Energy conserving particle-in-cell methods for relativistic Vlasov--Maxwell equations of laser-plasma interaction

TL;DR

This paper develops energy conserving particle-in-cell methods for relativistic Vlasov-Maxwell equations in laser-plasma interactions, ensuring discrete energy conservation and stability over long simulations.

Contribution

It introduces a novel combination of particle-in-cell, compatible finite element, and discrete gradient methods for energy conservation in relativistic plasma simulations.

Findings

Numerical experiments confirm energy conservation over long time.

Methods accurately capture parametric instability dynamics.

Discrete Poisson equation is satisfied by the numerical solution.

Abstract

Energy conserving particle-in-cell schemes are constructed for a class of reduced relativistic Vlasov--Maxwell equations of laser-plasma interaction. Discrete Poisson equation is also satisfied by the numerical solution. Specifically, distribution function is discretized using particle-in-cell method, discretization of electromagnetic fields is done using compatible finite element method in the framework of finite element of exterior calculus, and time discretization used is based on discrete gradient method combined with Poisson splitting. Numerical experiments of parametric instability are done to validate the conservation properties and good long time behavior of the numerical methods constructed.