Theory of electric field breakdown nucleation due to mobile dislocations

A model is described in which electrical breakdown in high-voltage systems is caused by stochastic fluctuations of the mobile dislocation population in the cathode. In this model, the mobile dislocation density normally fluctuates, with a finite probability to undergo a critical transition due to the effects of the external field. It is suggested that once such a transition occurs, the mobile dislocation density will increase deterministically, leading to electrical breakdown. Model parametrization is achieved via microscopic analysis of oxygen-free high thermal conductivity Cu cathode samples from the CERN compact linear collider project, allowing the creation and depletion rates of mobile dislocations to be estimated as a function of the initial physical condition of the material and the applied electric field. We find analytical expressions for the mean breakdown time and quasistationary probability distribution of the mobile dislocation density, and verify these results by using a Gillespie algorithm. A least-squares algorithm is used to fit these results with available experimental data of the dependence of the breakdown rate on the applied strength of the electric field and on temperature. The effects of the variation of some of the assumptions of the physical model are considered, and a number of additional experiments to validate the model are proposed, which include examining the effects of the temperature and pulse length, as well as of a time-dependent electric field, on the breakdown rate. Finally, applications of the model are discussed, including the usage of the quasistatic probability distribution to predict breakdowns, and applying the predictions of the model to improve the conditioning process of the cathode material.