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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

$\displaystyle P=0,$ (5.61)

or

$\displaystyle R=0,$ (5.62)

or

$\displaystyle L=0.$ (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

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

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

or

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

For the case of perpendicular propagation, resonance occurs when

$\displaystyle S = 0.$ (5.67)


next up previous
Next: Waves in Unmagnetized Plasmas Up: Waves in Cold Plasmas Previous: Wave Polarization
Richard Fitzpatrick 2016-01-23