One- and two-species equilibria for magnetic insulation in coaxial geometry

Abstract

A cold-fluid, self-consistent model of electron and ion flow in coaxial cylindrical geometries is applied to the problem of magnetically insulated diodes. The one species, nonrelativistic problem is studied to determine in what configurations and parameter domains equilibria corresponding to magnetic insulation exist. It is proved that when the outer electrode is the cathode, equilibria always exist. For an inner cathode, whether or not equilibria exist and whether they are unique depends on whether the field is azimuthal or longitudinal and on the ratio of the radii. The two-species relativistic problem is then analyzed with the help of a computational routine which integrates the cold-fluid differential equations and searches the parameter space for the point corresponding to space charge limited emission. As the critical field is approached from above, the resulting values of ion current show an enhancement over the single species prediction by a factor which increases with voltage and with anode radius. Patterns of nonexistence of equilibria similar to those observed for the one-species, nonrelativistic case are also found.