Accurate particle time integration for solving Vlasov-Fokker-Planck equations with specified electromagnetic fields

The Vlasov-Fokker-Planck equation (together with Maxwell's equations) provides the basis for plasma flow calculations. While the terms accounting for long range forces are established, different drift and diffusion terms are used to describe Coulomb collisions. Here, linear drift and a constant diffusion coefficient are considered and the electromagnetic fields are imposed, i.e., plasma frequency is not addressed. The solution algorithm is based on evolving computational particles of a large ensemble according to a Langevin equation, whereas the time step size is typically limited by plasma frequency, Coulomb collision frequency and cyclotron frequency. To overcome the latter two time step size constraints, a novel time integration scheme for the particle evolution is presented. It only requires that gradients of mean velocity, bath temperature, magnetic field and electric field have to be resolved along the trajectories. In fact, if these gradients are zero, then the new integration scheme is statistically exact; no matter how large the time step is chosen. Obviously, this is a computational advantage compared to classical integration schemes, which is demonstrated with numerical experiments of isolated charged particle trajectories under the influence of constant magnetic- and electric fields. Besides single ion trajectories, also plasma flow in spatially varying electromagnetic fields was investigated, that is, the influence of time step size and grid resolution on the final solution was studied.