Theory of the Plasma Resonance Probe

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Abstract
The dc electron current to a resonance probe, as a function of frequency and other pertinent parameters, is computed from a 1-dimensional plasma-sheath model. From linearized macroscopic plasma equations with damping, the longitudinal rf field that is caused in the two-slab model by the applied rf voltage is derived. The dielectric constant in the sheath is taken to be 1; the sheath thickness is estimated from the LANGMUIR-CHILD law. In accordance with MAYER, there occurs an rf resonance at a frequency ω′res ≲ ωp , where ωs/ωp is determined by the probe-sheath-plasma geometry. The dc electron current to the probe is computed numerically by means of an approximate classification of the (collisionless) electron orbits in the combined dc and rf fields. There follows a dc resonance at cores ≲ ωs, but none at the plasma frequency ωp . For ω « ωres and ω » ωres the correct limiting values of the dc current are reproduced. There is good qualitative agreement with recent experimental results by PETER, MÜLLER, and RABBEN, but disagreement with a theory by ICHIKAWA and IKEGAMI. Arguments are presented that speak against the validity of that theory.

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