Evaluation of quasi‐linear diffusion coefficients for whistler mode waves in a plasma with arbitrary density ratio

Abstract

Techniques are presented for efficiently evaluating quasi‐linear diffusion coefficients for whistler mode waves propagating according to the full cold plasma index of refraction. In particular, the density ratio ωpe/Ωe can be small, which favors energy diffusion. This generalizes an approach, previously used for high‐density hiss and electromagnetic ion cyclotron waves, of identifying (and omitting) ranges of wavenormal angle θ that are incompatible with cyclotron resonant frequencies ω occurring between sharp cutoffs of the modeled wave frequency spectrum. This requires a detailed analysis of the maximum and minimum values of the refractive index as a function of ω and θ, as has previously been performed in the high‐density approximation. Sample calculations show the effect of low‐density ratio on the pitch angle and energy diffusion coefficients modeling the effect of chorus waves on radiation belt electrons. The high‐density approximation turns out to be quite robust, especially when the upper frequency cutoff is small compared with Ωe. The techniques greatly reduce the amount of computation needed for a sample calculation, while taking into account all resonant harmonic numbers n up to ±∞.