Energy-conserving time propagation for a geometric particle-in-cell Vlasov--Maxwell solver

TL;DR

This paper introduces energy-conserving time discretization methods for finite element particle-in-cell simulations of the Vlasov--Maxwell system, ensuring energy conservation and compatibility with Gauss' law.

Contribution

It develops novel energy-preserving time discretizations using discrete gradient methods for a geometric particle-in-cell Vlasov--Maxwell solver.

Findings

Proposes a semi-implicit energy-conserving method.

Introduces an alternative discrete gradient conserving Gauss' law.

Shows how to incorporate substepping for fast species.

Abstract

This paper discusses energy-conserving time-discretizations for finite element particle-in-cell discretizations of the Vlasov--Maxwell system. A geometric spatially discrete system can be obtained using a standard particle-in-cell discretization of the particle distribution and compatible finite element spaces for the fields to discretize the Poisson bracket of the Vlasov--Maxwell model (see Kraus et al., J Plasma Phys 83, 2017). In this paper, we derive energy-conserving time-discretizations based on the discrete gradient method applied to an antisymmetric splitting of the Poisson matrix. Firstly, we propose a semi-implicit method based on the average-vector-field discretization of the subsystems. Moreover, we devise an alternative discrete gradient that yields a time discretization that can additionally conserve Gauss' law. Finally, we explain how substepping for fast species dynamics can be incorporated.