Streamer Length Calculations

Terry Fritz, Sat Aug 12 2006, 11:17PM

Hi All,

Part of the reason for the small SISG test coil and then the whole SISG thing was to figure out streamer propagation and distance calculations. Even though I wait eternally for more parts to arrive, "some" data is coming in now )

There appear to be "two" factors controlling streamer length.

The first is the top terminal energy (basically much like top terminal voltage) given by (I am just pasting the C-code):

LeaderLength_E = LeaderLengthVsecFactor * sqrt(0.5 * VCsec_max * VCsec_max * (C2 + C3))

LeaderLengthVsecFactor = ~~ 36.0
C2 = secondary capacitance
C3 = streamer capacitance

This is the peak top terminal energy stored in the secondary capacitance and steamer capacitance.

The second is our old friend the Freau equation but based on actual delivered streamer power now:

LeaderLength_P = LeaderLengthPowerFactor * sqrt(Estreamer * BPS)

LeaderLengthPowerFactor = ~~ 2.0
Estreamer = actual joules delivered to the streamer load

These "two" factors give "two" lengths. You "get" the "LOWEST"!!!

If you don't have enough top terminal energy (basically much like top terminal voltage), more power just makes hotter arcs, not longer ones. This is why increasing the BPS only helps a little in most cases even though the delivered power can be very high. If you have a 1000BPS 10kW coil that arcs 1 foot, you need more top voltage.

If you don't have the delivered power, then 50 million volts on the top terminal does not help either. This is why coils made to have very low secondary capacitance to get to super high voltage choke out... A 1 million volt Tesla coil with 2 watts of input power, is not going anywhere...

Hopefully the relationship and why "higher BPS" just does not go as far will be understood soon now... Since BPS is now a factor, it should probably be "scanned" too...

Arcs to ground are pretty simple. You just zero the secondary voltage and dump all that secondary energy into the secondary resistance as a bright arc. They occur in probably "less than" 10nS (!) so just as fast as the program can dump energy...

For arc to ground distance, if the normal air streamers are say 30 inches, the arc to ground is about 40 inches. So there is just a factor of about ~~1.3 there of air arc vs strike distance. How "long" ground strikes last is a bit of an issue... More testing needed there. Basically how "long" the secondary is "connected" to ground... Seems like about 5 cycles in some cases. Probably should be based on energy left in the coil system or something...

Streamer capacitance is also pretty easy based on simple tests as:

C3 = (LeaderLength - TerminalDiameter) / 6.0 * 1.0e-12

The 220K constant streamer resistance seems to be holding rock solid!!!

All the Rprimary, Rsecondary, Coupling, tuning, dwell time, L's and C's are trivial now and ScanTesla can tear through that in a short while... JavaTC knows the rest )

The SISG is wonderful since it eliminates so many variables as is perfectly repeatable!! I still need more data from "BIG" SISG systems like I am working on now to solidify the constants... It is sort of cool that we know so much about "lossy" coils that all the rest will just work out when their losses are added into the mess... I am "hoping" the DRSSTC portion will just work out happily too... The DRSSTCs lack of "fixed bang energy" made them "messy" to do these studies with...

ScanTesla is being modified for the new models, forever tweaked, and now has a separate parameter input file so a minor adjustment to a constant just changes an input file rather than the whole base program. It is not available yet and won't be for maybe weeks as it is polished. If anyone "needs" the 'current' version, let me know.

Cheers,

Terry