Streamer models used with Terry's new program

["Tesla list" <tesla@xxxxxxxxxx>]

Original poster: "Gerry  Reynolds" <gerryreynolds@xxxxxxxxxxxxx>

Hi All,

Terry asked me to post this to the group as I have privately shared with 
him some concerns with using a "fixed" top load streamer model for 
optimization.

I believe the fixed streamer model is probably fine as a start to get the 
program off the ground and I believe the program is a great step forward in 
allowing each one of us ultimately to pursue a better understanding of what 
the "best" is.   I do have reservations about reading too much into the 
results with respect to optimizing for maximum streamer growth at this 
time. The following are some of my concerns:

1. The model has a fixed streamer load present all the time.  This will 
retard the ringing up (cause of lower Q) and possibly distort the results.

2. The breakout level for the top load is not modeled.  This in combo with 
#1 may show good power to the streamer when in fact, breakout never happened.

3. The E field "reach" of the topload is not modeled.

4. Streamer growth is not modeled.  This forces us to use some other metric 
in an attempt to find what makes better streamers.  For example,  maximum 
power to the streamer channel resistance RL is one possible metric. 
Assuming the BPS and bang T1 times are fixed, this would suggest maximizing 
the topload voltage.  Most of us know that maximum theoretical top load 
voltage is obtained with a small topload (of course a small ROC topload 
will breakout at a lower voltage and this is not modeled).  A small topload 
will not have as much charge reserve to support streamer growth and its 
reach wont be as great.



Im thinking that a better model for streamers may be needed before the 
program can reach its true potential for optimization of streamer 
growth.  I have been thinking conceptually about how a model might work and 
offer the following maybe as a point of discussion:

The start point would be zero voltage on the topload and a bang is starting 
to ring up. One would integrate the RF current flowing into the topload and 
compute the accumulated charge and voltage on the topload using its 
capacitance (with no streamer loading present) and the time step used in 
the program.  The voltage would increase (in a sinusoidal way) until the 
breakout voltage was reached.  Any current flowing into the topload after 
breakout occurs would result in excess charge going into the streamer 
channel.  If one could estimate the channel size needed to absorb the 
excess charge perhaps using ambient temp and pressure, one could estimate 
the added capacitance this presented to the topload.  Now, the breakout 
voltage is altered by the geometry of this "first" streamer and charge from 
the topload would continue to flow into the streamer until an equilibrium 
is reached. All the while, this "first" streamer is building.  Once 
equilibrium is reached, the "first" streamer has completed and the size and 
capacitance can be computed and a streamer model (probably a series R 
followed by a capacitance to ground) would be added to the top load.  The 
AC voltage now reverses and this new and larger capacitance is discharged 
and then recharged to the opposite voltage.  Again, the current into the 
topload is integrated and the reversed voltage on the topload is computed 
until the new breakout voltage is reached.  Excess charge now goes into new 
streamer growth and so on.  This process would continue until the bang was 
over and then an ionization time contant would come into play to model what 
happens if it is too long before the next bang.  The RC model for the 
streamer might be modified to account for the ionization decay.  The RC 
model may be a single RC lumped model or it may be a ladder network to 
account for successive streamers.

Dont know if this is a correct way of thinking of streamers (either partly 
or completely), but I dont think accurate results will be possible until a 
better model for streamer formation is done.  The results from such a model 
can certainly be compared to actual measurements and maybe the model can 
evolve until good matches occur.  Seems like you need a model to develope a 
model.

One persons thoughts

Gerry R.