Propagator methods for plasma simulations: application to breakdown

Accurate simulation of plasmas often requires a solution of the kinetic equation, either directly by solving the Boltzmann equation (BE) or indirectly by means of 'particle' simulations. However, kinetic simulations are still too computationally intensive for many large scale 3D simulations. In this paper we examine the matching between a kinetic simulation and fluid models which we use in conjunction to form a 'hybrid' plasma model of the breakdown process. The kinetic model is tested for convergence with respect to mesh size Δx and time-step Δt. We then implement fluid models in an attempt to reproduce the results of the kinetic model. To do this it is necessary to have a fluid model which provides accurate simulations with a wide range of Δx and Δt. We accomplish this by means of a propagator (or Green's function) approach. The propagator method reduces to a finite difference scheme at small Δx, Δt and gives correct results across a wide range of parameters. For intermediate Δx, Δt it is necessary to take considerable care to derive the correct propagator. We apply the propagator method to two fluid models; one uses parameters which are functions of the electric field, and the other one uses parameters which are functions of the mean kinetic energy (this version also explicitly conserves energy locally). The details of the fluid models employed make a profound difference to the prediction of the breakdown.