The Impedance of a Resonance Probe

The solution of Laplace's equation for an electrically short cylindrical antenna by a finite-difference method is described. Numerical computations of the antenna impedance were carried out at various signal and collision frequencies and sheath thicknesses and the results are summarized graphically. A hot cathode, mercury arc discharge tube was constructed to produce electron densities greater than 10 8 electrons/cm 3 . Satisfactory agreement was found between measured and calculated probe impedances. It was found possible to determine the electron plasma frequency to within 8% of that obtained by Langmuir probe measurements. The effect of collapsing the ion sheath surrounding the probe was investigated. The effect of the radio frequency signal amplitude on the impedance characteristic of the probe was examined. Methods were developed to determine the resonant frequency rapidly. From this and a knowledge of the electron temperature it is shown that it is possible to estimate the electron plasma frequency by means of an empirical equation. Alternatively the electron plasma frequency is approximately 1-67 times the series resonant frequency. It was found that the probe exhibited a secondary resonance effect at a frequency below the electron plasma frequency. Numerical computations and experimental evidence indicate that this is associated with sharp discontinuities of the probe boundaries.