Breakdown voltage correlations in a large DC discharge tube for multiple gases

In 1889, Friedrich Paschen published a law that describes the voltage at which a gas breaks down into plasma. It describes the dependence of the breakdown voltage on the gas pressure, distance between the electrodes, the secondary electron emission coefficient, and some proportionality constants [1]. A study by V. A. Lisovskiy et al [2] concluded that the original Paschen´s law and the modification presented by Townsend in 1915 [3] were incorrect in assuming that breakdown voltage is dependent only on the product of the pressure times the inter-electrode distance (pd), and the coefficient of secondary electron emission (γs_e) from the surface of the cathode. The electron diffusion and mobility were considered in this modified breakdown condition [2]. Another researcher has related the famous proportionality constants A and B of the voltage breakdown equation to the electron-ion collision cross sections for the working gas [4]. This work presents a comparison of the experimental results for a large discharge tube to the modifications made in the breakdown voltage equations. This experimental device is 9.65cm (3.8 inches) in inner diameter with 7.62 cm (3 inches) aluminum electrodes. The distance between the electrodes can be varied from 12.7 cm (5 inches) to 25.4 cm (10 inches). The modifications will be tested for different noble gases and air at a multitude of pressures and inter-electrode distances. The study compares experimental results to published modified models, however, a newly modified equation will be discussed in which the collisional cross sections will be utilized instead of the proportionality constant for the electron mean free path. The voltage is obtained from the integral of the electric field over the inter-electrode distance. Applicability to different shaped electrodes, in comparison to parallel-planer electrodes, will be presented.