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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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