Experimental investigation of the low-frequency capacitive response of a plasma sheath

Several theoretical models are examined for the low-frequency capacitive response of the ion sheath surrounding both planar and cylindrical Langmuir probes in a collisionless plasma. It is found that a recent theoretical approach by Shkarofsky, based on the total probe surface charge derived from Gauss's law, predicts values for both the low-frequency, capacitance and the transient charge flow which are as much as an order of magnitude smaller than that predicted based on the electron current flow caused by the motion of the sheath edge, e.g., Kamke and Rose. This discrepancy is attributed to the neglect by Shkarofsky of the transient ion conduction current through the sheath. Additionally, a recent theory by Rosa for the complex impedance of a planar sheath is seen, in the limit of low frequency, to be in agreement with that predicted following Kamke and Rose. Experimental measurements have been made, for both pulsed and rf-driven probes, of the transient charge flow to the probe and the effective low-frequency sheath capacitance. These measurements show good agreement with the theoretical approach of Kamke and Rose, and Rosa. The plasma was formed in the positive column of a low-pressure helium dc discharge with plasma electron densities and temperatures in the ranges 5 × 1015 −3 × 1016 m−3 and 5 × 105 −7 × 105 °K, respectively. The pulsed probe measurements were made by integrating the probe current response to both small- and large-amplitude negative voltage pulses. The rf measurements were made using a tunnel diode oscillator circuit whose resonant frequency was chosen somewhat below the ion plasma frequency.