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. (468) and (469)-(471), cutoff occurs when

$$P=0,$$ (485)

or

$$R=0,$$ (486)

or

$$L=0.$$ (487)

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

According to Eq. (474), resonance takes place when

$$\tan^2\theta = -\frac{P}{S}.$$ (488)

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

$$R\rightarrow \infty,$$ (489)

or

$$L\rightarrow \infty.$$ (490)

For the case of perpendicular propagation, resonance takes place when

$$S = 0.$$ (491)