On the three-dimensional finite Larmor radius approximation: the case of electrons in a fixed background of ions

Daniel Han-Kwan (1)

1 DMA - Département de Mathématiques et Applications - ENS Paris

This paper is concerned with the analysis of a mathematical model arising in plasma physics, more specifically in fusion research. It directly follows \cite{DHK1}, where the tri-dimensional analysis of a Vlasov-Poisson equation with finite Larmor radius scaling was led, corresponding to the case of ions with massless electrons whose density follows a linearized Maxwell-Boltzmann law. We now consider the case of electrons in a background of fixed ions, which was only sketched in \cite{DHK1}. Unfortunately, there is evidence that the formal limit is false in general. Nevertheless, we formally derive a fluid system for particular monokinetic data. We prove the local in time existence of analytic solutions and rigorously study the limit (when the Debye length vanishes) to a new anisotropic fluid system. This is achieved thanks to Cauchy-Kovalevskaya type techniques, as introduced by Caflisch \cite{Caf} and Grenier \cite{Gre1}.

Mots clés: Finite Larmor Radius Approximation; Anisotropic quasineutral limit; Anisotropic hydrodynamic systems; Cauchy-Kovalevskaya theorem; Ill-posedness in Sobolev spaces

Domaines: Equations aux dérivées partielles [math.AP]

Daniel Han-Kwan. On the three-dimensional finite Larmor radius approximation: the case of electrons in a fixed background of ions. 2010. ⟨hal-00540385⟩