Quasi-linear simulations of inner radiation belt electron pitch angle and energy distributions

Peculiar or butterfly electron pitch angle distributions (PADs), with minima near 90 degrees, have recently been observed in the inner radiation belt. These electrons are traditionally treated by pure pitch angle diffusion, driven by plasmaspheric hiss, lightning-generated whistlers, and VLF transmitter signals. Since this leads to monotonic PADs, energy diffusion by magnetosonic waves has been proposed to account for the observations. We show that the observed PADs arise readily from two-dimensional diffusion at L = 2, with or without magnetosonic waves. It is necessary to include cross diffusion, which accounts for the relationship between pitch angle and energy changes. The distribution of flux with energy is also in good agreement with observations between 200keV and 1MeV, dropping to very low levels at higher energy. Thus, at this location radial diffusion may be negligible at subrelativistic as well as ultrarelativistic energy.