Low-Frequency Whistler Mode

Resonant growth (or damping) of electromagnetic waves propagating at an angle to the magnetic field in a model plasma is assumed to arise from a two component velocity distribution consisting of a dense, cold background plasma propagation medium, and a diffuse energetic nonthermal ``tail,'' responsible for resonant particle effects. The low-frequency whistler mode, cB/M+c « ω « eB/M−c, is treated in detail. When the energetic resonant electrons have a sufficiently hard-energy spectrum, and a pitch angle anisotropy corresponding to more electron energy perpendicular than parallel to the magnetic field, the whistler can be unstable over a significant cone of wave propagation angles to the magnetic field. Detailed computations of this growth rate for various energy and pitch angle distributions are presented as a function of wave normal angle to the field. The unstable cone is small when the high-energy tail is not well populated. For this reason, whistlers are usually thought to be heavily damped in low β (= 8πp/B2) plasmas. Whistler instability may limit the intensity of trapped high-energy electrons in the earth's Van Allen belts.