Modeling of Relativistic Plasmas with a Conservative Discontinuous Galerkin Method

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.