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A model is described, in which electrical breakdown in high-voltage systemsis caused by stochastic fluctuations of the mobile dislocation population inthe cathode. In this model, the mobile dislocation density normally fluctuates,with a finite probability to undergo a critical transition due to the effectsof the external field. It is suggested that once such a transition occurs, themobile dislocation density will increase deterministically, leading toelectrical breakdown. Model parametrization is achieved via microscopicanalysis of OFHC Cu cathode samples from the CERN CLIC project, allowing thecreation and depletion rates of mobile dislocations to be estimated as afunction of the initial physical condition of the material and the appliedelectric field. We find analytical expressions for the mean breakdown time andquasistationary probability distribution of the mobile dislocation density, andverify these results by using a Gillespie algorithm. A least-squares algorithmis used to fit these results with available experimental data of the dependenceof the breakdown rate on the applied strength of the electric field and ontemperature. The effects of the variation of some of the assumptions of thephysical model are considered, and a number of additional experiments tovalidate the model are proposed, which include examining the effects of thetemperature and pulse length, as well as of a time-dependent electric field, onthe breakdown rate. Finally, applications of the model are discussed, includingthe usage of the quasistatic probability distribution to predict breakdowns,and applying the predictions of the model to improve the conditioning processof the cathode material.

Theory of electric field breakdown nucleation due to mobile dislocations