Deterministic and Stochastic Methods for Nonlinear Landau-Fokker-Planck Kinetic Equations with Applications to Plasma Physics

Abstract

A short review of deterministic and stochastic methods for nonlinear, spatially uniform Landau-Fokker-Planck equations is given in the Introduction. Then we describe in more detail completely conservative difference schemes (obtained by the authors) for the Landau-Fokker-Planck equations and various applications of these schemes to problems of plasma physics. We also present some asymptotic solutions and compare them with numerical results. A new Direct Simulation Monte Carlo (DSMC) method is also presented and tested by comparison with numerical results based on completely conservative schemes.

Keywords:

• The Landau-Fokker-Planck nonlinear kinetic equation
• Completely conservative difference schcemes
• Coulomb collision operator
• Plasma physics