Modeling of outer radiation belt electrons by multidimensional diffusion process

In this study, we develop a new code which uses a hybrid finite difference (HFD) method to solve a 2-D bounce-averaged energy-pitch angle diffusion equation in the outer radiation belts. We implement the numerical algorithm by adopting a split operator technique, an implicit scheme for dealing with diagonal diffusion coefficients, and an alternative direction implicit scheme for off-diagonal (or cross) diffusion coefficients. We show that our code HFD can successfully overcome the unstable problem when the large and rapidly varying cross diffusion coefficients are included. Particularly, we examine whether resonant interactions with obliquely propagated whistler mode chorus and hiss waves result in a net acceleration or loss of relativistic electrons in the outer radiation belt L=4.5. Numerical simulations show that chorus waves can yield significant acceleration of relativistic electrons, while hiss waves are primarily responsible for scattering equatorially mirroring electrons toward the loss cone.