Analytical investigation into the resonance frequencies of a curling probe

The term 'active plasma resonance spectroscopy' (APRS) denotes a class of closely related plasma diagnostic methods which utilize the natural ability of plasmas to resonate on or near the electron plasma frequency omega(pe); an electrical radio frequency signal (in the GHz range) is coupled into the plasma via an antenna or a probe, the spectral response is recorded and a mathematical model is employed to determine plasma parameters such as the plasma density and the electron temperature. The curling probe, recently invented by Liang et al (2011 Appl. Phys. Express 4 066101), is a novel realization of the APRS concept which has many practical advantages. In particular, it can be miniaturized and flatly embedded into the chamber wall, thus allowing the monitoring of plasma processes without contamination nor disturbance. Physically, the curling probe can be understood as a 'coiled' form of the hairpin probe (Stenzel 1976 Rev. Sci. Instrum. 47 603). Assuming that the spiralization of the probe has little electrical effect, this paper investigates the characteristcs of a 'straightened' curling probe by modeling it as an infinite slot-type resonator that is in direct contact with the plasma. The diffraction of an incident plane wave at the slot is calculated by solving the cold plasma model and Maxwell's equations simultaneously. The resonance frequencies of the probe are derived and are found to be in good agreement with the numerical results of the probe inventors.