Electrical discharge initiation and a macroscopic model forformative time lags

Formative times in electrical discharges in overvoltaged 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. Thermal quasi-equilibrium is assumed in the discharge medium, and it is shown that d(In t_d)/_d(In &thetas;)=-1, i.e., &thetas;t_d=constant, where &thetas; is the fractional overvoltage and t_d is the formative time lag, in agreement with measured values of t_d for much of the experimentally explored range of &thetas;. Highly-time-resolved (~92 ps) experimental data are presented for the first 10 ns of electrical discharge initiation; these data suggest that the authors' model should provide a reasonable representation of t _d when t_d>10-100 ns