Three-dimensional VERB radiation belt simulations including mixed diffusion

The evolution of relativistic electron fluxes in the radiation belts is described by the modified Fokker-Plank equation in terms of the radial distance, energy and equatorial pitch angle. In this study we present numerical solutions of the two-dimensional (2-D) and 3-D Fokker-Planck equation including mixed diffusion terms. We use finite differences method with implicit numerical scheme, which is stable for any given time step. We evaluate the importance of the mixed diffusion in 2-D and 3-D cases of the Fokker-Planck diffusion equation for radiation belts simulations. In both cases the mixed diffusion tends to inhibit local acceleration and results in lower relativistic electron fluxes, as compared to the simulation without mixed diffusion. The effect of the mixed diffusion terms is most significant at small pitch angles. The inclusion of mixed diffusion also tends to delay the formation of the peak in phase space density in the recovery phase of a storm. We also perform sensitivity simulation to the assumed wave models, which indicates that an accurate knowledge of the wave parameters is the most important factor.