Spark length, SSTC vs. spark gap

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

Original poster: "Gary Johnson by way of Terry Fritz <twftesla-at-uswest-dot-net>" <gjohnson-at-ksu.edu>

One very desirable feature of Tesla coils is a long spark.  The longer the
better!  I have recently looked at spark length as a function of power for a
solid state driven coil and the results will be interesting to some.

John Freau reports that the spark length in inches for a well-constructed
spark gap coil is 1.7 times the square root of wallplug power in watts. My
tests show a spark length for a solid state coil of 0.17 times the square
root of peak apparent power into the coil. In other words, my sparks are one
tenth the length of his for a given power figure. Most list members will
assume that I am not as good a coiler as John, but I think the difference is
in how power is measured and how sparks are formed rather than differences
in technical ability. I think we are both correct, and an explanation of how
that can be should be instructive.

Power comes with many descriptive terms: real, reactive, apparent, average,
peak, and to our audiophile brethern !ugh! rms. John's wallplug watts would
be real or average power measured with an analog (or digital) wattmeter. The
needle will wiggle a little during Tesla coil operation, but there is no
problem getting the true value to within 2 or 3%.

In a solid state system power can be measured at three points: ac input to
the rectifier, dc output of the rectifier, and rf input to the coil. The dc
power is also easy to measure. Just multiply the average volts by the
average amps. It will be slightly less than the wallplug watts due to losses
in the rectifier. When we get to rf power, things get complicated.
Wattmeters are not readily available and the price would discourage use in a
Tesla coil environment. My HP 54645D scope calculates the rms values of two
voltage waveforms and the phase angle between them, (one voltage
proportional to current), so average power can be calculated from the
product of rms voltage, rms current, and cosine of the phase angle. There
are some other issues involved, since neither waveform is a single frequency
sinusoid. It appears that the average power is about 0.9 times the apparent
power VI in my system. Rather than try to make that correction each time and
have a formula expressed in average power, I just use 0.17 times the square
root of apparent power VI for spark length.

For my base driven coil, voltage stays fairly constant and current rings up
over many cycles, maybe 500 to 2000 microseconds, until the spark occurs.
The apparent power builds also. I get a screen of 50 microseconds length
just before the spark occurs, read off the rms voltage and current, and call
the product the peak apparent power. Another word besides peak might be
better since peak power might imply peak voltaqe and peak current, which is
not the case here. Anyhow, if one uses enough words, the meaning of peak
apparent power should be understandable.

A spark gap coil will build up power much more quickly than a solid state
coil. The spark may occur within 2 to 5 rf cycles, or within 10 to 25
microseconds for a 200 kHz systems. Once the spark occurs, power decreases
rapidly. Richie Burnett has a waveform on his web site that shows this
effect. If a spark does not occur, power sloshes back and forth between
primary and secondary, but when it does, dissipation is rapid. 

I believe that if we were able to measure the apparent power in John Freau's
secondary, we would see a peak about 100 times his wallplug watts. The power
in the secondary would rise to this peak in a few tens of microseconds, stay
there for a similar length of time while the spark was present, then decay
to a lower value for a few hundred microseconds, and go to zero until the
next spark, 8333 microseconds later for a 120 bps spark gap. There are many
curves of power variation that would satisfy the observation of the peak
being 100 times the average.

The peak power establishes the length of the spark. The power that flows
into the spark after the peak establishes the thickness of the spark. In my
solid state system, at a particular voltage it might take 1 ms for a spark
to occur. A 2 ms burst will produce a thin spark. A 10 ms burst will produce
a white, rich spark that looks similar to a spark gap coil spark. A 100 ms
burst will produce a spark with a very thick trunk for one third to two
thirds of total length, say 1 inch thick for a 10 inch spark.

There is a hypothesis among coilers that ions remaining in the air after the
previous spark will help the next spark to grow to a greater length. I have
looked carefully for that effect and have been unable to see it. Ions will
help the next spark start, but this reduces the peak apparent power and
reduces the spark length. In CW mode, the peak power is just the average
power, and sparks are shorter than in the disruptive mode, where the peak
power can grow to a larger value.  Neither the case of several short bursts
closely spaced nor a longer single burst will increase the length of a spark.

I hesitate to say that the hypothesis is wrong for all cases, but I don't
think it works for sparks up to 12 inches long. Sparks are so nonlinear that
it is difficult to make sweeping generalizations about them. I have noticed
a nonlinearity that might explain the difference. I have commented in the
past that once a spark occurs, the combination of secondary and spark become
a constant current sink. Actually the current will grow during a long burst.
For example, I was applying about 750 V rms to the base of my 14 ga coil.
Current rises to about 7.5 A at 0.44 ms. The spark occurs and current drops
to 2 A at 0.69 ms. Then the current grows to 3.4 A at 10 ms, remaining
constant for the next 20 ms. The apparent power into the coil is 5500 VA at
peak, 1500 VA at 0.69 ms and 2500 VA at 10 ms. This type of nonlinearity
could conceivably cause spark growth at much higher power levels.

I am still trying to get all this stuff written down. Hopefully it will
happen in this lifetime.

Gary Johnson
Manhattan, Kansas