Quasineutral limit of the Vlasov-Poisson system with massless electrons

TL;DR

This paper investigates the quasineutral limit of the Vlasov-Poisson system with massless electrons, deriving fluid models like the Isothermal Euler and shallow water equations, and explores effects of strong magnetic fields.

Contribution

It introduces a rigorous derivation of classical fluid models from kinetic plasma equations in the quasineutral limit, including the impact of magnetic fields.

Findings

Derivation of Isothermal Euler equations from kinetic models.

Extension to regimes with strong magnetic fields.

Application of the relative entropy method for analysis.

Abstract

In this paper, we study the quasineutral limit (in other words the limit when the Debye length tends to zero) of Vlasov-Poisson like equations describing the behaviour of ions in a plasma. We consider massless electrons, with a charge density following a Maxwell-Boltzmann law. For cold ions, using the relative entropy method, we derive the classical Isothermal Euler or the (inviscid) Shallow Water systems from fluid mechanics. In a second time, we study the combined quasineutral and strong magnetic field regime for such plasmas.