Solving Vlasov-Poisson-Fokker-Planck Equations Using $NRxx$ method

Abstract

We present a numerical method to solve the Vlasov-Poisson-Fokker-Planck (VPFP) system using the $NRxx$ method proposed in [4, 7, 9]. A globally hyperbolic moment system similar to that in [23] is derived. In this system, the Fokker-Planck (FP) operator term is reduced into the linear combination of the moment coefficients, which can be solved analytically under proper truncation. The non-splitting method, which can keep mass conservation and the balance law of the total momentum, is used to solve the whole system. A numerical problem for the VPFP system with an analytic solution is presented to indicate the spectral convergence with the moment number and the linear convergence with the grid size. Two more numerical experiments are tested to demonstrate the stability and accuracy of the $NRxx$ method when applied to the VPFP system.