High-frequency plasma discharges are often sustained by collisionless heating of electrons; the nature of these mechanisms is a central problem in the theory of such discharges. In capacitive discharges, collisionless heating occurs near boundaries, and is usually attributed to inelastic collisions of electrons with oscillating plasma sheaths, regarded as moving rigid barriers. We show that, when current conservation is required, such heating necessarily vanishes, and we conclude that this model of the heating process is not correct. We develop an alternative view that associates the heating with acoustic disturbances in the electron fluid. An analytic model, based on moments of the Vlasov equation, gives results in good agreement with particle-in-cell simulations. In terms of individual particle dynamics, this acoustic heating may be interpreted as a transit-time effect.

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Low-pressure capacitive rf plasmas can be maintained chiefly by collisionless heating in the rf modulated sheaths adjacent to the electrodes. Theoretical models dealing with this mechanism are often based on a 'hard wall' approximation where the electrons are considered to collide elastically with the oscillating sheath edge. The power transfer is then calculated by averaging forward and reverse power fluxes over an rf period. There are, however, several drawbacks to this approach: the models are sensitive to assumptions regarding the incident electron distribution, transit time effects in the sheath electric field are neglected, electron loss is not considered and current conservation is not satisfied. In order to examine the validity of the theoretical models, we use a Monte Carlo approach to study electron interactions with the model and self-consistent fields providing modifications that can lead to a more consistent treatment of the electron dynamics inside the sheath. Of particular importance is the presence of a small field behind the moving electron sheath edge which maintains quasi-neutrality between the electron sheath position and the bulk plasma. In addition, a semi-infinite particle-in-cell (PIC) simulation is used to investigate in detail sheath dynamics. The errors that the 'hard wall' approximation gives are calculated and power deposition scalings with current drive, frequency and electron temperature are provided. Our results indicate that collisionless heating cannot be attributed to the stochastic heating mechanism based on the 'hard wall' approximation and that in contrast electron inertia plays a dominant role as far as collisionless heating is concerned.

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