Influence of Electrode Curvature on Electrical Breakdown in Vacuum

Abstract

It has been observed by others that a decrease in curvature of one (or both) electrode(s) of a vacuum gap can lead to either an increase or decrease, depending upon the gap parameters, in the breakdown voltage. This electrode curvature effect is investigated theoretically for a system consisting of two isolated spheres. For each sphere the maximum surface field intensity and the area over which the field magnitude is no less than a given fraction of this maximum are found. These results are considered in conjunction with several theories of vacuum breakdown in order to predict the expected dependence of breakdown voltage upon electrode curvature at varying gap lengths. Comparisons with applicable published experimental results are made. The following conclusions are drawn: (1) The cathode crossover effect, that is, the observation that a decrease in curvature of the cathode can produce a decrease in breakdown voltage at short gap lengths and an increase in breakdown voltage at long gap lengths, can be predicted explicitly for a two-sphere system using any major vacuum breakdown theory. This crossover is confirmed experimentally. (2) The anode crossover effect is experimentally supported, but not as firmly as the cathode crossover. The theoretical analysis suggests that this anode crossover effect results from a transition, at a critical gap length, in the dominant mechanism in electrical breakdown in vacuum. (3) The increase in breakdown voltage accompanying an increase in curvature of one (or both) electrode(s) at short gap lengths is explained on the basis of a decrease in breakdown area (sites).