The hollowish beam gun for high power microwave tubes

Guns using spherical cathodes have been analyzed to establish some of their basic limitations and to determine design parameters which will maximize available beam power for a given cathode size. The two fundamental limitations for the achievable beam power are voltage breakdown and cathode loading. The voltage breakdown criterion is derived from experimental results in tubes operating in the 25 to 250 kilovolt range. These results are expressed in empirical formulas for short and long pulse and CW operation. An approximate theory is developed to account for non-uniform emission over the cathode for large values of the ratio of anode aperture to cathode-anode spacing thus covering the entire range from fully solid to essentially hollow beam guns. Choosing the normalized anode spacing and thus the preveance as the variable, maximum realizable beam power for given cathode diameter and half-angle of convergence is calculated, subject to the voltage breakdown and cathode loading limitations.