STOCHASTIC ELECTRON HEATING IN A CAPACITIVE RF DISCHARGE WITH NON-MAXWELLIAN AND TIME-VARYING DISTRIBUTIONS

In capacitively coupled radio frequency discharges, the electrons gain and lose energy by reflection from oscillating, high voltage sheaths. When time-averaged, this results in stochastic heating, which at low pressure is responsible for most of the electron heating in these disc harges. Previous derivations of stochastic heating rates have generall y assumed that the electron distribution is a time-invariant, single-t emperature Maxwellian, and that the sheath motion is slow compared to the average electron velocity, so that electrons gain or lose a small amount of energy in each sheath reflection. Here we solve for the stoc hastic heating rates in the opposite limit of fast sheath motion and c onsider the applicability of the slow and fast sheath equations in the intermediate region. We also consider the effect of a two-temperature Maxwellian distribution on particle balance and the effect of a time- varying temperature on the heating rates and densities.