A Theory of Electric Field and Charge Density Distributions inside a Cylindrical Hollow Cathode

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Abstract
A simplified theory which describes the radial distributions of electric field and ion density in the cathode fall region of a cylindrical hollow cathode discharge is presented. The continuity equation for ion density and Poisson's equation for space-charge controlled field are used. An analytical form is derived on the assumptions that the drift velocity of ions obeys the high-field approximation, that the rate constant of ionization is constant over the cathode fall region, and that the radial distribution of ionizing particles (electrons or photons) is in the form which obeys Beer's law as applied to cylindrical symmetry. The application of the derived formula to the analysis of observed data of Ar hollow cathode discharges is briefly discussed.

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