Re: Secondary Modeling with Streamer Load

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

Original poster: "Jim Lux by way of Terry Fritz <twftesla-at-uswest-dot-net>" <jimlux-at-earthlink-dot-net>

I think that one could probably do a pretty good electrical model, just
assuming that the streamer is a hollow tube  1 cm in diameter (B&R claim
that this is a good nominal diameter for the arc, from a field standpoint)
that grows at an appropriate rate..and with the appropriate series
resistance and inductance.  That is model it as a series of rings.

B&R comment that this would neglect all sorts of interesting effects (like
branching)...

They have an interesting graph showing the charge density as a function of
distance from the anode, which is apparently greatly affected by the
diameter of the anode.  The nominal leader/streamer leaving a small anode
has a very different E field than that from a large diameter anode, which
changes how the "leading end" of the streamer works (i.e. how fast it can
perturb the field enough to breakdown for the next "jump").

Also, you'd need to take into account the non-negligble source inductance of
the topload feeding a streamer that is growing VERY fast.

However, some sort of time stepped finite element model is definitely the
way to go.  B&R advocate using a variable sized computation mesh (fine at
the ends of the spark (where the "action" is), coarser in the middle), but
one has to trade off the significant human time required to code this vs the
fairly cheap machine time to run a fine grid over everything.

The other problem is that the problem can become "ill-conditioned" and the
simulation might not be numerically stable.

I've been looking at some parallelized versions of FE codes like POISSON and
SUPERFISH...
>
> One could also consider a model where the secondary is "filled" with
energy
> from the primary and then quenched so as to remove the primary from the
> system.  Then a real time streamer load (z(t)) could be added without
> primary to secondary energy transfer and coupling issues.  Not quite
"real"
> but the data would point to where to go next.  This case is not terribly
> different from a single shot disruptive coil's operation.  Taking real
> measurements for that case is relatively simple.
>
> I too think a 2D model would be very accurate,  Simply have the streamer
> firing straight up thought the axis of the coil so that all the present
> cylindrical modeling tools would apply.  A theoretically very accurate
case
> but still friendly to model...  I have played with that a little with
> E-Tesla and it seems to work fine.
>