The charge carrier velocity model of the spark gap

Determination of time lags and processes for a spark gap filled with transformer oil under a given electrical potential has long been a problem. Various electrical breakdown models for different voltage ranges exist and proffer conflicting solutions. J. C. Martin's model has long been used to calculate a so called "streamer" velocity for the spark gap in transformer oil. It is an empirical formula and provides an approximation for determining time lags. Martin's model is deficient in its energy considerations, has a velocity discontinuity at 1MV, and is inconsistent in the high and low voltage regimes. A charge carrier velocity model based on the carrier mobility and carrier limiting thermal velocity is proposed. It is applicable over a wide range of applied electric fields and temperatures yielding a time lag that agrees with observations under severely overvolted conditions. The proposed model is investigated, a comparison is drawn, and some calculations are presented.