Space averaged kinetic analysis of stochastically heated electronegative RF capacitive discharges

Summary form only as given. In low pressure capacitive RF plasma discharges, stochastic sheath heating, combined with potentials that exclude low energy electrons from reaching the sheath, produce an electron energy probability function (EEPF) which approximates a two-temperature Maxwellian, as seen in both experiments and numerical simulations. We have used the fundamental kinetic equation to drive a space- and time-averaged kinetic equation to analytically calculate this EEPF. We improve over our model for stochastic heating by allowing the stochastic heating to be gradually turned on over a range of electron energy, instead of abruptly. A complete set of equilibrium conditions are used so that ail the unknown parameters can be solved self-consistently. The theory is applied to oxygen discharges, for which the equilibrium equations for the two ion species are coupled with the electron kinetic equation. The spatial diffusion profiles and the EEPF both agree well with PIC simulations.