Well-posedness of continuum models for weakly ionized plasmas

Continuum fluid models of weakly ionized plasmas are useful in the design and control of plasma-assisted deposition and etching processes. The equations in these models are numerically stiff. Their stiffness is affected by the imposed boundary conditions. In this work, a DC discharge model is studied and the effect of the boundary conditions on the model solution is investigated. It is established, both analytically and numerically, that depending on the choice of boundary conditions the model may range from being ill-posed to being solvable with standard software. It is also established that excessive truncation error maybe present in numerical simulations which appear to qualitatively capture plasma structure. Accurate numerical simulations of the considered model, with alternate boundary conditions, are shown to capture many characteristics of a DC discharge, albeit at lower values of applied voltage than those reported in the literature. Finally, model shortcomings are discussed.>