Diffusion-advection modeling of wave-particle interactions in the radiation belts

Properly treating wave-particle interactions is crucial to modeling and predicting the behavior of radiation belt electrons. The usual quasi-linear theory alone cannot capture the effects likely to be caused by nonlinear interactions with coherent waves, particularly chorus. Detailed analytical estimates of nonlinear particle motion in a specified wave have been developed, and and combined with detailed wave models can be used to formulate a combined diffusion-advection equation for the electron phase space density. Quasi-linear diffusion is recovered for small amplitude waves, but phase bunching and phase trapping, caused by larger amplitude waves, can also be included.