A model for switching impulse leader inception and breakdown of long air-gaps

A mathematical model is described for continuous leader inception and breakdown of long gaps under positive switching impulses with critical time-to-crest. The model deals with rod, sphere, and conductor-plane gaps. It provides novel analytical expressions for continuous leader inception voltage, height of the final jump, and breakdown voltage as well as analytical tools to determine the critical electrode radius for any gap spacing. The theory is extensively compared with previous experimental results and is tested against several formerly developed empirical formulas, relevant to several discharge parameters, for different electrode forms and over a wide range of gap spacings