Timescales for radiation belt electron acceleration and loss due to resonant wave-particle interactions: 1. Theory

[ 1] Radiation belt electrons can interact with various modes of plasma wave in their drift orbits about the Earth, including whistler-mode chorus outside the plasmasphere, and both whistler-mode hiss and electromagnetic ion cyclotron waves inside the plasmasphere. Electrons undergo gyroresonant diffusion in their interactions with these waves. To determine the timescales for electron momentum diffusion and pitch angle diffusion, we develop bounce-averaged quasi-linear resonant diffusion coefficients for field-aligned electromagnetic waves in a hydrogen or multi-ion (H+, He+, O+) plasma. We assume that the Earth's magnetic field is dipolar and that the wave frequency spectrum is Gaussian. Evaluation of the diffusion coefficients requires the solution of a sixth-order polynomial equation for the resonant wave frequencies in the case of a multi-ion ( H+, He+, O+) plasma, compared to the solution of a fourth-order polynomial equation for a hydrogen plasma. In some cases, diffusion coefficients for field-aligned waves can provide a valuable approximation for diffusion rates for oblique waves calculated using higher-order resonances. Bounce-averaged diffusion coefficients for field-aligned waves can be evaluated generally in minimal CPU time and can therefore be profitably incorporated into comprehensive kinetic radiation belt codes.