40MHz Spark Gap Behavior

From:  terryf-at-verinet-dot-com [SMTP:terryf-at-verinet-dot-com]
Sent:  Tuesday, April 14, 1998 9:46 PM
To:  Tesla List
Subject:  Re: 40MHz Spark Gap Behavior

At 10:41 PM 4/13/98 -0500, you wrote:
>From:  Jim Lux [SMTP:jimlux-at-earthlink-dot-net]
>Sent:  Monday, April 13, 1998 11:37 AM
>To:  Tesla List
>Subject:  Re: 40MHz Spark Gap Behavior
>Terry, I don't know if your energy/power calculation is valid.


>For an arc less than a cm long, I can't imagine the voltage drop at a
>current of 4000A being as high as 2000V. It is more likely that the voltage
>across the gap drops pretty dramatically (and very quickly, nanoseconds) as
>the current comes up.  You might be able to calculate another number for
>the energy by figuring out how much energy it takes to heat up a cylinder
>of air some 0.1 cm long and .1 cm in diameter (i.e. the spark) to 10000K.
>Somehow, I don't think it is in the tenths of joules range. 

Very very good point!  I didn't scope the waves well enough to check this.
I will look at this.

>I get a volume of  0.0007853975 cc. Make a (erroneous, but within an order
>of magnitude) assumption that the specific heat of the air is 1.2 kJ/(kg K)
>(at 3000 K) (the specific heat of gases changes pretty significantly as
>they get really hot). Then, to heat our 1e-9 kg (= 7.8E-4 cc * 1.29 kg/m^3
>* 1e-6 m^3/cc) of air some 10,000 degrees, it will take: 1.2 kJ/(kg K) *
>1E4 K *1E-9 kg = 1.2E-5 kJ = 1.2E-2 J = .012 Joules

0.012 J is still 30% of the total power I have stored in the cap!

>Some errors here are: The specific heat of a gas changes a lot (it gets
>bigger) as the gas gets really hot. The arc is probably not .1 cm in
>diameter (lightning -at- 50 kA is only .2-.5 cm) but more like .01 cm in
>diameter (reducing the heat energy by a factor of 100).

I have blown little holes in paper before with arcs.  They are very thin.
The 0.01cm sounds too big.  Maybe 0.001cm??

>So then, where else might the energy go? Into light? No, the light comes
>from the gas cooling from an incandescent 10000K (neglecting ionization and
>photon emission as the atoms drop back to ground state). Into the magnetic
>field of the arc? (it is a conductor carrying current) This is pretty low.
>Figuring using 1 uH/meter, our .1 cm arc is about 1E-9 H. The stored energy
>would be .5 *L*I^2 = .5 * 1e-9 * 4E3^2 = 8E-3 joules. And of course, we
>would get that back when the current stopped (it would go into either the E
>field (capacity) or induce a current in the rest of the circuit).
>Anyway you look at it, it seems that the gap isn't all that lossy. You
>might want to carefully look at the relative time of the voltage and
>current waveforms, since that has a huge influence on instantaneous power.
>A few nanoseconds phase shift ( a few feet of coax...) could turn a 8 MW
>pulse (4 kA -at- 2 kV at the same time) into a 8 W pulse (not at the same

Now that the voltage probe is working, I should be able to look at the phase
very easily.  The channels are very closely matched for phase and time delay.

>As for other techniques for measuring current which work better for fast
>pulses, how about a Rogowski coil? or, measuring the magnetic field next to
>the conductor with a Hall Effect sensor of some sort, or, using the Faraday
>effect (wrap that glass fiber around the conductor a bunch of times and
>measure the polarization shift.)

I looked at a few Hall devices today but the ones I saw with an analog
output were only good to 5KHz.  Not familiar with the Rogowski coil but I'll
study it.  The polarization sounds very hard to measure?  Is it possible
without spending a ton of money (I just gave all mine to the IRS)?

>Great work, Terry... you are raising the right sorts of questions.

Great input about the power!  I knew I was way high.  You have narrowed it
down considerably.  I suppose I can calculate the power loss / cycle by
looking at the peak wave voltage across the cap and then try to figure out
were it is going.  I was trying to think of a practical way to test the
current shunt's performance at ~50MHz.  A 250kW TV transmitter would be
nice. :-))  Perhaps using a very small primary cap and inductor to go into
the mid MHz region.  I will have to think about that.  Must watch out for
the FCC!  :-)  They could spot that a thousand miles out.

Just installed new scope software to get much better pictures.  I can now
calculate instantaneous power and export raw data to Excel.  I will be able
to do instantaneous resistance over time, FFTs, and V vs I graphs too....
Don't know what good that is but it sure sounds fun!  It is getting real
complicated and I haven't even put the secondary in place yet!  I just got
20Meg more space for my web page and hope to be putting up more on all this
soon.  Too busy playing right now however.  Wish there was more time in the
day.  Much to do.....