Nonlinear pitch angle scattering of energetic electrons by coherent VLF waves in the magnetosphere

Abstract

A computer simulation approach is used to study the nonlinear cyclotron resonant interaction of energetic electrons and coherent VLF waves, with special emphasis on the pitch angle scattering of the particles. Complete equations of motion in an inhomogeneous magnetosphere are used, and the effects of various parameters are studied. Comparison is made with linear theory, and a quantitative and easy‐to‐use criterion to determine the applicability of linear theory under any given conditions is presented. For example, in the case of equatorial scattering by a 5‐kHz CW pulse near L = 4 it is found that linear theory begins to break down when the wave amplitude exceeds 3 mγ. The full distribution of particles is simulated by test electrons appropriately distributed in energy and pitch angle. By computing the scattering of these test particles and integrating over energy and pitch angle, the precipitated flux is obtained. The method used is quite general and can be used for any particle distribution. It is shown that significant particle fluxes are precipitated by waves of moderate intensity. For instance, energetic (1–2 keV) electron fluxes as high as ∼10−1 erg/cm² s can be precipitated by a CW wave of 10‐mγ amplitude and 5‐kHz frequency on the L ≃ 4 field lines. Such fluxes appear to be measurable with presently available instruments. Since the energy density of the precipitated flux is 50 dB above that of the wave, the leverage involved in the wave‐induced precipitation process is quite high. Our results indicate that coherent VLF waves can have a significant effect on the dynamics and lifetimes of energetic electrons trapped in the magnetosphere on magnetic shells illuminated by the waves.