On massless electron limit for a multispecies kinetic system with external magnetic field

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:260

Article

Herda, Maxime¹ 

[1] Univ Lyon 1, CNRS, UMR 5208, Inst Camille Jordan, 43 Blvd 11 Novembre 1918, F-69622 Villeurbanne, France

关键词: Multispecies;    Plasma physics;    Magnetic field;    Vlasov Poisson;    Vlasov-Poisson-Fokker-Planck;    Drift-diffusion;   

DOI  :  10.1016/j.jde.2016.02.005

来源: Elsevier

【 摘 要 】

We consider a three-dimensional kinetic model for a two species plasma consisting of electrons and ions confined by an external nonconstant magnetic field. Then we derive a kinetic-fluid model when the mass ratio m(e)/m(i) tends to zero. Each species initially obeys a Vlasov-type equation and the electrostatic coupling follows from a Poisson equation. In our modeling, ions are assumed non-collisional while a Fokker Planck collision operator is taken into account in the electron equation. As the mass ratio tends to zero we show convergence to a new system where the macroscopic electron density satisfies an anisotropic drift-diffusion equation. To achieve this task, we overcome some specific technical issues of our model such as the strong effect of the magnetic field on electrons and the lack of regularity at the limit. With methods including renormalized solutions, relative entropy dissipation and velocity averages, we establish the rigorous derivation of the limit model. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free