Fundamental Quantities
Before proceeding further, it is helpful to define a few fundamental quantities.
Of course, quasi-neutrality demands that [18]
![$\displaystyle n_i \simeq n_e.$](img480.png) |
(2.16) |
We can
estimate typical particle speeds in terms of the so-called thermal speed [18],
![$\displaystyle v_{t\,s} = \left(\frac{2\,T_s}{m_s}\right)^{1/2}.$](img481.png) |
(2.17) |
The typical gyro-radius of a charged particle
gyrating in the magnetic field of a tokamak is given by
![$\displaystyle \rho_s = \frac{v_{t\,s}}{\vert{\mit\Omega}_s\vert},$](img482.png) |
(2.18) |
where
![$\displaystyle {\mit\Omega}_s = \frac{e_s\,B}{m_s}$](img483.png) |
(2.19) |
is the gyro-frequency associated with the
gyration [18]. (Note that
, indicating that electrons gyrate around magnetic field-lines in the opposite direction to ions.)
The electron-ion and ion-ion collision times are
written
respectively [18].
Here,
is
the Coulomb logarithm [42]. Note that
is the typical time required for the cumulative effect of electron-ion collisions to
deviate the path of an electron through
. Likewise,
is the typical time required for the cumulative effect of ion-ion collisions to
deviate the path of an ion through
.
The electron and ion collision frequencies are simply the inverses of the corresponding
collision times:
Finally, the mean-free-paths between collisions (i.e.,
scattering events) for electrons and ions are
respectively.
Table 2.1 gives estimates for some of the fundamental plasma parameters defined in this section in a low-field and a high-field tokamak fusion reactor. Here, use has been made of
the data shown in Table 1.2. It has also been assumed that
, for the sake of simplicity.
Table: 2.1
Fundamental plasma parameters in a low-field and a high-field tokamak reactor. Here,
is the toroidal
magnetic field-strength,
the plasma major radius,
the plasma minor radius,
the electron
number density,
the electron temperature,
the ion temperature,
the electron gyro-frequency,
the ion gyro-frequency,
the electron gyro-radius,
the ion gyro-radius,
the electron collision time,
the ion collision time,
the electron mean-free-path,
and
the ion mean-free-path.
|
Low-Field |
High-Field |
![$B({\rm T})$](img240.png) |
5.0 |
12.0 |
![$R_0({\rm m})$](img243.png) |
7.6 |
3.2 |
![$a({\rm m})$](img244.png) |
2.5 |
1.1 |
![$n_e(10^{20}\,{\rm m}^{-3})$](img242.png) |
0.89 |
5.1 |
![$T_e({\rm keV})$](img241.png) |
7.0 |
7.0 |
![$T_i({\rm keV})$](img501.png) |
7.0 |
7.0 |
![$\vert{\mit\Omega}_e\vert({\rm THz})$](img502.png) |
0.88 |
2.1 |
![${\mit\Omega}_i({\rm GHz})$](img503.png) |
0.19 |
0.46 |
![$\rho_e({\rm\mu m})$](img504.png) |
56 |
24 |
![$\rho_i({\rm mm})$](img505.png) |
3.8 |
1.6 |
![$\tau_e({\rm ms})$](img506.png) |
0.14 |
0.025 |
![$\tau_i({\rm ms})$](img507.png) |
13.6 |
2.36 |
![$l_e({\rm km})$](img508.png) |
7.0 |
1.2 |
![$l_i({\rm km})$](img509.png) |
10 |
1.7 |
|