Re: Streamer modeling

["Tesla list" <tesla@xxxxxxxxxx>]

Original poster: Terry Fritz <teslalist@xxxxxxxxxxxxxxxxxxxxxxx>

Hi Antonio,

At 08:14 PM 6/30/2005, you wrote:
> Tesla list wrote:
> > Original poster: Terry Fritz <teslalist@xxxxxxxxxxxxxxxxxxxxxxx>
> > Hi All,
> > I had a chance to look through the book "Spark Discharge" and it appears 
> > they have things pretty much figured out!!  They come up with most of the 
> > same numbers we do and add some wonderful things like "optimal rise time" 
> > :-))))   111uS for a 2 meter streamer ;-))
> > They get about 1.9pF/foot for streamer capacitance which is pretty close 
> > to our "average" number taking various factors (slow resonant rise) into 
> > account.  It is pretty straight forward adding a dynamic model to ScanTesla...
> > They have some pretty good math behind their numbers but they obviously 
> > really "checked it" too ;-))
> > The book is actually worth $130!  It is from CRC Press too (which 
> > apparently has presses made of gold, diamond, and platinum....) so it is 
> > cheap for their books!
> > I will do some test (or maybe E-Tesla can do it) to better lock down the 
> > numbers for our case and see if I can get it into ScanTesla...
>
> It's simple to change the code to allow time-varying elements. I am testing
> now a version of the calculation engine where the capacitances and resistances
> can change. The present model for the streamer load, C2 (part), R3, and C3,
> can then be made to change to simulate breakout and streamer growth.
> The problem is how they change. In a first approximation I am trying to
> leave R3 constant and increasing C2 and C3 when the terminal voltage
> exceeds a certain breakout voltage, by equal amounts that return the terminal
> voltage to about the breakout voltage. The result is that the load capacitance
> increases at the voltage peaks, and more power is dissipated in the fixed
> streamer resistance R3. Detuning limits the increase at some point.
> If this makes sense, streamer length can be estimated by the increase in
> the streamer capacitance.
>
> Antonio Carlos M. de Queiroz

I modeled the streamer out to ten feet.  The capacitance is probably a 
little too low at the beginning because of the way the model had to work 
with field shrouding:

http://hot-streamer.com/temp/Leader-model.gif

But this is what I came up with:

http://hot-streamer.com/temp/Leader-model-1.gif

The capacitance in pF is:

C = 0.066666 x L        from 0 to 30 inchs

C = 0.15 x L - 0.25     from 30 to ? inches

One could write very complex equations, but this gets one close without a 
lot of calculation time.

I was thinking of leaving R3 constant for now and finding the power at a 
given point in time and use the Freau formula to give streamer 
length.  Something like:

L(t) = 2.4 x SQRT( LoadEnergy(t) )

That is where I am at...

Cheers,

        Terry