Numerical Solutions of the Fokker-Planck Charged-Particle-Transport Equation

摘要

Two numerical methods are developed to solve the Fokker-Planck charged particle transport equation by simple and efficient means, and without approximation to the collision term. The first of these methods demonstrates that the kinetic transport equation can be integrated to yield the time dependent distribution function of test particles f/sub a/ (r,v,t) in a fully implicit manner by a combination of S/sub n/ methodology with a matrix factorization technique. The second technique that is developed is an implicit Monte Carlo method which is suitable for transport problems in field-free and externally magnetized plasmas. Here the transport of test particles in background Maxwellian plasmas is based on probabilities derivable from the FP equation, such as the expected time for deflection and the expected time of energy exchange. (ERA citation 07:016958)