A Second-order Divergence-constrained Multidimensional Numerical Scheme for Relativistic Two-Fluid Electrodynamics

TL;DR

This paper introduces a novel multidimensional numerical scheme for relativistic two-fluid electrodynamics that accurately models plasma dynamics, including resistivity and dispersive effects, with applications in high energy astrophysics.

Contribution

It presents a second-order divergence-constrained numerical scheme for RTFED that extends RMHD and captures small-scale two-fluid effects with divergence preservation.

Findings

Successfully models shocks and discontinuities in RMHD limit

Captures dispersive effects at small scales

Demonstrates applicability to high energy astrophysics

Abstract

A new multidimensional simulation code for relativistic two-fluid electrodynamics (RTFED) is described. The basic equations consist of the full set of Maxwell's equations coupled with relativistic hydrodynamic equations for separate two charged fluids, representing the dynamics of either an electron-positron or an electron-proton plasma. It can be recognized as an extension of conventional relativistic magnetohydrodynamics (RMHD). Finite resistivity may be introduced as a friction between the two species, which reduces to resistive RMHD in the long wavelength limit without suffering from a singularity at infinite conductivity. A numerical scheme based on HLL (Harten-Lax-Van Leer) Riemann solver is proposed that exactly preserves the two divergence constraints for Maxwell's equations simultaneously. Several benchmark problems demonstrate that it is capable of describing RMHD shocks/discontinuities at long wavelength limit, as well as dispersive characteristics due to the two-fluid effect appearing at small scales. This shows that the RTFED model is a promising tool for high energy astrophysics application.