AND

A matrix factorization method is used to solve the Fokker-Pianck (Landau) charged particle transport equation. By treating all phase space variables as discrete in analogy to S, 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. In the study of charged particle transport in plasmas, numerical techniques for solving the Fokker-Planck equation have been developed which closely parallel those used in neutron transport. This was a natural step in the development of solution methods in charged particle transport (CPT) in view of the fact that the theory and methods of neutron transport have been well developed [ 1,2]. Moreover, since ~~~~ of the pioneering work in CPT was carried out in conjunction with the ongoing effort to build controlled fusion devices, the early methodologies developed to solve the transport equation were made more applicable to those machines. In the well--known analysis of transport in mirror machines by Killeen and Marx [3], for example, the calculations of spatial changes along the magnetic field are based on an assumption that the distribution function of ions remain approximately constant along a gui center orbit, an assumption which is sufficiently accurate and more appropriate for mirror confinement systems. * Work supported by United States Department of Energy Contract W-7405.Eng. 36. The U.S. Government’s right to retain a nonexclusive royalty-free license in and to the copyright covering this paper, for governmental purposes, is acknowledged