Electron plasma profiles from a cathode with an r2 potential variation

A simple one-dimensional model of Maxwellian injection into a cylindrical Penning–Malmberg trap is presented. This model is used to predict the radial density profile of an electron column produced by a biased cathode with an r2 potential variation. The column density n(r) is assumed to depend upon the cathode potential voltage Vk(r) and the self-consistent space-charge potential φ(r) as n(r)∝exp{e[φ(r)−Vk(r)]/T}. A one-parameter family of theoretical solutions describes the radial density profiles. The model’s predictions agree well with electron density profiles resulting from a spiral tungsten filament measured over a wide range in cathode voltages.