Linear and Non linear stability for the kinetic plasma sheath on a bounded interval
Stabilité linéaire et non linéaire pour la gaine cinétique sur un intervalle borné
Résumé
Plasma sheaths are inhomogeneous equilibrium that form when a plasma is in contact with an absorbing wall. We prove linear and non linear stability of a kinetic sheath equilibrium for a Vlasov-Poisson type system in a bounded interval. Notably, in the linear setting, we obtain exponential decay of the fluctuation provided the rate of injection of particles at equilibrium is smaller that the rate of absorption at the wall. In the non linear setting, we prove a similar result for small enough equilibrium and small localized perturbation of the equilibrium.
Mots clés
Vlasov-Poisson equations boundary value problem plasma sheath linear stability non linear stability first order delayed integral equation non linear Poisson equation exit geometric conditions
Vlasov-Poisson equations
boundary value problem
plasma sheath
linear stability
non linear stability
first order delayed integral equation
non linear Poisson equation
exit geometric conditions
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