An efficient energy conserving semi-Lagrangian kinetic scheme for the Vlasov-Maxwell system

Abstract

In this paper, we develop an efficient energy conserving semi-Lagrangian (ECSL) kinetic scheme for the Vlasov-Maxwell (VM) system. The proposed ECSL scheme is the first semi-Lagrangian VM solver to achieve unconditional stability with respect to the plasma period while conserving total energy, without requiring nonlinear iterations. The new method is built on three key components: an efficient field solver, an exact splitting (ES) method, and a conservative Semi-Lagrangian (CSL) scheme. Specifically, the efficient field solver is developed by semi-implicitly coupling the Ampère and Vlasov moment equations, removing the numerical constraints imposed by the plasma period. Furthermore, the ES method is applied to the Vlasov equation and integrated with an implicit Maxwell solver, ensuring energy conservation in rotational dynamics. The ES method reduces the multidimensional Vlasov equation to one-dimensional advections exactly in time, which are then solved with the CSL scheme to ensure mass conservation and remove CFL restrictions. These synergistic components enable the ECSL scheme to conserve both total energy and mass at the fully discrete level, regardless of spatial and temporal resolution. Finally, several numerical experiments are presented to demonstrate the accuracy, efficiency, and conservation properties of the proposed method.