Using a Re-entrant Microwave Resonator to Measure and Model the Dielectric Breakdown Electric Field of Gases

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A gas will breakdown in a high electric field and the mechanisms of this breakdown at DC and high frequency fields have been an object of study for the past century. This paper describes a method to induce breakdown in a uniform microwave field using a reentrant sub-quarter wave resonator. Slater's theorem is used to determine the magnitude of the threshold electric field at which breakdown occurs. The breakdown threshold is modeled using the effective electric field concept, showing that breakdown varies with pressure as Ebd=CPm (1+(ω/ B·P)2)1/2 where P is the pressure, B and C are fit parameters, and m was found experimentally to equal 1/2. This function exhibits a minimum at Pmin=ω/B. Breakdown data from the literature for nitrogen at various microwave frequencies were found to exhibit breakdown minima at the pressure predicted by our own determination of B, further validating the model.