Relativistic resistive magnetohydrodynamics for a two-component plasma

TL;DR

This paper derives a relativistic resistive magnetohydrodynamics model for a two-component ultrarelativistic plasma from kinetic theory, capturing charge and shear dynamics with improved accuracy in specific regimes.

Contribution

It introduces a new derivation of relativistic resistive MHD equations directly from kinetic theory for a two-component plasma, including coupled charge and shear evolution.

Findings

Accurate for small viscosity to entropy ratio and weak magnetic fields.

Strong electric fields cause nonlinear back-reaction effects.

Shear-stress can develop without flow due to electric fields.

Abstract

We derive relativistic resistive magnetohydrodynamics for a two-component ultrarelativistic plasma directly from kinetic theory. Starting with the Boltzmann--Vlasov equation and using the 14-moment approximation in the Landau frame, we obtain coupled evolution equations for the charge diffusion four-current and the shear-stress tensor. Benchmarking against the usual Israel-Stewart type relaxation form shows that this simplified description is accurate for small viscosity to entropy ($\eta/s$) ratio, vanishing magnetic field, and not so strong electric field. Outside this regime the dynamics depart in a controlled way, i.e., strong electric fields introduce nonlinear back-reaction that delays and reduces current peaks, and a sizable shear-stress is produced even without a flow profile.