Distributional solutions to the Maxwell-Vlasov equations

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.

31 pages, 3 figures

References in corpus (3)

• Asymptotic analysis of ultra-relativistic charge
• Multiple currents in charged beams
• The Einstein-Vlasov system

Cited by in corpus (5)

• Spatially Dispersive Inhomogeneous Electromagnetic Media with Periodic Structure
• Covariant Constitutive Relations and Relativistic Inhomogeneous Plasmas
• Inhomogeneous Spatially Dispersive Electromagnetic Media
• Averaged dynamics of ultra-relativisitc charged particles beams
• On electromagnetism and generalized energy-momentum tensor of the electromagnetic field in spaces with Finsler geometry