Asymptotic theory of a collision-dominated space-charge sheath with a velocity-dependent ion mobility

Abstract

The method of matched asymptotic approximations is used to examine an ordering of the physical quantities in a collisional plasma–collisional sheath model that has not been previously explored, namely in the constant ion mean free path model with high electric field. The asymptotic theory for a collision- dominated space-charge sheath at a negative surface is developed for the case when the ions interact with neutral particles as rigid spheres while the electric field is high both in the sheath and in the quasineutral plasma. The ion mobility is inversely proportional to the square root of the electric field in such a case. The ratio λD/L of the Debye length at the center of the quasineutral plasma to a characteristic dimension of the plasma is considered as a small asymptotic parameter. The general structure of the asymptotic solution obtained is similar to that in the case of low electric field (or in the framework of the model of constant collision frequency), considered by previous workers; however, the scalings are different. In particular, the thickness of the sheath is found to have the order λ4/5DL1/5, while the respective order in the case of low electric field is λ2/3DL1/3.