Quasineutral limit of the Vlasov-Poisson system with massless electrons

Daniel Han-Kwan (1)

1 DMA - Département de Mathématiques et Applications - ENS Paris

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.

Mots clés: vlasov-poisson; massless electrons; maxwell-boltzmann law; quasineutral limit; strong magnetic field

Domaines: Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]; Physique mathématique [math-ph]

Daniel Han-Kwan. Quasineutral limit of the Vlasov-Poisson system with massless electrons. 2010. ⟨hal-00470201v3⟩