An asymptotic-preserving conservative semi-Lagrangian scheme for the Vlasov-Maxwell system in the quasi-neutral limit

Abstract

In this paper, we present an asymptotic-preserving conservative Semi-Lagrangian (CSL) scheme for the Vlasov-Maxwell system in the quasi-neutral limit, where the Debye length is negligible compared to the macroscopic scales of interest. The proposed method relies on two key ingredients: the CSL scheme and a reformulated Maxwell equation (RME). The CSL scheme is employed for the phase space discretization of the Vlasov equation, ensuring mass conservation and removing the Courant-Friedrichs-Lewy restriction, thereby enhancing computational efficiency. To efficiently calculate the electromagnetic field in both non-neutral and quasi-neutral regimes, the RME is derived by semi-implicitly coupling the Maxwell equation and the moments of the Vlasov equation. Furthermore, we apply Gauss's law correction to the electric field derived from the RME to prevent unphysical charge separation. The synergy of the CSL and RME enables the proposed method to provide reliable solutions, even when the spatial and temporal resolution might not fully resolve the Debye length and plasma period. As a result, the proposed method offers a unified and accurate numerical simulation approach for complex electromagnetic plasma physics while maintaining efficiency in both quasi-neutral and non-quasi-neutral regimes. Several numerical experiments, ranging from 3D to 5D simulations, are presented to demonstrate the accuracy, stability, and efficiency of the proposed method.