Quasilinear theory of collisionless electron heating in radio frequency gas discharges

On the basis of quasilinear kinetic theory, the electron heating of rf discharges is treated for characteristic scale lengths of the heating field much shorter than the electron mean free path. The analysis considers plasmas bounded by walls providing specular reflection. The expressions for the coefficients of electron diffusion in energy space are obtained and analyzed for inductively and capacitively coupled plasmas. Accounting for the oscillatory spatial structure of the penetrating electric field in the regime of anomalous skin effect leads to a decrease of the diffusion coefficient for high, and an increase for low, energy electrons. It is shown that the presence of a second boundary in the case of collisionless plasma slabs results in a similar effect. The formation of energy distribution functions in various regimes of collisionless heating is discussed. The diffusion coefficients are presented taking into account ambipolar electric fields.