On 4/12/11 8:29 AM, Carl Noggle wrote:
All true, except that I would disagree that the spark gap resistance
is a major factor. The current in the primary of a moderate sized TC
(mine, at 1600 watts, for example) is of the order of 100 amps.
Going through a spark channel that is a fraction of a mm in dia gives
a very high current density, not too different from lightning. A
plasma at these current densities has a resistivity that is lower
than any metal. A spark gap is a remarkably good switch for high
currents.
Uhh.. not really. It's a good switch (and fast), but not as good as
metal. There's the cathode drop of several tens of volts plus the IR
loss in the spark channel. A lot of research says that the spark/arc
is about 7000K, so you can go look out the bulk resistivity. .
the lightning channel (per Uman) is on the order of 1cm diameter,
carrying some tens of kA. If our spark gap is 1sq mm, that's 100
times smaller, corresponding to some hundreds of Amps. (I don't know
that TC primary currents actually get that high... The L is too big)
Most authors (e.g. Uman, Rakov, etc.) give energy dissipated in a
lightning stroke on the order of 3-10 kJ/meter over a few tens of
microseconds: that is, 5kJ/20E-6 = 250 MW. So can figure it out..
250E6 = 20E3^2 * R => 250E6/400E6 or around an ohm/meter.
say it's 1square mm and 1 mm long.. That implies about 100 ohms/meter
for the spark in the gap, or 0.1 ohm for a 1mm long gap. 1 sq mm =
0.0015 sq inch ( that's roughly AWG 17)
A foot of AWG10 wire has a resistance of about 0.001 ohm. AWG 16 has
4 times the resistance, and is fairly close to the diameter of the
spark, so 0.004 ohm for 300 mm, call it 0.004 milliohms...
Orders of magnitude less than the resistance of the spark.
The main source of resistance in the pri circuit is the coil wire,
due to the very shallow skin depth. The bigger the better, stranded
might help a little, the best would be a lot of small insulated wires
bundled into Litz wire, but who wants to go to that much work?
A fair amount of research (in the archives) has shown that for round
numbers, about half the primary power is dissipated in the sparkgap.
I think the Litz wire approach has also been discussed.
An interesting thing to be gleaned from the table is that the RF
resistance of any reasonable wire used for the secondary will have
hardly any increase of R at TC frequencies, so the ohmmeter
resistance of the secondary is the RF resistance. The secondary coil
Q should be high too. It seems that losses in the TC are small, and
almost all the energy should be going into the coronas. If you look
though them in the daytime, you can see quite a bit of heat
distortion, even though it's hard to see the sparks themselves.
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