  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.
