Monte Carlo methods and their analysis for Coulomb collisions in multicomponent plasmas

A general approach to Monte Carlo methods for Coulomb collisions is proposed. Its key idea is an approximation of Landau–Fokker–Planck equations by Boltzmann equations of quasi-Maxwellian kind. It means that the total collision frequency for the corresponding Boltzmann equation does not depend on the velocities. This allows to make the simulation process very simple since the collision pairs can be chosen arbitrarily, without restriction. It is shown that this approach includes the well-known methods of Takizuka and Abe (1977) [12] and Nanbu (1997) as particular cases, and generalizes the approach of Bobylev and Nanbu (2000). The numerical scheme of this paper is simpler than the schemes by Takizuka and Abe [12] and by Nanbu. We derive it for the general case of multicomponent plasmas and show some numerical tests for the two-component (electrons and ions) case. An optimal choice of parameters for speeding up the computations is also discussed. It is also proved that the order of approximation is not worse than O ( ε ) , where ε is a parameter of approximation being equivalent to the time step Δ t in earlier methods. A similar estimate is obtained for the methods of Takizuka and Abe and Nanbu.