Pitch angle diffusion of trapped particles in the presence of a loss cone: Calculating the distribution of particles precipitating from the earth's radiation belts

Abstract

The distribution of stably capped particles in a magnetic mirror field evolves according to a Fokker-Planck diffusion equation in phase space. In the earth's trapped radiation belts this diffusion equation has usually been averaged over the field lines. The correct treatment of the loss cones demands a detailed integration along the field lines. A method is described here for integrating the pitch angle diffusion equation by finite difference techniques. The pitch angle variable is replaced by an adiabatic invariant variable, and a triangular coordinate grid is constructed for the finite differences. The integration can be iterated back and forth along the field lines until convergence is established. Results are presented for trapped protons. Applications to the scattering of electrons in the atmosphere are discussed.