Variational radial sheath solutions for a kinetic model of a cylindrical Langmuir probe

Abstract

We study qualitative and quantitative properties of the solutions of a Vlasov–Poisson system modeling the interaction between a plasma and a cylindrical Langmuir probe. In particular, we exhibit a class of radial sheath solutions for which the electrostatic potential is increasing and strictly concave with a strong variation in the vicinity of the probe which scales as the inverse of the Debye length. These solutions are proven to exist provided the incoming distributions of particles from the plasma verify the so‐called generalized Bohm condition of plasma physics. It extends our previous studies.