Effects of Cyclotron-Drift and Bounce-Drift Cross Diffusion on Evolution of Radiation Belt Phase-Space Densites

Abstract:

Pitch-angle scattering coupled with drift-shell splitting in an asymmetric magnetic field can give cyclotron-drift and bounce-drift cross diffusion terms in the radiation belt Fokker-Planck equation. More specifically, cyclotron-resonant pitch-angle scattering coupled with pitch-angle dependent second and third adiabatic invariants gives rise to non-zero D_ML and D_KL cross diffusion coefficients (where M is the first invariant, K is the usual geometric bounce invariant, and L is the Roederer L-shell), plus an additional “anomalous” contribution to the radial diffusion coefficient, D^A_LL [O’Brien, GRL, 2014]. In this paper we describe calculations of these additional terms and we present solutions of the corresponding radiation belt Fokker-Planck equation. The D_ML, D_KL, and D^A_LL diffusion coefficients are calculated assuming a Tsyganenko 1989 magnetic field model and a chorus wave model from Shprits et al. [JGR, 2011] that includes dayside and nightside chorus waves. Solutions to the corresponding Fokker-Planck diffusion equation are obtained using the REM diffusion code, which uses stochastic differential equation (SDE) methods to solve the fully 3-D diffusion equation in adiabatic invariant coordinates. One of the advantages of the SDE methods is that off-diagonal diffusion tensor terms are easily incorporated and the resulting phase-space densities are always non-negative. Initial results show that the new drift-shell splitting contributions are stronger for electrons of a few hundred keV near geosynchronous orbit, with associated changes in MeV electron phase-space densities over a range of L-values and at later times.