Study of resonant properties of hairpin probe for high-density operation

Summary form only given. A well-defined sharp drop in the amplitude of the reflected signal characterizes the resonance signal of the hairpin probe (HP) when the frequency is varied over a given range typically of the order of electron plasma frequency. A quantity that defines the ratio of width of the resonance signal, Δf (f_upper - f_lower) to the central frequency, f_central is the quality/Q factor of the HP. For lower Q it is difficult to resolve the f_central against the background noise. The factors governing the Q are the losses of the energy stored in the resonator due to the resistive heating of the probe that depends on the probes temperature and the specific resistivity of the wire material as shown in figure. The coupling between the adjacent loop antenna and the hairpin also determines the shape of the resonance peak. In the plasma, the losses are further enhanced due to resistive heating of the oscillating electrons influenced by the electric field between the probe tips and the presence of external magnetic field. In this work, we present an analytical model based on the transmission line theory of the hairpin resonator circuit that explains the physical factors responsible for the observation of broad resonance peaks.