Small-signal transit-time analysis of a planar mobility-dominated ion sheath

The effective impedance of a planar collision-dominated ion sheath for frequencies below the electron plasma frequency has been obtained from a solution of the small-signal equations of motion expressed in Eulerian coordinates. The analysis assumes a well-defined sheath boundary and is similar to a previous study by Llewellyn on collisionless diodes. The results of the present analysis show a sheath capacitance component which is highly dependent on the probing frequency relative to the ion transit time in the sheath. Good agreement is obtained between theoretical predictions and experimental measurements of the sheath capacitance as a function of frequency, probe potential, and probe current. The plasma source was the positive column of a high-pressure (10 Torr) helium dc discharge with a plasma electron density between 5 × 1015 and 4 × 1017 m−3 and a temperature ≈ 23 000°K.