Nonresonant velocity averaging and the Vlasov-Maxwell system

Abstract

The Vlasov equation governs the number density in single-particle phase space of a large particle system (typically a rarefied ionized gas or plasma), subject to some external force field (for instance the Lorentz force acting on charged particles). Most importantly, collisions between particles are neglected in the Vlasov equation, unlike the case of the Boltzmann equation. Hence the only possible source of nonlinearity in the Vlasov equation for charged particles is the self-consistent electromagnetic field created by charges in motion: each particle is subject to the electromagnetic field created by all the particles other than itself.