Generalised relativistic Ohm's laws, extended gauge transformations and magnetic linking

TL;DR

This paper develops generalized relativistic Ohm's laws incorporating plasma particle dynamics, enabling the definition of electromagnetic fields that transform correctly under Lorentz boosts and satisfy Maxwell's equations.

Contribution

It introduces new relativistic Ohm's laws that include plasma particle effects and define generalized electromagnetic fields with proper Lorentz transformation properties.

Findings

Generalized fields obey homogeneous Maxwell's equations.

Applicable to space and laboratory plasma scenarios.

Allows consistent Lorentz transformations of electromagnetic fields.

Abstract

Generalisations of the relativistic ideal Ohm's law are presented that include specific dynamical features of the current carrying particles in a plasma. Cases of interest for space and laboratory plasmas are identified where these generalisations allow for the definition of generalised electromagnetic fields that transform under a Lorentz boost in the same way as the real electromagnetic fields and that obey the same set of homogeneous Maxwell's equations.