Collision-dominated to collisionless electron-free space-charge sheath in a plasma with variable ion temperature

Abstract

A theory of the near-cathode space-charge sheath in the case when the near-cathode voltage is high enough and the presence of electrons in the sheath is unessential is developed on the basis of a fluid description of the ion motion with account of ion-atom collisions and of variable ion temperature. The model spans the range of conditions from a collision-free to collision-dominated space-charge sheath. Detailed analytical and numerical results are presented for two models of ion-atom interaction, the model of rigid spheres (constant mean free path) and the model of Maxwell molecules (constant frequency of momentum transfer). It is found, in particular, that the assumption of cold ions provides a good accuracy in the problem considered. An analytical solution has been obtained under this assumption for the model of Maxwell molecules.