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Re: Streamer modeling



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