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Re: Modeling and simulation



Original poster: "Antonio Carlos M. de Queiroz" <acmq-at-compuland-dot-com.br> 

Tesla list wrote:
 >
 > Original poster: "Jim Lux" <jimlux-at-earthlink-dot-net>

 > I was under the impression that it's actually even a bit fancier than a
 > straight Newton's method (or perhaps, that's what differentiates vendor A's
 > spice from vendor B's?)... better/faster convergence and all that...

Yes, it is a bit fancier. The straight method is too dependent on the
initial approximation, and it's too easy to find circuits where it
doesn't work. But all the problem is in finding a good approximate
solution from where to start. This is the point where the fancy
solutions are applied. A common one is to add linear resistors in
parallel with the nonlinear devices, and then obtain successive
solutions starting with low values for these resistors and ending
with high values. This guides the solution in the right direction.
See the gmin parameter in SPICE.

 > Precisely the problem I was alluding to.. nice smooth behaviors work fine,
 > discontinuous less so...

Real discontinuities don't appear in real circuits, but can appear in
oversimplified models.

 > But, still no matter how complex, you're still approximating the actual
 > behavior, just at a finer and finer scale (as with a piece wise linear),
 > and, of course, the performance starts to get pretty wretched as the model
 > complexity grows.  I also suspect, without being analytically sure, that
 > overly complex models tend to be very sensitive to small changes

Creating good models is a "black art"...

 > But, to take spark growth, for example, there's not a heck of a lot of
 > suitable observations to build that behavioral model on.  The physics isn't
 > even all that well understood, although there are some physics based FEM
 > dynamic models being used.  Then there's the problem of model validation...
 > how do you validate the "fine scale" structure of the model.. The gross
 > behavior is adequately well predicted by fairly simple models (e.g. the 200K
 > + 3pF/meter model for a streamer)

Without trying to make the model, I could suggest something as a series
of RLC blocks interconnected by switches. The switches would turn on or
off based on conditions in the RLC blocks, as the temperature of the
resistors (that could be calculated by suitable subcircuits).
Maybe linear blocks are enough for a good approximation.
Things as forking would be more difficult to predict,
since they are probably caused by random events, as dust in the air,
but could be included too in a dedicated simulator.

 > Yep.. although, I think where the ragged edge is, is where there's poor
 > understanding of the behavior (spark growth in the fine scale)... For
 > instance, at a qualitative level, the physical configuration of the topload
 > should have an effect on spark growth (other than from radius of curvature),
 > because the energy to have the leader grow the next step has to come from
 > the topload, but there isn't a good behavioral model or sufficient empirical
 > data to make a definitive statement whether, for instance, a 30 pF topload
 > with overall diameter A and tube diameter B is better or worse than overall
 > diameter C and tube diameter D...  From the behavioral models, and even the
 > FEM models, they would be the same... the quasi static field looks the same,
 > the resonances look the same, etc.

I would consider the topload, in a first approximation, as just a
capacitance with a breakout voltage.
It may have some interaction with a growing streamer, however, since
their dimensions are similar. But streamers would have significantly
more resistance and inductance that the surface of the topload, so
these effects can probably be safely ignored.

Elaborating a bit the series of RLC blocks idea:
The blocks would have a switch, a resistor and an inductor in series,
and a capacitor to ground.
The switch would close when the voltage over the RL circuit is above a
certain level, and would open when the voltage and the current are
below certain levels (add a capacitor across the block to avoid
interrupting the current in the inductor). These levels would depend
on the temperature of the resistor, being lower for higher temperature.
The dependency between breakdown voltage and temperature is known.
For the first block, the initial closing voltage would be the breakout
voltage of the terminal. For the others somewhat less, because the
previous block ends in a point (the breakout voltage between points
is about 10 kV/cm at room temperature).
Each block would correspond to a certain lenght of streamer.
Sparks to ground can be simulated by grounding the end of the last
segment.
The primary gap can be simulated by a single block, maybe with a gap
capacitance across it.
This model would have the correct qualitative behavior, simulating
streamer growth even between successive "bangs". The question
would then to find suitable parameters to match actual observations.
What is missing is the direction of streamer growth, certainly
following approximately the electric field around the coil, with
a tendency of the segments to rise due to convection (the simulation
could even produce "banjo" effects). The convection could also stretch
the segments, lowering their temperature, eventually leading to
the dissipation of formed streamers.
A dedicated simulator, adding random direction effects, multiple
breakouts, and forkings, plotting the results, would be funny.

Antonio Carlos M. de Queiroz