Analysis of electron thermal flux boundary condition in fluid plasma models

Plasma fluid models used to describe sheath dynamics rely on electron thermal flux approximation to the wall. This assumption works well for describing ion dynamics. In collisionless DC sheath, the continuity of electron flux predicts electrons drift velocity toward the biased wall approaching the electron sonic speed [1]. On the other hand, high electron drift speed at the wall contradicts the assumption of negligible electron drift used for deriving the expression for the thermal electrons flux to the wall. In this report, we present an electron boundary condition based on the expression for the particle flux for the drifting Maxwellian distribution [2]. One-dimensional steady state plasma fluid models coupled with both electron boundary conditions are compared with 1D Particle-In-Cell simulations. Finally, we discuss the accuracy of the new boundary condition, and the influence of electron drift velocity at wall.

 

[1] Valentini, H. B., and F. Herrmann. "Boundary value problems for multi-component plasmas and a generalized Bohm criterion." Journal of Physics D: Applied Physics 29.5 (1996): 1175.

[2] Bird, Graeme Austin. "Molecular gas dynamics." NASA STI/Recon Technical Report A 76 (1976): 40225.