A variational approach to resistive relativistic plasmas

TL;DR

This paper introduces a variational framework for modeling resistive relativistic plasmas, integrating dissipative effects into a unified action principle, and develops a phenomenological resistivity model consistent with thermodynamics.

Contribution

It presents a novel variational approach combining electromagnetic and dissipative relativistic fluid dynamics, including a new resistivity model based on Onsager's principle.

Findings

Established a general relabeling invariance in matter space formulations.

Derived field equations for resistive relativistic multi-fluids.

Developed a minimal resistivity model for electron-proton heat systems.

Abstract

We develop an action principle to construct the field equations for a multi-fluid system containing charge-neutral fluids, plasmas, and dissipation (via resistive interactions), by combining the standard, Maxwell action and minimal coupling of the electromagnetic field with a recently developed action for relativistic dissipative fluids. We use a pull-back formalism from spacetime to abstract matter spaces to build unconstrained variations for both the charge-neutral fluids and currents making up the plasmas. Using basic linear algebra techniques, we show that a general "relabeling" invariance exists for the abstract matter spaces. With the field equations in place, a phenomenological model for the resistivity is developed, using as constraints charge conservation and the Second Law of Thermodynamics. A minimal model for a system of electrons, protons, and heat is developed using the Onsager procedure for incorporating dissipation.