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4hv.org :: Forums :: Tesla Coils
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An arc measurement

Author Post
Uspring
Sat May 18 2013, 05:07PM Print View
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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.






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PhilGood
Sun May 19 2013, 03:15AM
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Really interesting measurements and calculations, very instructive !
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dex
Sun May 19 2013, 09:11AM
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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?
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Steve Conner
Sun May 19 2013, 05:48PM
Joined: Fri Feb 03 2006, 10:52AM
Location: Glasgow, Scotland
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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.
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dex
Sun May 19 2013, 06:17PM
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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?
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Steve Conner
Sun May 19 2013, 07:21PM
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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.
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dex
Sun May 19 2013, 07:47PM
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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?
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Steve Conner
Sun May 19 2013, 08:55PM
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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.
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Uspring
Sun May 19 2013, 09:09PM
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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?
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dex
Sun May 19 2013, 10:01PM
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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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Uspring
Mon May 20 2013, 09:28AM
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Dex, the way you phrase this it sounds more like an assumption about a spark being like a wire than a measurement. How would you measure the actual secondary resonant frequency during operation? Not that this can't be done, I've posted about this some time ago, but it requires measuring primary and secondary currents and phases inbetween. Very complicated.

The Elektrum data does indeed show not very much capacitance. I'd guess the top capacitance to be about 100pF. The current going into the arc is about 10% of that going into the top, so arc capacitance would be at most 10pF.

Burst length of the Elektrum is relatively short and the operating frequency much lower, so it needs a much higher voltage to grow long sparks. High voltage and low arc current amount to low arc capacitance.
The Elektrum arc is not anywhere near its equilibrium state. I think, that if you could sustain the million volts during the burst for say 1 ms, you'd get large capacitances and much longer arcs.
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dex
Mon May 20 2013, 09:38AM
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Uspring wrote ...


The Elektrum data does indeed show not very much capacitance. I'd guess the top capacitance to be about 100pF. The current going into the arc is about 10% of that going into the top, so arc capacitance would be at most 10pF.



so,you really think that capacity of a gigantic 30' long sgtc spark is comparable with capacity of a 3' long drsstc spark? or even smaler?
lol..


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Uspring
Mon May 20 2013, 11:36AM
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Steve Conner wrote:
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.

I believe, that in DRSSTCs and particularly QCW ones, secondary sizes can be small due to the relatively low voltages they need for long arcs. Low voltages can produce long arcs, given enough burst length. Probably also high frequencies reduce voltage requirements.

Dex wrote:
so,you really think that capacity of a gigantic 30' long sgtc spark is comparable with capacity of a 3' long drsstc spark? or even smaler?

You need to distinguish between the whole capacitance of e.g. a 30' wire and that actually seen by the coil. In a simple model an arc looks like a resistor/capacitor series circuit. The resistor will shield much of the capacitance. A large resistor will make the arc look mostly like a resistive load. And resistances will be large for short bursts, since the arc does not have enough time to accumulate heat and become very conductive.
The capacitances I was talking about were thought to be directly parallel to the top load. I chose to specify them in this way, since that value is the relevant one for detuning.

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Steve Ward
Sat Aug 10 2013, 05:27AM
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Udo, Wonderful measurements! Especially because you get very similar R/C values to what ive been plugging into my DRSSTC models to look at tuning and driving methods. I arrived at my numbers by doing steady-state measurements of primary current, secondary current and secondary voltage and adjusting the streamer lumped RC to get the model to settle out at the same amplitudes for all these measurements. My QCW arc models had to get resistance down to ~20k ohms and series capacitance of 20pF for a 6 foot spark (with maybe 1 or 2 branches in it). "Transient" arcs modeled well with 80k+15p for about 40" max arc length even but they are highly branched sparks.
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Uspring
Sat Aug 10 2013, 02:40PM
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I'm glad to hear, that you could confirm these measurements.
Can you tell us, at what frequencies the QCW and transient measurements were made? For settled arcs, I believe very much in Conners hungry streamer model, which states that R is approximately 1/(2*pi*f*C), i.e. 45 degrees phase shift between arc voltage and current. My measurements indicate a somewhat larger C during arc growth.



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HV Enthusiast
Sun Aug 11 2013, 07:02PM
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Isn't the secondary arc current the same current that is flowing in the RF ground of the secondary?

If you look at the path of current, from RF ground, to secondary coil, to toroid, to break-out, neglecting any stray losses, it should be the same current, right?

I was always under the understanding that the RF ground current would be the same as through a grounded current strike from the topload.

Is my thinking wrong on that one?
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Steve Conner
Sun Aug 11 2013, 09:38PM
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The current that goes into the bottom of the secondary is (to a first approximation) the same as what comes out of the top into the toroid. That current splits two ways into conduction current in the streamer root, and displacement current in the toroid-to-ground capacitance. The whole point of Uspring's experiment is to measure these two currents separately.
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HV Enthusiast
Sun Aug 11 2013, 09:40PM
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Steve Conner wrote ...

The current that goes into the bottom of the secondary is (to a first approximation) the same as what comes out of the top into the toroid. That current splits two ways into conduction current in the streamer root, and displacement current in the toroid-to-ground capacitance. The whole point of Uspring's experiment is to measure these two currents separately.


And i'm guessing the displacement current may not be current that is actually visible? Just leakage due to the stray capacitance between toroid and ground?
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Steve Ward
Mon Aug 12 2013, 03:05AM
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And i'm guessing the displacement current may not be current that is actually visible? Just leakage due to the stray capacitance between toroid and ground?


Visible? You mean, plasma?

Its important to point out where this secondary base current is measured, and that would be between the bottom winding of the secondary coil and your RF earth connection. This current will reflect the circuit current of the secondary. If you arent producing sparks, then nearly all of this base current is simply charging the coils capacitance (MOST of the capacitance is from toroid to ground, only a small fraction of it is internal to the winding itself). Also, considering the impedance of a toroid at Fres, it will take many amps of charging current for most TC designs to get the right voltage out. The toroid current is probably higher than the average streamer current in most tesla coils. It might seem like a waste, but that is a requirement for resonance and high Q.

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Uspring
Mon Aug 12 2013, 09:35AM
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Steve Conner wrote:
The current that goes into the bottom of the secondary is (to a first approximation) the same as what comes out of the top into the toroid. That current splits two ways into conduction current in the streamer root, and displacement current in the toroid-to-ground capacitance. The whole point of Uspring's experiment is to measure these two currents separately.

Exactly, and thanks to Greg Leyh for that idea.
Trying to get an estimate of secondary voltage by measuring secondary base current has 2 problems. One is, that this current does not come out fully at the top to charge the toroid, since the secondary winding has a capacitance of its own. The other is, that a significant part of the current coming out of the top doesn't charge the toroid but goes into the arc.
I remember a discussion on pupman set off by a measurement of Steve Ward, where he could not reconcile the secondary base current with the top voltages, which he obtained differently. I believe the reasons for that are just these problems.

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Steve Ward
Tue Aug 13 2013, 07:34PM
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I remember a discussion on pupman set off by a measurement of Steve Ward, where he could not reconcile the secondary base current with the top voltages, which he obtained differently. I believe the reasons for that are just these problems.


I'll restate the confusion for anyone who cares: if you assume your secondary has some Zo thats calculated by Zo = 2*pi*f*Lsec, and then try to calculate the top voltage based on Vtop = Ibase*Zo, then you can arrive at the wrong answer (it predicts a voltage too high). Why? Well because i broke down the circuit of a TC too far by assuming it was just some HF current going through a single coil of wire at some frequency. A better answer must account for the existance of the primary, and the fact that my setup was running at the upper pole frequency, which meanse Lsec should have some correction factor applied which makes it look much smaller (hey, after all, it IS ringing at a higher frequency than is "natural").

"Transient" arcs modeled well with 80k+15p for about 40" max arc length even but they are highly branched sparks.


Looks like i had some bogus memory, i just retried my simulations and i find the streamer needs to be ~50k + 5p (series) for my transient model of my system. 15p drags the voltage and current down too far unless the resistance drops sufficiently low (like in the QCW case, it seems to get down to ~20k +18p series). I should mention, these figures are for my small tesla coil gun, so the sparks are generated from the same driver/TC in both cases.
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