Linear electron stability for a bi-kinetic sheath model

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:453

Article

Badsi, Mehdi¹ 

[1] UPMC Paris06, CNRS, Lab Jacques Louis Lions, UMR 7598, 4 Pl Jussieu, F-75252 Paris 05, France

关键词: Plasma wall interaction;    Debye sheath;    Kinetic equations;    Vlasov-Poisson-Ampere system;    Linear stability;    Degenerate transport equations;   

DOI  :  10.1016/j.jmaa.2017.04.055

来源: Elsevier

【 摘 要 】

We establish the linear stability of an electron equilibrium for an electrostatic and collisionless plasma in interaction with a wall. The equilibrium we focus on is called in plasma physics a Debye sheath. Specifically, we consider a two species (ions and electrons) Vlasov-Poisson-Ampere system in a bounded and one dimensional geometry. The interaction between the plasma and the wall is modeled by original boundary conditions: On the one hand, ions are absorbed by the wall while electrons are partially re-emitted. On the other hand, the electric field at the wall is induced by the accumulation of charged particles at the wall. These boundary conditions ensure the compatibility with the Maxwell-Ampere equation. A global existence, uniqueness and stability result for the linearized system is proven. The main difficulty lies in the fact that (due to the absorbing boundary conditions) the equilibrium is a discontinuous function of the particle energy, which results in a linearized system that contains a degenerate transport equation at the border. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

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