Charge-and-energy conserving moment-based accelerator for a multi-species Vlasov-Fokker-Planck-Ampère system, part II: Collisional aspects

In this study, we extend the moment-based acceleration algorithm for the charge, momentum, and energy conserving Vlasov-Ampère discretization developed in Ref. [1] by including a reduced Fokker-Planck operator. We propose an energy conserving discretization for the Fokker-Planck collision operator. We show by numerical experiment that the new algorithm 1) efficiently converges the nonlinearly coupled Vlasov-Fokker-Planck-Ampère system, and 2) accurately steps over stiff time-scales such as the inverse electron plasma frequency, and the electron-electron collision time-scale. We demonstrate that discrete energy conservation is critical to eliminate numerical heating issues when strong density gradients exist.