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.  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.