Clebsch representation of relativistic plasma and generalized enstrophy

TL;DR

This paper extends the Clebsch representation of plasma dynamics to a Lorentz covariant form, revealing how relativistic effects modify the conservation of generalized enstrophy and proposing a relativistically conserved version.

Contribution

It introduces a Lorentz covariant formulation of plasma dynamics using Clebsch fields and defines a modified enstrophy conserved under relativistic conditions.

Findings

Relativistic effects break the conservation of classical generalized enstrophy.

A new relativistically modified enstrophy is conserved in the plasma model.

The formulation provides a covariant framework for plasma dynamics.

Abstract

The dynamics of plasma can be formulated as a subalgebra of the Poisson manifold of the Clebsch fields. In this work, we extend this formulation to a Lorentz covariant form. We show that the generalized enstrophy, which means the "charge" of the Clebsch field, is no longer conserved by the relativistic effect, implying that the conservation of circulation is broken. Instead, we formulate a relativistically modified generalized enstrophy that is conserved in the relativistic model.