Langevin-based Coulomb collision algorithm extended for arbitrary momentum distribution in particle-in-cell simulations

Two kinds of Coulomb collision algorithms, binary collision and Langevin-based algorithms, have been actively studied, still each of them has its own advantages and disadvantages. Binary collision algorithms can handle any particle distribution functions, which is important because the fully kinetic nature is a crucial advantage of particle-in-cell simulations. However, Langevin-based algorithms need assumptions to distribution functions or other physical quantities. This is to remove the complexity in calculating drag and diffusion coefficients of Langevin equation that states motion of particles. Theoretical background of Langevin-based algorithms has been well-established owing to mathematical theory of stochastic differential equations (SDE). Ordinary discretization of Langevin equation gives first-order approximation of particle distribution. Binary collision algorithms had taken decades to be given its not-so-straightforward formal proof and convergence order being 0.5 to 1.0, which is worse than Langevin-based algorithms. In this study, we developed a new Langevin-based algorithm that can handle arbitrary distribution function. Discretization technique of Langevin equation will be presented for energy and momentum conservation with the help of theory of SDE.