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On the Massless Electron Limit for a Multispecies Kinetic System with External Magnetic Field

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We consider a three-dimensional kinetic model for a two-species plasma consisting of electrons and ions confined by an external non-constant 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 modelling, 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 usually adapted to the diffusion limit of collisional kinetic equations and including renormalized solutions, relative entropy dissipation and velocity averages, we establish the rigorous derivation of the limit model.

[Maxime Herda. On massless electron limit for a multispecies kinetic system with external magnetic field. April 2015]

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