Calculations of Cathode-Fall Characteristics

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Abstract
Calculations of the variation of cathode‐fall voltage, the cathode‐fall distance, and the Aston dark space with current density have been made for the rare gases and a few molecular gases on an electronic computer. The calculations were based upon Townsend's ionization equations, but included the field distortion due to space charge. New analyses of the field variation of Townsend's first ionization coefficient and ion mobilities are presented. The length of the dark space has been obtained from the calculated distribution of light output across the gap and agrees with the cathode‐fall distance calculated from the field distribution. Comparisons of the calculated cathode‐fall characteristics with published experimental results indicate the probable validity of the model used for the calculations.