Abstract
The equation of motion of the ions in an ion-rich plasma sheath as well as the appropriate initial conditions that hold for all frequencies well below the electron plasma frequency are obtained. The problem of ion motion in the case when a small amplitude rf voltage is applied to the sheath is solved. One thus obtains the sheath admittance as a function of the plasma parameters, the applied dc voltage and frequency. One reaches the conclusion that, besides the electron contribution, there also exists an ion contribution to the sheath conductance and that the sheath susceptance, although dominated by a capacitive term, cannot be wholly ascribed to this one alone. Simple equivalent circuits are proposed to represent the plasma sheath in the low and in the high frequency limits.