Re: The Hungry Streamer Theorem

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Original poster: "Bob (R.A.) Jones" <a1accounting-at-bellsouth-dot-net> 


 > Original poster: "Steve Conner" <steve.conner-at-optosci-dot-com>
 >
 > Hi all
 >
 > For my DRSSTC modelling work I needed a simple relation that would tell me
 > the streamer resistance and capacitance if I knew the power input.
 >
 > I started by modelling the capacitance of the streamer assuming it was a
 > thin cone or cylinder of conductive material of roughly the same
dimensions
 > as a streamer seemed to have. Assuming a cylinder, I got 25pF per meter of
 > length. (With a cone it would not be linearly proportional as the area of
a
 > cone varies as length squared)
 >
 > Next I invoked the "Hungry Streamer" theorem that says a streamer will
 > always grow up to the point of maximum power transfer, but no further. (I
 > think this was proposed on here a few years back?) If we assume the
streamer
 > resistance is in series with its capacitance, then maximum power transfer
 > will be when the resistance is equal to the capacitive reactance.
 >
 > So that gives 25pF per metre, and approximately 100/L kOhms (L is length
in
 > metres) of resistance at 60kHz (it will vary with frequency)
 >
 > If we substitute that into the famous "Freau formula" L=1.7*sqrt(P):
 >
 > Streamer load resistance = 170/sqrt(P) kohms at 60kHz
 > Load capacitance= 42.5*sqrt(P) pF
 >
 > This is for a series RC circuit, you can transform these values to get an
 > equivalent parallel RC.
 >
 > Does anyone have any thoughts on the validity of this approach?
 >
 > Steve C.
 >

Hi Steve,

You method may be a starting point but I think you need more information.
Your method for the streamer impedance appears to assumes the time scale of
the streamer is long compared with 60KHz. Is there any experimental results
that back that up?

Have you found any justification for the Freau formula? My under standing is
that its a correlation between spark length and the VA in of  best (longest
sparks) coils.
This does not necessarily mean there is a particular static impedance for a
given streamer length. It could be that the  impedance changes in a
complicated way during formation and that at a particular length a
particular amount of energy has been consumed.

Bob