Three-dimensional simulations of outer radiation belt electron dynamics including cross-diffusion terms

Using our recently introduced hybrid finite difference method, we develop a three-dimensional (3-D) code to solve a fully bounce-averaged pitch-angle and energy diffusion equation, including radial diffusion and particularly the cross-diffusion terms. We show that our 3-D code can successfully prevent the unstable numerical problems resulting from the large and rapidly varying cross diffusion coefficients. We present one of the first simulations to examine the effects of radial diffusion and chorus-electron interaction with/without cross diffusion terms on the radiation belt electron dynamics. Simulated results demonstrate that chorus waves may yield significant accelerations of energetic (similar to MeV) electrons, leading to peaks in phase space density (PSD), which are subsequently smoothed by inward and outward radial diffusion. Moreover, neglecting cross-diffusion rates generally produces relatively large overestimates in the PSD evolution, implying that cross diffusion terms are very critical in the 3-D modeling of radiation belts dynamics. However, test case simulations show that such overestimates are sensitively dependent on the initial conditions together with wave models, deserving further thorough investigations.