Lorentz invariant "potential magnetic field" and magnetic flux conservation in an ideal relativistic plasma

TL;DR

This paper introduces Lorentz invariant scalar functions of the magnetic field in relativistic plasmas, demonstrating their advective properties and formulating a Lorentz invariant Alfvén theorem for magnetic flux conservation.

Contribution

It defines Lorentz invariant magnetic field invariants and uses them to establish a relativistic, Lorentz invariant formulation of magnetic flux conservation in ideal plasmas.

Findings

Invariants are advected by plasma flow.

Recovered Cauchy conditions for magnetic fields.

Formulated Lorentz invariant Alfvén theorem.

Abstract

Lorentz invariant scalar functions of the magnetic field are defined in an ideal relativistic plasma. These invariants are advected by the plasma fluid motion and play the role of the {\it potential magnetic field} introduced by R. Hide in Ann. Geophys. 1, 59 (1983) on the line of Ertel's theorem. From these invariants we recover the Cauchy conditions for the magnetic field components in the Eulerian-Lagrangian variable mapping. In addition the adopted procedure allows us to formulate Alfv\`en theorem for the conservation of the magnetic flux through a surface comoving with the plasma in a Lorentz invariant form.