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An arc measurement

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Uspring

Sat May 18 2013, 05:07PM

Registered Member #3988 Joined: Thu Jul 07 2011, 03:25PM
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Posts: 711

Around the turn of the century a measurement of arc voltages and currents was made by Greg Leyh.

The measurements were taken by a guy sitting inside the top load, who scoped the secondary top current and the current going into the breakout point. The secondary current can easily be converted into voltage values, since the top load is just a capacitor. My coil isn't stable enough to sit on so I used a mini DSO. It picks up the voltage across a 0.5 Ohm resistor between the top lead of the secondary and the toroid and also along a 1 Ohm resistor between the toroid and the breakout rod.

The DSO is protected by a wire mesh over it and also by TVSs across its inputs. To get the data it was set into single trigger mode with pretriggering, so that one half of its buffer was filled with pretrigger data and the other half after it. Then I ramped up the variac until the scope triggered. I used the secondary current as trigger. Coil frequency is about 140kHz and I ran at 100bps and around 600us burst length. Below are diagrams of the currents for different trigger levels at 1A, 2A and 4A.

Low power. Toroid current in amps (blue). Arc current (red) multiplied by 4. X axis is in samples (3MHz sample rate)

Medium power. Arc current multiplied by 2

High power (about 80cm arc). Arc current multiplied by 2

The currents shown are not quite raw data. I noticed, that at very low variac settings, there was still current going into the breakout rod, even though there was almost no corona visible. That current was about 1/10 of the secondary current and is due to the capacitance of the breakout rod. I subtracted that out of the secondary current. Another more surprising effect is, that at high power, the arc current was more than half of that going into the toroid. Since I want to derive the voltage of the toroid from this current, I subtracted the arc current from the top secondary current to get only the current that charges up the toroid. These corrected currents are shown in the diagrams.
The high power diagram (bottom) shows a typical behaviour of my coil. The voltage ramps up to a certain point at which the arc current rises steeply and the arc capacitance pulls it into resonance. The energy stored in the primary is dumped into the secondary and the voltage drops down after this. I believe, that the oscillations in amplitude after the initial surge are "tuning oscillations". After the initial burst the coil is again out of tune, so that primary current ramps up again which pulls it into resonance and so on.

In the diagrams below I've plotted the voltage (yellow in kV), the phase shift between voltage and current (blue in degrees) and arc conductivity (green in units of 0.33uA/V). The arc load during the surge is really enormous at high power, about 20uA/V i.e. 50kOhms. Using the phase shift and the operating frequency, that would amount to a resistive load of about 90k and a capacitance parallel to it of about 19pF. This is more than the capacitance of my toroid, which is about 15pF. This load almost clamps the voltage.

What surprised me most, is that after the delayed response of the arc current to the voltage rise, the arc current drops rather suddenly after the drop of the voltage. This fast response is also seen for the later bumps.

The arc starts, when some free electrons are accelerated enough by the electric field to ionise air molecules when they hit them. This requires strong fields of about 30kV/cm , since electrons are braked by the air. When the arc heats the air, it expands and becomes thinner, reducing the braking effect. At e.g. 3000K, the air will be about 10 times thinner than at 300K, reducing breakdown field strength to about 3kV/cm. As soon as the field drops below the level needed for ionisation, the ions will recombine quickly with the electrons and the conductivity of the arc decreases. This effect is quite fast and happens in a few us. The heating up of the arc is much slower and takes hundreds of us.

When the arc channel heats up beyond 6000K (plasma), air molecules will ionise each other, when they hit. There is no voltage needed for conduction other than a supply of energy to keep the arc hot. I believe, that the arc is a mixture of hotter (near breakout) and colder parts, where former are plasma and latter conduct by voltage induced ionisation.

I've devised a model to calculate the arc current from voltage. The arc is modelled by a series of RC low passes, where the resistances depend on the energy deposited in them. Here are some preliminary results. The input voltage was taken from the above measurements. Only a single set of parameters was used for all 3 power levels. I'll report on details some later time.

PhilGood

Sun May 19 2013, 03:15AM

Registered Member #3806 Joined: Sat Apr 02 2011, 09:20PM
Location: France
Posts: 259

Really interesting measurements and calculations, very instructive !

dex

Sun May 19 2013, 09:11AM

Registered Member #2566 Joined: Wed Dec 23 2009, 05:52PM
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Posts: 147

Uspring wrote ...

The arc load during the surge is really enormous at high power, about 20uA/V i.e. 50kOhms. Using the phase shift and the operating frequency, that would amount to a resistive load of about 90k and a capacitance parallel to it of about 19pF. This is more than the capacitance of my toroid, which is about 15pF. This load almost clamps the voltage.

hmm,80 cm long arc can hardly add 19 pF of capacity to the secondary system.looks too much.
perhaps,this is just a feature of model you use?

Steve Conner

Sun May 19 2013, 05:48PM

Registered Member #30 Joined: Fri Feb 03 2006, 10:52AM
Location: Glasgow, Scotland
Posts: 6706

Very interesting!

These results are much more useful than Greg Leyh's were. The implication is that streamer loading is heavier than we thought.

Dex, re the capacitance of streamers: Terry Fritz used the capacitance of a single wire. This would be OK for a single straight streamer. But the more it branches, the higher the fractal dimension and so the higher the capacitance for a given length. Taken to the limit (dimension of 3) you'd have an 80cm diameter ball of plasma and that could easily add 19pF.

Now ponder that the "ball" would have almost the same capacitance if it were just a skeleton made of wires, or indeed of streamers.

dex

Sun May 19 2013, 06:17PM

Registered Member #2566 Joined: Wed Dec 23 2009, 05:52PM
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don't you think detuning (frequency shift of loaded secondary system) would be higher than observed if the streamer capacity was that large?

Steve Conner

Sun May 19 2013, 07:21PM

Registered Member #30 Joined: Fri Feb 03 2006, 10:52AM
Location: Glasgow, Scotland
Posts: 6706

Well... For a start, Uspring wasn't observing the detuning here. It might have been pretty big for all we know.

Also, in a DRSSTC, we can never measure the frequency shift of the secondary itself, we see the change in frequency of the whole system, which is also a function of the primary circuit. I think when this is taken into account, a shift in secondary frequency manifests itself partly as a shift in system frequency, but mostly as a change in the voltage step-up ratio. The latter is the most important effect. It leads to the "tuning oscillations" mentioned above, when the system is operating on the lower of its two resonant frequencies.

dex

Sun May 19 2013, 07:47PM

Registered Member #2566 Joined: Wed Dec 23 2009, 05:52PM
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Steve Conner wrote ...

Also, in a DRSSTC, we can never measure the frequency shift of the secondary itself, we see the change in frequency of the whole system, which is also a function of the primary circuit. I think when this is taken into account, a shift in secondary frequency manifests itself partly as a shift in system frequency and partly as a change in the voltage step-up ratio.

but frequency shifts due to streamer loadings were measured on spark gap coil systems in the past (free oscillations).equivalent streamer capacity was in range 4-8 pF/m.why should drsstc streamer be so different selfcapacity-wise?

Steve Conner

Sun May 19 2013, 08:55PM

Registered Member #30 Joined: Fri Feb 03 2006, 10:52AM
Location: Glasgow, Scotland
Posts: 6706

I think the main reason is that DRSSTCs make streamers that are bigger compared to the secondary length, than any SGTC ever did while it was being measured.

Uspring

Sun May 19 2013, 09:09PM

Registered Member #3988 Joined: Thu Jul 07 2011, 03:25PM
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dex wrote:

hmm,80 cm long arc can hardly add 19 pF of capacity to the secondary system.looks too much.
perhaps,this is just a feature of model you use?

In addition to the branching effects Steve wrote about, there probably are charge clouds you don't see, i.e. outside the arc.

don't you think detuning (frequency shift of loaded secondary system) would be higher than observed if the streamer capacity was that large?

The effects of detuning are obscured by the low secondary Q during peak load.

but frequency shifts due to streamer loadings were measured on spark gap coil systems in the past (free oscillations).equivalent streamer capacity was in range 4-8 pF/m.why should drsstc streamer be so different selfcapacity-wise?

I'd be interested in hearing about such measurements. Can you explain the free oscillations method?

dex

Sun May 19 2013, 10:01PM

Registered Member #2566 Joined: Wed Dec 23 2009, 05:52PM
Location:
Posts: 147

Uspring wrote ...

Can you explain the free oscillations method?

classical tc system.the change of resonant tunning point due to spark loading compared to resonant point without secondary spark.iirc,they concluded adding wire of the same lenght as spark to toroid had the same effect .only difference being less damping.

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