Paschen’s Law in Extreme Pressure and Temperature Conditions

Paschen’s law gives the inception voltage for an electrical discharge as a function of the product of gas pressure and the gap distance between the two infinite planar electrodes. It is known that the deviations from Paschen’s law occur when the temperature is increased. Historically, two theoretical corrections, the Peek and Dumbar corrections, are proposed to predict the deviation from Paschen’s law by increasing the temperature. To carry out an experimental investigation on the deviation from Paschen’s law by increasing the temperature, a customized system was designed, which can operate at temperatures up to 400 °C and at pressure up to 1 MPa, calculated at room temperature, with an interelectrode distance between $100~\mu \text{m}$ and 6.6 mm and an error on the interelectrode distance measurement of $20~\mu \text{m}$ . In this paper, first, the results from the experimental investigation on the deviation from Paschen’s law at temperature up to 400 °C are presented. The results are then compared with theoretical corrections, and finally, a theory to explain the results is proposed and discussed.