Approximate analytical solutions for the trapped electron distribution due to quasi-linear diffusion by whistler mode waves

International audienceThe distribution of trapped energetic electrons inside the Earth’s radiation belts is the focusof intense studies aiming at better describing the evolution of the space environment in the presence ofvarious disturbances induced by the solar wind or by an enhanced lightning activity. Such studies areusually performed by means of comparisons with full numerical simulations solving the Fokker-Planckquasi-linear diffusion equation for the particle distribution function. Here we present for the first timeapproximate but realistic analytical solutions for the electron distribution, which are shown to be in goodagreement with exact numerical solutions in situations where resonant scattering of energetic electronsby whistler mode hiss, lightning-generated or chorus waves, is the dominant process. Quiet timedistributions are well recovered, as well as the evolution of energized relativistic electron distributionsduring disturbed geomagnetic conditions. It is further shown that careful comparisons between theanalytical solutions and measured distributions may allow to infer important bounce- and drift-averagedwave characteristics (such as wave amplitude). It could also help to improve the global understanding ofunderlying physical phenomena