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Cutoff and Resonance

For certain values of the plasma parameters, $n^2$ goes to zero or infinity. In both cases, a transition is made from a region of propagation to a region of evanescense, or vice versa. It will be demonstrated later on that reflection occurs wherever $n^2$ goes through zero, and that absorption takes place wherever $n^2$ goes through infinity. The former case is called a wave cutoff, whereas the latter case is termed a wave resonance.

According to Eqs. (492) and (493)-(495), cutoff occurs when

\begin{displaymath}
P=0,
\end{displaymath} (509)

or
\begin{displaymath}
R=0,
\end{displaymath} (510)

or
\begin{displaymath}
L=0.
\end{displaymath} (511)

Note that the cutoff points are independent of the direction of propagation of the wave relative to the magnetic field.

According to Eq. (498), resonance takes place when

\begin{displaymath}
\tan^2\theta = -\frac{P}{S}.
\end{displaymath} (512)

Evidently, resonance points do depend on the direction of propagation of the wave relative to the magnetic field. For the case of parallel propagation, resonance occurs whenever $S\rightarrow \infty$. In other words, when
\begin{displaymath}
R\rightarrow \infty,
\end{displaymath} (513)

or
\begin{displaymath}
L\rightarrow \infty.
\end{displaymath} (514)

For the case of perpendicular propagation, resonance takes place when
\begin{displaymath}
S = 0.
\end{displaymath} (515)


next up previous
Next: Waves in an Unmagnetized Up: Waves in Cold Plasmas Previous: Polarization
Richard Fitzpatrick 2011-03-31