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Definition:
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Equation

Parameters

Diagram

Calculate Streamer
Velocity:                  top

Parameter

Value

Units

Special Values

Inputs:

V (peak
voltage)

voltskilovoltsMegavolts____________________

d (gap length)

meterscentimetersmillimetersmicrometersnanometersinchesfeetmilsyardsmileskilometerslightyears____________________

Enhanced Electrode:

Positive (+)Negative (-)____________________

Outputs:

(water
V>1MV)

meter/second (m/s)centimeter/secondcentimeter/uscentimeter/nsmeters/usmeters/nsfoot/second (ft/s)kilometer/hour
(km/h)knot {naut. mile/hour}mile per hour (mi/h)____________________

t (closure time)

secondsmillisecondsmicrosecondsnanosecondspicosecondsminutes____________________

Outputs:

(water
V<1MV)

meter/second (m/s)centimeter/secondcentimeter/uscentimeter/nsmeters/usmeters/nsfoot/second (ft/s)kilometer/hour
(km/h)knot {naut. mile/hour}mile per hour (mi/h)____________________

t (closure time)

secondsmillisecondsmicrosecondsnanosecondspicosecondsminutes____________________

Outputs:

(oil)

meter/second (m/s)centimeter/secondcentimeter/uscentimeter/nsmeters/usmeters/nsfoot/second (ft/s)kilometer/hour
(km/h)knot {naut. mile/hour}mile per hour (mi/h)____________________

t (closure time)

secondsmillisecondsmicrosecondsnanosecondspicosecondsminutes____________________

Outputs:

(polyethylene)

meter/second (m/s)centimeter/secondcentimeter/uscentimeter/nsmeters/usmeters/nsfoot/second (ft/s)kilometer/hour
(km/h)knot {naut. mile/hour}mile per hour (mi/h)____________________

t (closure time)

secondsmillisecondsmicrosecondsnanosecondspicosecondsminutes____________________

Output
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Notes:

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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.

Copyright ?2003  Raymond J. Allen