Re: Streamer modeling

["Tesla list" <tesla@xxxxxxxxxx>]

Original poster: Steve Conner <steve@xxxxxxxxxxxx>



> 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 sounds a bit funny to me. The way I understand it, the instantaneous 
streamer length isn't a function of the instantaneous power, but of how 
much energy has been burnt in the streamer load between the start of the 
burst and "now". That would be:

EnergyToNow=sum from t=start of burst to t=now(voltage across R3*current 
through it*size of timestep in seconds)

I kind of lost track of what LoadEnergy is in your code since you sometimes 
use "power" and "energy" interchangeably too :-P


You should probably add in the energy that was burnt in previous bangs, 
weighted with an exponential decay function of some kind, to account for 
how the channel cools and deionizes between bangs. This would help accuracy 
at bps much different to 120. I suggest using exponential averaging for that.


So the streamer length calculation done at each timestep is:

StreamerLength=Some_Constant*sqrt(EnergyToNow(1-DecayFactor))+(EnergyFromLastBang*DecayFactor));

Some_Constant is chosen so it turns out the same answer as Freau's formula 
at 120bps. That would be 1.7 * (1/120) * (1/39.xxx inches in a meter)


After calculating a whole bang you would update EnergyFromLastBang-

EnergyFromLastBang=(EnergyToNow(1-DecayFactor)+(EnergyFromLastBang*DecayFactor));

You choose DecayFactor according to the BPS and the thermal dynamics of air 
::) Or fudge it so sparks start to coalesce around 70-100bps as we observe 
in experiments. If DecayFactor=0 then it reduces to the method you're using 
just now.

The disadvantage is that you now have to model several bangs, enough to 
reach a steady state. You can probably modify the code somehow to include 
the assumption that this bang was preceded by a large number of bangs just 
like it, to get the answer in one shot. But I don't know how to do that.

Steve Conner