Hysteresis effects in the plasma-electrode boundary sheath for frequencies of the order of the ion plasma frequency

The well-known boundary sheath theory applicable to low frequencies is extended for frequencies of the order of the ion plasma frequency. Phase shifts in the linear and nonlinear oscillations exist at different points of the sheath. A hysteresis effect is observed for the current-voltage characteristics and for the dependence of the sheath capacity on the voltage. An analytical approximation of the hysteresis curve is given. A comparison with experiments confirms the applicability of the theory. A simple analytical approximation formula for the sheath thickness as a function of the applied voltage is given.