Boundary conditions at the limiter surface obtained in the modelling of plasma wall interaction with a penalization technique

Isoardi et al. recently proposed a penalization technique to model solid plasma facing components that treats a solid obstacle as a sink region corresponding to the strong plasma recombination in the solid state material. A major advantage of this approach is that it produces a system that can be solved in an obstacle free domain, thus allowing the use of powerful numerical algorithms. Such a technique implemented in a minimal transport model for ionic density and parallel momentum appeared to exhibit a Mach-1 transition at the boundary layer between the plasma presheath and the limiter region. In this paper, we reconsider this result by analysing the physics of detached plasmas that are governed both by strong recombination and plasma pressure decrease, as imposed by the penalization technique within the limiter region. The analysis provides a unique control parameter A=Γcsmi/Π (Γ being the parallel particles flux, cs the sound speed, mi the ionic mass and Π the total plasma pressure) that allows one to understand the results of the penalization technique for the Mach-1 transition.