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Re: [TCML] Spark gap Resistance



David N. Van Doren wrote:
Does anyone have any data on spark gap resistance?
and for that matter Streamer impedance?
I've been doing some simulations, and for the lack of any better number I've been using 4 ohms for spark gap R's and have tried using 220kohm+1.5pf'/ft for streamers, but doesn't always seem to look right in the sims. Trying to characterize plasma is always difficult at best.

Thanks

Dave
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Hi Dave,

As you are likely aware, the "resistance" of a spark gap is a very nonlinear function of spark current and spark duration. Although a single spark never really reaches any equilibrium state, a rapid series of sparks (as in the main spark gap in a Tesla Coil) gets closer, and a sustained arc can achieve dynamic equilibrium. A fairly good model for a "on" state of a single spark gap is a bidirectional Zener diode with a voltage drop of 100-200 volts (depending on spark duration). The actual voltage drop across a firing spark gap is a function of the metals used in the electrodes, whether one or both electrodes become incandescent, and the overall length of the spark gap.

Moving from one electrode to the other, there are a series three distinct regions accompanied by voltage drops. There are regions near each electrode (the anode and cathode regions) and the main spark column. Associated with these regions are voltage drops - the "anode drop", the voltage drop across the spark column itself (called the "positive column"), and the "cathode drop". The anode and cathode drops are each of the order of volts or tens of volts, and the voltage drop across the positive column is a function of spark length and an inverse function of spark current (for an unconstrained free-air spark). For a given gap, the sum of the voltage drops is surprisingly constant for currents in the range of a few amperes to thousands of amperes. In other words, the "resistance" of the spark decreases as we increase spark current - this behavior is sometimes called having a "negative resistance characteristic". If your Tesla Coil spark gap has more than one gap connected in series, the total conducting voltage drop will be the sum of each gap, but the series of gaps will still exhibit the negative resistance characteristic. For practical purposes, the "resistance" of a typical Tesla Coil spark gap is of the order of ohms, so your estimate of 4 ohms is reasonable.

Streamers (particularly those terminating in air and not to ground) are considerably more complex in structure and behavior. They are composed of hot, branching leaders, each tipped by countless tiny hair-like barely visible discharges that rapidly wink into and out of existence. The latter, called "streamers", or corona (in error) by some coilers, are responsible for transferring HV charge between the leaders and the surrounding air. The "resistance" of the hotter leader is relatively low and arc-like, while the much cooler streamers have considerably higher "resistance".

The "resistance" of the spark channels increase as we move away from the HV terminal, since branching reduces the current flowing through the smaller channels that feed the main leader. Their dynamic characteristics are exceedingly difficult to model to any degree of precision. Terry Fritz (former moderator of the Tesla Coil Mailing List - TCML) made a series of measurements in order to develop a model for the loading effects of streamers. His model used the 220k and 1.5 pF/foot values you mention. However, subsequent measurements, using solid state Tesla Coils, have determined that this model does not hold very well. In fact, for a given coil, the output spark length appears to stabilize at a relatively fixed length - adding more power merely increases the thickness and how "frantic" they appear, but does not increase their length. Electrically, the secondary appears to be "clamped" at a maximum voltage (sort of like a multi-hundred kilovolt Zener diode).

Unfortunately, there are not many articles, books, or spark models that you can easily apply within circuit modeling tools for Tesla Coils. Streamer behavior is simply too complex to be accurately represented by simple closed-form models. Some distributed models may offer some usable approximations within limited regimes.

If you truly want to gain a better understanding of spark, streamer, leader, and/or arc phenomena, the following titles are suggested. Because many are very pricey, check with your local library or university library system to see if they can loan you a copy:

"Spark Discharge", Bazelian, E. M., Raizer, Y. P., CRC Press, 1997, ISBN 0849328683

"Gaseous Conductors; Theory and Engineering Applications", James D. Cobine, McGraw-Hill, 1941 (or more recent Dover reprints)

"Electrical Breakdown and Discharges in Gases, Part A, Fundamental Processes and Breakdown", E. E. Kuhnhardt, Plenum Press, 1983, ISBN 0306411946

"Theory of Gaseous Conductors and Electronics", Maxfield, Frederick A., Benedict, Ralph R., McGraw-Hill, 1941

"Gas Discharge Physics", Yuri P Raizer, Springer-Verlag, ISBN 0387194622 (1991), or ISBN 3540194622 (1997 reprint)

"Gas Discharge Closing Switches", Schaefer, Gerhard, Plenum Press, ISBN 0306436191 (1991 and 2003) Note - this title has recently become available at a fairly reasonable price on the web. This is an EXCELLENT book on the behavior of all types of spark gaps.

If you have access to the scientific literature, there are a number of papers that might help. Contact me off-list for more information.

Bert
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