Re: Streamer modeling

["Tesla list" <tesla@xxxxxxxxxx>]

Original poster: Terry Fritz <teslalist@xxxxxxxxxxxxxxxxxxxxxxx>

Hi Antonio,

At 11:15 AM 7/2/2005, you wrote:
> Tesla list wrote:
> > Original poster: Terry Fritz <teslalist@xxxxxxxxxxxxxxxxxxxxxxx>
> > Hi Antonio,
> > At 08:14 PM 6/30/2005, you wrote:
> >
> > > > ....
> > >
> > >
> > > It's simple to change the code to allow time-varying elements.
> >
> > I just "tore the guts" out of scan Tesla to do it ;-))  But the resulting 
> > code is much cleaner now ;-))
> > http://drsstc.com/~terrell/modeling/ScanTesla740.ZIP
> > NOT a well tested version!!!
>
> There are two details that change in the simulation of a time-varying
> network:
> The capacitor charges C(t)v(t) shall be simulated, instead of the capacitor
> voltages. Otherwise terms dC/dt appear in the equations.
> (For inductors, it's simpler to simulate fluxes L(t)i(t), but in this
> case the inductors are fixed.)
> The updating equation uses information from the present time interval
> (t+dt) and from the past time interval (t). Two sets of state equations 
> appear:
> X(t+dt)=([I]-(dt/2)*[A(t+dt)])^(-1) 
> (X(t)+(dt/2)*[A(t)]*X(t)+(dt/2)*(B(t)*vin(t)+B(t+dt)*vin(t+dt)))
> The code that I am testing is available at:
> http://www.coe.ufrj.nr/~acmq/programs/DRSSTCTV.C

Cool!!!  I am looking forward to seeing how this works!!  I am not taking 
charge conservations or any of those "details" into account.  I am just try 
to get it to sort of "look right" ;-))


> > If one enters a positive value for Cload increment (C3_inc) it works 
> > normally.  But if the value is negative, it simulates a streamer dynamic 
> > load with C3_start as a "seed" value.  The code will skip the time 
> > wasting stuff when it can...  It just skips redoing the A matrix stuff if 
> > the C3 variable is not changing all the time.  So the program works just 
> > like before if C3 is not dynamic with the same fast speed...
>
> My code also avoids recomputing the inverse at every step, just regenerating
> it when something changes.

Hmmmm ;-)))


> > I found that it is hard to get the streamer load "started"!!!!  If C3 
> > starts out as zero, the load power is zero and it never starts....  I 
> > fiddled with it and this is the best I could come up with at 12:30 am 
> > tonight ;-))
>
> My code is using a breakout voltage to start the streamer. Maybe some
> combination of streamer power and breakout voltage is the correct
> mechanism.

Apparently, it start as a corona until some ion jumps and a streamer 
starts...  In the beginning, it seems like a "corona" thing...


> > // Dynamic streamer model****************
> >         LeaderLength = 2.4*sqrt(Eload*BPS);
> > if (C3_inc < 0)
> >         {
> >         if (LeaderLength <= 30.0) {C3 = 
> > 0.06666666667*LeaderLength*1e-12;} else {C3 = (0.15*LeaderLength-0.25)*1e-12;}
> >         if (C3 < C3_start) C3 = C3_start;
> >         }
> > // Dynamic streamer model****************
>
> Note that in order to conserve charge, when a capacitor changes its
> voltage must change too, to keep the same charge. The simulation of
> charges instead of voltages takes care of this automatically. It seems
> possible to simulate the voltages and just adjust the capacitor voltages
> too when the capacitors change, keeping C*V constant. But two sets of
> state equations must be used in the update relation at each change.

Yep!  I probably have that messed all up ;-))


> > C2 should "really" never change...  I try to mess only with C3...  Maybe 
> > make an arm waving "corona capacitance" and stuff ;-))
>
> I am considering that the streamer capacitance is equally distributed
> between the two halves of the streamer. So, I increase C2 and C3 by equal
> amounts. Not exact, but I think that is a reasonable assumption.

Ok!  Sounds good ;-))

Cheers,

        Terry



> Antonio Carlos M. de Queiroz