When pulsed voltage is applied between two
electrodes, streamers will form once one electrode breaks down. The
streamers (narrow channels of plasma) grow towards the other electrode and
will short out the gap once they bridge the gap. If one electrode is highly
field enhanced, then streamers forms at the beginning of the pulse and the
streamer velocity is the gap length divided by the time until the gap is
shorted and voltage collapses.
Sources: Private communication with Ian Smith
(for water when V>1MV [although he writes it as Ft^0.5 = 0.09 where F is the
electric field]) and a report by H.G.Herbert left for me by Ron Boller and
labelled "SSWA/HGH/6610/104" that describes the emperical fit to data from
breakdown experiments with a sewing needle and a 2" ball (for all others).
Pulse generators were a 1.0 MV transformer with 500 ns rise time and 1.3 MV
Blumlein with 45 ns pulse width. input parameter "d" is not required to
calculate velocity for oil and polyethylene (just for water) although it is
required to calculate closure time for all three cases. These equations can
be used to estimate the closure time of a switch where one electrode is
highly enhanced or to determine the minimum possible gap closure time.
