Re: Streamer modeling

["Tesla list" <tesla@xxxxxxxxxx>]

Original poster: Terry Fritz <teslalist@xxxxxxxxxxxxxxxxxxxxxxx>

Hi Steve,

At 05:47 AM 7/2/2005, you wrote:


> > 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)

Load energy is actually the integration of energy per dt so it does that...


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

Load energy is the energy per burst.  Power is the load energy per second 
(needs BPS factor) to get a total Joules/sec (watts).

> 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 far I only deal with "one" bang...  Many bangs is next with the factors 
you mention!



> 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.

Apparently, from DRSSTC studies, 25 bangs is pretty much steady state for 
coils of the present type.  We would have to "time skip" over the quiet 
times but still integrate them properly...  After about 200 attempts, I 
will probably get it right :o)))

Cheers,

        Terry



> Steve Conner