Power absorption corresponding to ion losses in parallel-plate RF discharges

A simple model of a symmetric parallel-plate RF discharge is studied to illustrate how such discharges may absorb power from an RF power supply in order to sustain DC power losses corresponding to the steady acceleration of ions through the sheaths. The motions of the sheath boundaries over one period are derived assuming that the current density varies sinusoidally. One finds that the sheath thickness increases discontinuously at one sheath whenever the plasma contacts the opposing electrode. This implies that the external power supply delivers an electron pulse from the electrode at higher potential to the electrode at lower potential, so that some power is being absorbed in a pulsed fashion. The power absorbed by the discharge is also calculated for the portions of the RF cycle where the current varies sinusoidally. It is found that power is supplied by the discharge in this phase of the RF cycle, with the energy coming from the deflating sheaths. It is further shown that the sum of the pulsed power absorption and smooth power generation, averaged over one RF period, is equal to the DC ion power losses arising from ions falling through the time-averaged sheath potentials