Numerical approximation of the Vlasov–Poisson–Fokker–Planck system in one dimension

A numerical method is developed for approximating the Vlasov–Poisson–Fokker–Planck system in one dimension. This system of equations is a mathematical model for an electrostatic plasma in which collisions between the electron distribution and a surrounding medium are taken into account. The numerical procedure combines a deterministic particle type computation with a process for periodically reconstructing the distribution function on a fixed grid. The method is tested on some computational examples and shown to be stable and accurate on an extended interval of time. Some comparisons are also made with other methods of approximation for the Vlasov–Poisson–Fokker–Planck system.