/|u|rightarrowinfty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img2544.png"
 ALT="$\vert u\vert\rightarrow\infty$">|; 

$key = q/|v_parallel|=v,(1-BslashB_m)^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img472.png"
 ALT="$\vert v_\parallel\vert = v (1-B/B_m)^{1/2}$">|; 

$key = q/|x|ll1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img3213.png"
 ALT="$\vert x\vert\ll 1$">|; 

$key = q/|y_+-y_-|slashall1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img563.png"
 ALT="$\vert y_+-y_-\vert/a\ll 1$">|; 

$key = q/|zeta_e|ll1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2579.png"
 ALT="$\vert\zeta_e\vert\ll 1$">|; 

$key = q/|zeta_i|gg1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2580.png"
 ALT="$\vert\zeta_i\vert\gg 1$">|; 

$key = q/|z|;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img425.png"
 ALT="$\vert z\vert$">|; 

$key = q/|{bfV}_1times{bfB}_1|=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img3154.png"
 ALT="$\vert{\bf V}_1\times {\bf B}_1\vert=0$">|; 

$key = q/|{bfV}_2times{bfB}_2|=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img3157.png"
 ALT="$\vert{\bf V}_2\times {\bf B}_2\vert=0$">|; 

$key = q/|{bfg}_{ss'}+u_{ss'},{bfl}|=u_{ss'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img759.png"
 ALT="$\vert{\bf g}_{ss'}+u_{ss'} {\bf l}\vert=u_{ss'}$">|; 

$key = q/|{bfl}times{bfg}_{ss'}|=u_{ss'},sinchi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img760.png"
 ALT="$\vert{\bf l}\times{\bf g}_{ss'}\vert=u_{ss'} \sin\chi$">|; 

$key = q/|{bfu}_{ss'}'|=|{bfu}_{ss'}|;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.76ex; " SRC="|."$dir".q|img755.png"
 ALT="$\vert{\bf u}_{ss'}'\vert=\vert{\bf u}_{ss'}\vert$">|; 

$key = q/|{bfu}_{ss'}times{bfu}_{ss'}'|=u_{ss'}^2,sinchi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.51ex; vertical-align: -0.76ex; " SRC="|."$dir".q|img756.png"
 ALT="$\vert{\bf u}_{ss'}\times {\bf u}_{ss'}'\vert=u_{ss'}^2 \sin\chi$">|; 

$key = q/|{mitDelta}_1'slash{mitDelta}_m'|;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.77ex; " SRC="|."$dir".q|img3578.png"
 ALT="$\vert{\mit\Delta}_1'/{\mit\Delta}_m'\vert$">|; 

$key = q/|{mitOmega}_e|'>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img2053.png"
 ALT="$\vert{\mit\Omega}_e\vert'&gt;0$">|; 

$key = q/|{mitOmega}_e|;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img1837.png"
 ALT="$\vert{\mit\Omega}_e\vert$">|; 

$key = q/|{{mitOmega}}_e|;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img1838.png"
 ALT="$\vert{{\mit\Omega}}_e\vert$">|; 

1;

