Collisionless heating by capacitive radio frequency sheaths

Summary form only given. It is generally accepted that capacitive radio frequency discharges can be sustained predominantly by a non Ohmic heating process involving the interaction of electrons with the oscillating sheaths. It has usually been supposed that such heating is localized at the sheath edge, and can be computed by considering the interaction of an assumed electron flux with the moving sheath edge, which is considered to be a rigid barrier. This approach is commonly called a 'hard wall' model. In this paper we show that models of this character are not selfconsistent, in that current is not conserved through the sheath region. Moreover, attempts to repair such 'hard wall' models have the side effect of causing the heating to vanish identically. Therefore, it seems to us that it is impossible to to construct a self-consistent heating model of this type. We will also show that an alternative model based on moments of the Vlasov equation with a simple kinetic closure assumption can be used to calculate the heating effect, and this model is in good agreement with particle in cell simulations. In some parts of the parameter space, there are substantial differences between the heating predicted by this model and the earlier 'hard wall' model. The effect of electron collisions will also be discussed.