Similarity laws for pulsed gas discharges

The feasibility of applying the similarity law to different types of pulsed discharges is analyzed. The analysis is based on the dependence $p\tau=f(E/p)$, where $\tau$ is the charge formation time, $p$ is the gas pressure, and $E$ is the pulsed field strength at which the breakdown occurs. The law holds for the Townsend and streamer breakdowns for a relatively long discharge gap $d$ (for atmospheric air, $d>1$ cm). For millimeter gaps, this law applies to many gases only in the case of the multielectron breakdown initiation down to the picosecond range. In this case, the time $\tau$ is measured from the instant the voltage amplitude sets in to the onset of current buildup and of the drop in voltage across the gap during the simultaneous development of a large number of electron avalanches. In the initiation by a small number of electrons, the time $\tau$ is longer than in the multielectron initiation by nearly an order of magnitude; this is due to the relatively low rate of free-electron accumulation in the gap, with runaway electrons (REs) playing an important role in this process. But the time $\theta$ of the fast voltage drop and current buildup obeys the similarity law $p\theta=F(E/p)$ in both cases. It is hypothesized that the source of REs is the field emission from cathodic micropoints, which terminates at the onset of explosive electron emission to limit the RE current pulse duration to $10^{-10}$ s. The similarity law $p\tau=f(E/p)$ is shown to hold for a pulsed microwave breakdown.