Mehdi Badsi (Nantes Université)
Biography
TITLE: Plasma sheath solutions for a bi-species Vlasov-Poisson-BGK model
ABSTRACT: The Debye sheath is a positively charged boundary layer that forms when a plasma is in contact with a metallic wall. It has been shown that it is possible to construct sheath type solutions for the Vlasov-Poisson equations (in a bounded domain) provided the ions distribution function verifies the so called Bohm condition of plasma physics.
When particles experience collision or friction, the role played by the Bohm condition is unclear. We will show that for a simple Vlasov-Poisson-BGK model it is possible to construct solutions for which the density is non negative and the electric potential is strictly monotone. Our method of proof shows that there is a competition between the Debye length and the collision frequency. We will discuss numerically whether one can enlarge the range of the physical parameters.
