Approximate analytical solutions for the trapped electron distribution due to quasi-linear diffusion by whistler-mode waves
The distribution of trapped energetic electrons inside the Earth\textquoterights radiation belts is the focus of intense studies aiming at better describing the evolution of the space environment in the presence of various disturbances induced by the solar wind or by an enhanced lightning activity. Such studies are usually performed by means of comparisons with full numerical simulations solving the Fokker-Planck quasi-linear diffusion equation for the particle distribution function. Here, we present for the first time approximate but realistic analytical solutions for the electron distribution, which are shown to be in good agreement with exact numerical solutions in situations where resonant scattering of energetic electrons by whistler-mode hiss, lightning-generated or chorus waves, is the dominant process. Quiet-time distributions are well-recovered, as well as the evolution of energized relativistic electron distributions during disturbed geomagnetic conditions. It is further shown that careful comparisons between the analytical solutions and measured distributions may allow to infer important bounce and drift averaged wave characteristics (such as wave amplitude). It could also help to improve the global understanding of underlying physical phenomena.
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Journal of Geophysical Research: Space Physics