Electrical discharge initiation and a macroscopic model for formative time lags

Formative times in electrical discharges in over-voltaged gaps are analyzed with a model having no spatial dependence and with simple assumptions about discharge channel temperature T and discharge voltage. The model treats the early temporal evolution of the discharge. Specifically, the dissipative voltage drop V*, across the discharge is taken to be a step function of T. The authors assume thermal quasi-equilibrium in the discharge medium and show d(In td)/d(In θ) = -1, i.e., θtd = constant, where θ is the fractional overvoltage and td is the formative time lag, in agreement with measured values of td for much of the experimentally explored range of θ. They present highly time-resolved (∼92 ps) experimental data on the first 10 ns of electrical discharge initiation; these data suggest that their model should provide a reasonable representation of td, when td > 10--100 ns