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 r 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 f(r) as n(r)}exp$e@f(r)2Vk(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. © 1998 American Institute of Physics. @S1070-664X~98!00805-2#