A discrete ordinates solution of the Fokker-Planck equation characterizing charged particle transport

Abstract

A formalism for obtaining a discrete ordinates solution of the time and space-dependent Fokker-Planck equation governing the transport of charged particles in multispecie plasmas is developed. In the absence of macroscopic electromagnetic fields and assuming isotropic Rosenbluth potentials, the Fokker-Planck equation is solved for a test particle distribution; both angular dispersion and velocity diffusion are accounted for. Difference relations are obtained and a series of validation problems are discussed. The conservation of both particles and energy are continuously monitored. In addition to providing the single-particle distribution function f (r, [mu], [nu], t), spatially dependent energy deposition profiles are calculated. Comparisons with reported energy deposition profiles for a central source of 3.5-MeV alpha particles in a spherical D-T plasma are made and are found to be in good agreement.