Cutoff and Resonance

For certain values of $n_e$, $B_0$, and $\theta$, the wave refractive index, $n$, is zero. For other values, the refractive index is infinite. In both cases (assuming that $n$ is a slowly varying function of position), a transition is made from a region in which the wave in question propagates to a region in which the wave decays, or vice versa. It is demonstrated in Section 6.3 that wave reflection occurs at those points where $n$ is zero, and in Section 6.4 that wave absorption occurs at those points where $n$ is infinite. The former points are called wave cutoffs, whereas the latter are termed wave resonances.

According to Equations (5.44) and (5.45)–(5.47), cutoff occurs when

$$P=0,$$ (5.61)

or

$$R=0,$$ (5.62)

or

$$L=0.$$ (5.63)

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

According to Equation (5.50), resonance takes place when

$$\tan^2\theta = -\frac{P}{S}.$$ (5.64)

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

$$R\rightarrow \infty,$$ (5.65)

or

$$L\rightarrow \infty.$$ (5.66)

For the case of perpendicular propagation, resonance occurs when

$$S = 0.$$ (5.67)