Solution of the Fokker-Planck transport equation by matrix factorization

Abstract

A matrix factorization method is used to solve the Fokker-Planck (Landau) charged particle transport equation. By treating all phase space variables as discrete in analogy to Sn neutronics, the collision term takes on a five-point difference form which is readily treatable by this method. In order to illustrate this technique, the energy deposited by fast ions in a geometrically spherical, Maxwellian background plasma is calculated. Although this technique can be generalized to other geometries, its essential elements are best illustrated in this simple context.