Statistics of vacuum electrical breakdown clustering and the induction of follow-up breakdowns

Understanding the underlying physics of vacuum electrical breakdown is of relevance for the development of technologies where breakdown is of significance, either as an intended part of device operation or as a cause of failure. One prominent contemporary case of the latter is high-gradient linear accelerators, where structures must be able to operate with both high surface electric fields and low breakdown rates. Temporal clustering of breakdowns has for long been observed in accelerating structures. In this work, the statistics of breakdown clustering were studied using data collected by a system applying DC voltage pulses over parallel disk electrodes in a vacuum chamber. It was found that the obtained distributions of cluster sizes can be explained by postulating that every breakdown induces a number of follow-up breakdowns that are Poisson-distributed with λ < 1. It was also found that the primary breakdown rate, i.e., the breakdown rate after discounting follow-up breakdowns, fluctuates over time but has no discernible correlation with cluster size. Considered together, these results provide empirical support for the interpretation that primary and follow-up breakdowns are categorically different kinds of events with different underlying causes and mechanisms. Furthermore, they support the interpretation that there is an actual causal relationship between the breakdowns in a cluster rather than them simply being concurrent events with a common underlying cause.