The effects of nonlinear series resonance on Ohmic and stochastic heating in capacitive discharges

The flow of electron and ion conduction currents across a nonlinear capacitive sheath to the electrode surface self-consistently sets the dc bias voltage across the sheath. We incorporate these currents into a model of a homogeneous capacitive sheath in order to determine the enhancement of the Ohmic and stochastic heating due to self-excitation of the nonlinear series resonance in an asymmetric capacitive discharge. At lower pressures, the series resonance can enhance both the Ohmic and stochastic heating by factors of 2–4, with the Ohmic heating tending to zero as the pressure decreases. The model was checked, for a particular set of parameters, by a particle-in-cell (PIC) simulation using the homogeneous sheath approximation, giving good agreement. With a self-consistent Child-law sheath, the PIC simulation showed increased heating, as expected, whether the series resonance is important or not.