An explicit, energy-conserving particle-in-cell scheme for relativistic plasmas

TL;DR

This paper introduces an explicit, energy-conserving particle-in-cell scheme for relativistic plasmas, extending previous non-relativistic methods to improve energy conservation in simulations.

Contribution

The paper develops a relativistic PIC scheme based on an analytically solvable optimization problem that enforces exact energy conservation, compatible with common electromagnetic solvers.

Findings

The scheme achieves dramatic improvements in energy conservation over traditional PIC methods.

It is compatible with Yee/FDTD and PSATD electromagnetic solvers.

The scheme is verified on standard relativistic test problems, confirming conservation properties.

Abstract

We extend the recently-developed explicit, energy-conserving particle-in-cell (PIC) scheme of [1] to the relativistic Vlasov-Maxwell system. As in the non-relativistic case, the method is built on an optimization problem that is analytically solvable, local to each particle, and designed to enforce exact energy conservation. Although the solution to this optimization problem is not guaranteed to be real, we show that such instances are rare enough for practical simulation parameters to permit dramatic improvements in energy conservation over traditional explicit PIC schemes. We show that, as in the non-relativistic case, the scheme is compatible with popular field-solvers for electromagnetic PIC schemes, including the Yee/FDTD and pseudo-spectral analytic time-domain (PSATD) methods. The scheme is verified on standard relativistic test problems, where its conservation properties are confirmed.