Streamer Velocity

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Definition:                                             top

Equation

Parameters

Diagram

Calculate Streamer Velocity:                  top

 

Parameter

Value

Units

 

Special Values

Inputs:                

V (peak voltage)   

 

d (gap length)

 

 

Enhanced Electrode:

 

 

 

 

 

 

 

 

Outputs:

 (water V>1MV)

 

 

t (closure time)

 

 

 

           

Outputs:

 (water V<1MV)

 

 

t (closure time)

 

 

 

 

 

 

 

 

 

Outputs:

 (oil)

 

 

t (closure time)

 

 

 

 

 

 

 

 

Outputs:

 (polyethylene) 

 

 

t (closure time)

 

 

 

Output Format:                                      top

Select Format: Scientific Engineering Fixed

 

Notes:                                                    top

bulletWhen 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.
bullet

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.

bulletInput 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.
bulletThese 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