Modeling of Relativistic Plasmas with a Conservative Discontinuous Galerkin Method

TL;DR

This paper introduces a high-order, conservative discontinuous Galerkin method for solving the relativistic Vlasov--Maxwell system, effectively handling high-energy-density plasmas with a novel velocity-space mapping.

Contribution

It develops a new numerical scheme that discretizes the kinetic equations directly on phase space, avoiding Monte Carlo noise and efficiently managing relativistic plasma energy scales.

Findings

Noise-free, high-order numerical scheme for relativistic plasmas

Effective treatment of wide energy scales including QED effects

Enables detailed analysis of plasma dynamics and emissions

Abstract

We present a new method for solving the relativistic Vlasov--Maxwell system of equations, applicable to a wide range of extreme high-energy-density astrophysical and laboratory environments. The method directly discretizes the kinetic equation on a high-dimensional phase-space grid using a discontinuous Galerkin finite element approach, yielding a high-order, conservative numerical scheme that is free from the Poisson noise inherent to traditional Monte-Carlo methods. A novel and flexible velocity-space mapping technique enables the efficient treatment of the wide range of energy scales characteristic of relativistic plasmas, including QED pair-production discharges, instabilities in strongly magnetized plasmas surrounding neutron stars, and relativistic magnetic reconnection. Our noise-free approach is capable of providing unique insight into plasma dynamics, enabling detailed analysis of electromagnetic emission and fine-scale phase-space structure.