Relativistic Guiding-Center Motion: Action Principle, Kinetic Theory, and Hydrodynamics

TL;DR

This paper develops a relativistically covariant framework for guiding-center motion in plasmas, deriving kinetic and hydrodynamic theories that are applicable even in strongly coupled regimes where traditional kinetic theory fails.

Contribution

It introduces a new covariant action principle for guiding-center dynamics, extending drift velocity expressions to curved spacetime and formulating a simplified hydrodynamics with only three equations.

Findings

Derivation of a relativistic guiding-center kinetic theory.

Formulation of a three-equation hydrodynamics for guiding-center motion.

Application to strongly coupled plasmas where kinetic theory is inadequate.

Abstract

We treat the guiding-center dynamics in a varying external Maxwell field using a relativistically covariant action principle which reproduces the known Vandervoort expression for the drift velocity and extends it to curved spacetime. We derive the corresponding kinetic theory and ideal hydrodynamic theory. In contrast to conventional five-equation hydrodynamics, the guiding-center hydrodynamics needs only three equations due to a constraint on the motion across magnetic field. We argue that such a hydrodynamics is applicable to strongly coupled plasmas where kinetic theory fails.