Re: Modeling and simulation

["Tesla list" <tesla-at-pupman-dot-com>]

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

 >
 >  > 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.

I had once fooled with using a transmission line with a very slow
propagation speed as the model..

 >
 >  > 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.

But the current flow into the streamer as it builds up charge getting ready
for the next little jump forward is a very fast activity, and I suspect that
treating the top load as a bulk device isn't going to really work well.  You
probably could model it as a network of L's and C's interconnected in a
mesh.  You'd have to model the current flows in the top load, though... The
time scale of streamer growth is nanoseconds, and the run of the mill
topload is several nanoseconds across.

For spark growth, anyway, I think you need some very sophisticated
customized modeling code... Bazelyan and Raizer allude to as much in their
book where they talk about 1.5 and 2.5D simulations.
 >
 > > 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.

A dedicated simulator, while requiring enormous computer time, would let you
look at all those things. You'd have to approach it statistically though.
Run zillions of sims and look at statistical measures.

There is also the problem of validating the simulation... (akin to
sub-critical nuclear testing to validate simulation codes)

The person(s) who develops such a simulator, assuming it has a reasonably
facile interface, would be doing a great service to the science of
electrical discharge...