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 trapped particles in a magnetic mirror field evolves according to a FokkerPlanck 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.
 Publication:

Journal of Computational Physics
 Pub Date:
 June 1979
 DOI:
 10.1016/00219991(79)900494
 Bibcode:
 1979JCoPh..31..301D
 Keywords:

 Electron Precipitation;
 Finite Difference Theory;
 FokkerPlanck Equation;
 Magnetically Trapped Particles;
 Particle Diffusion;
 Proton Precipitation;
 Radiation Belts;
 Lines Of Force;
 Numerical Integration;
 PhaseSpace Integral;
 Pitch (Inclination);
 Space Radiation;
 Aurorae;
 Geomagnetic Field;
 Earth Magnetosphere;
 Earth Radiation Belts