On application of stochastic differential equations for simulation of nonlinear wave-particle resonant interactions

Long-term simulations of energetic electron fluxes in many space plasma systems require accounting for two groups of processes with well separated time-scales: microphysics of electron resonant scattering by electromagnetic waves and electron adiabatic heating/transport by mesoscale plasma flows. Examples of such systems are Earth's radiation belts and Earth's bow shock, where ion-scale plasma injections and cross-shock electric fields determine the general electron energization, whereas electron scattering by waves relax anisotropy of electron distributions and produces small populations of high-energy electrons. The applicability of stochastic differential equations is a promising approach for including effects of resonant wave-particle interaction into codes of electron tracing in global models. This study is devoted to test of such equations for systems with nondiffusive wave-particle interactions, i.e. systems with nonlinear effects of phase trapping and bunching. We consider electron resonances with intense electrostatic whistler-mode waves often observed in the Earth's radiation belts. We demonstrate that nonlinear resonant effects can be described by stochastic differential equations with the non-Gaussian probability distribution of random variations of electron energies.