On the accuracy of the direct discrete simulation of the Landau collision integral by the Boltzmann integral

Abstract

The Landau (Fokker–Planck) integral of Coulomb collisions is an integral component of the physical and mathematical models of both laboratory and space plasma, in which the intermediate collisionality regime is important. This paper discusses the method for the direct statistical simulation of the Monte Carlo type for a kinetic equation with a nonlinear operator of the Landau–Fokker–Planck (LFP) Coulomb collisions. This method is based on the approximation of the Landau collision integral by the Boltzmann collision integral. The paper has two main objectives: firstly, to obtain numerical estimates of the order of approximation of the Landau collision integral by the Boltzmann integral and, secondly, to explore the possibilities of optimizing the algorithm for multiply charged ions. The results are illustrated by the calculations of the problem on the relaxation of the initial distribution to equilibrium for one and two components.