Analysis of the cathode fall in high-voltage low-current gas discharges

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Abstract
An analytic investigation is made of the cathode-fall region in high-voltage low-current gas discharges. Explicit expressions for the variation of electric field, voltage drop, charge density, Joule heating, and cathode-fall thickness are obtained as functions of pressure, current density, gas properties, and distance from cathode. To first order, it is shown that the former two quantities depend on the two-thirds power of the ratio of the current density to pressure squared, that the electric field varies linearly in the cathode-fall region, and that the fall thickness is independent of the operating current and varies inversely with pressure. To illustrate the order of magnitudes involved, a numerical calculation is made using helium as the working gas.