Distributional solutions to the Maxwell-Vlasov equations

TL;DR

This paper formulates distributional solutions to the Maxwell-Vlasov equations, analyzing submanifold distributions and conditions for these solutions to serve as sources in Maxwell's equations, with applications to various charge models.

Contribution

It introduces a distributional framework for Maxwell-Vlasov equations and identifies conditions for solutions to act as sources in Maxwell's equations, including specific charge models.

Findings

Distributional solutions are formulated for Maxwell-Vlasov equations.

A sufficient condition for solutions to source Maxwell's equations is spacetime being globally hyperbolic.

Cold fluid, multicurrent, and water bag models are special cases of the distributional system.

Abstract

The distributional form of the Maxwell-Vlasov equations are formulated. Submanifold distributions are analysed and the general submanifold distributional solutions to the Vlasov equations are given. The properties required so that these solutions can be a distributional source to Maxwell's equations are analysed and it is shown that a sufficient condition is that spacetime be globally hyperbolic. The cold fluid, multicurrent and water bag models of charge are shown to be particular cases of the distributional Maxwell-Vlasov system.