Asymptotic analysis of the Poisson equation coupled with Boltzmann’s relation. Quasi-neutrality for plasmas. (Analyse asymptotique de l’équation de Poisson couplée à la relation de Boltzmann. Quasi-neutralité des plasmas.)(French. Abridged English version)Zbl 0839.76096

Summary: We consider a model for electron-ion plasmas where the ions are assumed to be fixed and the electron density satisfies the Boltzmann relation. If the Debye length is small with respect to the characteristic lengths of the flow, we prove that the plasma is quasi-neutral except near the electrodes where boundary layers occurs.

MSC:

 76X05 Ionized gas flow in electromagnetic fields; plasmic flow 35Q35 PDEs in connection with fluid mechanics 35Q60 PDEs in connection with optics and electromagnetic theory