Quasineutral Limit of the Vlasov-Poisson System with Massless Electrons

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 behavior 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. We then study the combined quasineutral and strong magnetic field regime for such plasmas.