Author Topic: A dynamical arc model v2  (Read 963 times)

Offline Uspring

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A dynamical arc model v2
« on: June 14, 2019, 01:18:38 PM »
While quite a bit of knowhow regarding TCs can be found in the net, quantitative information about TC arcs remains a white region in the maps of knowledge. This is mostly due to the scarcity of measurements available. These are difficult, since arc currents need to be measured between the top load and the breakout point. The first measurement of this kind can be found here: http://web.archive.org/web/20160329212336/http://lod.org/Projects/electrum/techdata/waveforms.htm . Since the Electrum was a huge coil, it was possible that someone could sit in the top load and operate a scope there. Since battery operated scopes are now readily available, other measurements became feasible, like mine: https://4hv.org/e107_plugins/forum/forum_viewtopic.php?153922 and Hydrons: https://highvoltageforum.net/index.php?topic=117.0 .

Starting from the available data at that time I've tried to develop an electrical arc model. That was posted here: https://4hv.org/e107_plugins/forum/forum_viewtopic.php?156391 . An arc simulation can be extremely useful. It can serve as a tool to choose primary and secondary tank parameters, will give a hint at achievable arc lengths, allows a guess at primary currents in a DRSSTC, can answer questions like "Are bigger top loads better than smaller ones", are higher or lower operating frequencies better, is there a choice between long and thin versus short and fat sparks, what is the effect of shorter or longer bursts, how does upper pole perform in comparison to lower pole operation etc.

The model posted 2013 on 4hv was based on my measurements alone. It could reasonably well reproduce the current waveform of an arc at different power levels. So I was very excited by Hydrons data, which he posted about 2 years ago, since it allowed a check of the model at much larger power, i.e. 2m arcs instead of 1m and at a different frequency, i.e. 70Khz instead of 140kHz. Sadly the model failed drastically. It predicted more than twice the currents that Hydron measured. I've now revised the model, so that it can reproduce both my old measurements and Hydrons.

The model is basically a chain of RC circuits as shown below.



The resistors aren't really resistors in this case but are a conductivity models, where the current is calculated from the voltage and and arc temperature based on the energy deposited at that point by the arc. The capacitors are charge buckets, which represent the space charges floating in and around the arc. The top diagram of the arc model is below.



On the left is a simple DRSSTC circuit taken from what I know about Hydrons coil. On the right is a chain of blocks. Along the upper 2 wires the arc current is conducted. The lower 2 wires carry position information. The voltages there are centimeters from the end of the breakout point. This information is necessary for the calculation, since I've noticed, that the field of the toroid has an significant impact on the arc currents. With a meter stick like this, I'm able to calcualte the toroids field at each point of the arc and include this effect. The length of the chain depends on the arc length you expect. Each block is worth about 7cm of arc. The voltage at the end of the chain shouldn't exceed more than 30-40kV, because that is about where the arc ends. You can make the chain longer than necessary, but that will cause LTSpice to run slower.

Below is a schematic of the block.



The block is a short chain of subcircuits. The only reason to have this is to avoid a too long chain in the main diagram. Again, the upper 2 connections conduct the arc current and the lower 2 comprise the meter stick.

The meat of the arc model is in the circuit below. I won't go into the details here, they justify another post. A short description anyway: B2 calulates the power dissipated, B3 the conductivity, G1 the arc current and B4 takes the effect of the top load field into account. The only user supplied values are the parameters RTOR, which is the radius of the toroid measured from the center to the outer rim and LBRP, which is the length of the breakout rod measured from the toroid rim to the rods end.



I've checked the model by applying the measured voltages to the model and comparing predicted and measured currents. I've done this for the 3 power levels of Hydrons measurement and mine. Below are shown simulations and real data. The blue traces are top load voltages and the red the arc currents.

Hydron max power:




Hydron high power:




Hydron medium power:




Generally the simulated current rises faster initially than the measured ones. So the model is far from perfect.

Uspring max power:




Each unit on the left in the lower diagram is to be interpreted as about 90kV.
I've left out my lower power measurements, since I've already shown too many diagrams. The model performs quite well there. Below is a simulation for Hydrons coil at max power. In this case not by using the measured voltages as an input to the model, but a complete simulation with the voltage supplied by the DRSSTC circuitry.



The blue trace is the voltage, current is red. Primary current rises up to about 900A, which is quite a bit larger than Hydrons OCD setting of 750A. I'm not sure, why. It might be because I don't have his primary specs right or because of the too large load my model predicts initially, which brings the coil out of tune.

A zip file for the circuitry is appended. Comments and questions are welcome. A later post will detail the thoughts behind the model.
* arcv2.zip
« Last Edit: June 14, 2019, 01:39:11 PM by Uspring »

Offline Hydron

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Re: A dynamical arc model v2
« Reply #1 on: June 16, 2019, 03:10:15 PM »
Very interesting, I'll certainly be having a play with it.

I'll also hopefully be in the position soon of gathering some more data to help fit the model - I actually got some more data from my big coil (along with some physical and electrical measurements) in January, but there were some issues with it:
- I didn't have time to get such a comprehensive data-set as before
- It being summer (in NZ) stopped me from troubleshooting much on the single night I had to setup and test - getting dark late means a narrow window to make noise before it's unreasonable to neighbours trying to sleep
- I also had breakout from multiple points so not all arc current was captured - this is the main reason why I haven't done much with it, as it probably invalidates most of the measurements.
- I did however get some primary/secondary-base coil measurements to go along with the topload ones, all synced up with a fibre optic trigger.

I plan to have another go with both the original big coil and a small QCW coil that's been (very) slowly worked on here in the UK - I have _just_ got enough room in the latter to put a scope in a special toroid and it can probably also run low power in non-QCW mode. No guarantees as to when though sorry! (I know I have promised this before, and unfortunately been unable to do it in the short times I've had on holiday/vacation back in NZ)

Offline VNTC

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Re: A dynamical arc model v2
« Reply #2 on: June 17, 2019, 04:19:07 AM »

Very interesting! Thanks for sharing  I'll try running it against the simulation. I think i will study a lot from this topic.
Thank you!

Offline Uspring

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Re: A dynamical arc model v2
« Reply #3 on: June 17, 2019, 02:40:06 PM »
@Hydron:
I didn't mention that in the post, but I'm certainly eagerly awaiting new data. Do you have any specifics about your big coils primary tank? My simulations predict a somewhat larger current there as your OCD setting, so I am a bit puzzled. Your new data on primary and secondary base currents would definitely be helpful. The breakout points also play a big role. I've taken the extension of your point from the video. I hope I got that right. (7.6cm?) I believe, the length of the rod plays a significant role wrt to the voltages of the top load.

I'm sorry to hear about the less favorable circumstances of your last measurements. But if you post them, I will surely have a look at them anyway.

Wrt QCW: QCW arcs are pretty much steady state arcs, so they are likely easier to simulate. A big problem with current simulations is now, that the temperature rise of the arc is influenced by both the heat capacitance of the heated air and also by heat conduction losses to the surroundings. The heat capacitance determines, how fast the temperature rises and the heat conduction how far. In a steady state arc, the effect of heat capacitance can be neglected. In my simulation, there is a considerable uncertainty about the speed of heat up.

The arcs temperature plays a big role in the calculation. At higher temperatures, the heat causes ionisation by fast air molecules bumping into each other. That begins at 3000-4000K. But also at lower temperatures, there is an effect, because the air expands, making it thinner and causing breakdown voltages to drop. There is also a time dependency there, since the expansion is not immediate but takes a few us. Short, but possibly not negligible. So to sum up, QCW data would be quite interesting.

Offline Mads Barnkob

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Re: A dynamical arc model v2
« Reply #4 on: June 17, 2019, 08:54:41 PM »
Thank you for sharing your model data, looks very promising that you have it fit over 3 datasets, is there however any pitfalls or common causes in all 3 sets?

An arc simulation can be extremely useful. It can serve as a tool to choose primary and secondary tank parameters, will give a hint at achievable arc lengths, allows a guess at primary currents in a DRSSTC, can answer questions like "Are bigger top loads better than smaller ones", are higher or lower operating frequencies better, is there a choice between long and thin versus short and fat sparks, what is the effect of shorter or longer bursts, how does upper pole perform in comparison to lower pole operation etc.

Can the simulation do some calculations as well, depending on maybe some more input data, so it automatically calculates some parameters from the model you set up for a specific spark appearance? I know this sounds a bit the wrong way around, but could be a confirmation of the model.

The arcs temperature plays a big role in the calculation. At higher temperatures, the heat causes ionisation by fast air molecules bumping into each other. That begins at 3000-4000K. But also at lower temperatures, there is an effect, because the air expands, making it thinner and causing breakdown voltages to drop. There is also a time dependency there, since the expansion is not immediate but takes a few us. Short, but possibly not negligible. So to sum up, QCW data would be quite interesting.

This was something we discussed many years ago on 4hv, the differences between Kizmo's 1uF, Dalus' 1.5uF and mine 0.8uF, but only at a surface level of calling it low vs. high impedance and compare spark brightness/thickness. So while the low impedance also have lower losses in the primary circuit, shorter ring up time it might still be the preferable choice due to higher arc temperature from the start? Or is the "few us", more than a few, so a high impedance coil with long on-time gets in the same range anyway?
http://www.kaizerpowerelectronics.dk - Tesla coils, high voltage, pulse power, audio and general electronics

Offline Uspring

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Re: A dynamical arc model v2
« Reply #5 on: June 18, 2019, 11:45:53 AM »
Mads wrote:
Quote
...is there however any pitfalls or common causes in all 3 sets?
I'm not sure, what you mean here. Can you explain?

Quote
Can the simulation do some calculations as well, depending on maybe some more input data, so it automatically calculates some parameters from the model you set up for a specific spark appearance? I know this sounds a bit the wrong way around, but could be a confirmation of the model.

The model is parameter free in the sense, that there are no parameters specific for a particular arc appearance. It just calculates, what happens, when you have a given top load voltage. I've done a lot of parameter fitting to reproduce the measured currents, but there are no specific settings for either top load voltage or TC frequency.

In the lowest level schematic, there is a node N4, which is very rougly proportional to temperature. If you would be looking for a fat or bright spark, you'd need to supply different voltages, frequencies or burst length to the model and maximize the voltage at node N4.

Quote
This was something we discussed many years ago on 4hv, the differences between Kizmo's 1uF, Dalus' 1.5uF and mine 0.8uF, but only at a surface level of calling it low vs. high impedance and compare spark brightness/thickness. So while the low impedance also have lower losses in the primary circuit, shorter ring up time it might still be the preferable choice due to higher arc temperature from the start? Or is the "few us", more than a few, so a high impedance coil with long on-time gets in the same range anyway?

Yes, that can be studied with the model along the lines outlined above. I'm not sure, though, how well it will perform under more exotic circumstances. Very short bursts, e.g. the ones used for high notes in musical TCs, tend to produce more branched arcs. My model uses just a single arc, the branching is taken care of in its internal parametrisation. Maybe good enough to estimate the arc currents, but maybe not good enough to judge the arcs appearance. Steve Ward once asked me, whether my previous arc model could find the requirements for straight QCW arcs. Not yet.
« Last Edit: June 18, 2019, 11:52:11 AM by Uspring »

Offline Mads Barnkob

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Re: A dynamical arc model v2
« Reply #6 on: June 19, 2019, 10:43:32 AM »
Mads wrote:
Quote
...is there however any pitfalls or common causes in all 3 sets?
I'm not sure, what you mean here. Can you explain?

I was just wondering if there was something too much in common for the coils, so as the model is limited to coils generating 1-2 meter sparks and everything below and above gets more and more out of alignment with reality. I know you got no clear answer as you have no available data for this, but what is your gut feel about it?

I will take the model for a spin one of the coming evenings :)
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Offline Uspring

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Re: A dynamical arc model v2
« Reply #7 on: June 19, 2019, 01:40:16 PM »
A good question and difficult to answer. I wrote, that my first attempts to reproduce Hydrons measurements with my old model failed pretty badly. The reasons for this were partly a not quite correct way, the old model handled the frequency difference. But mostly it was, because I had completely neglected the effect, that the top load field has on the space charges of the arc. A diferently sized top load and a different length of the breakout rod have a strong effect on breakout and further arc growth. In hindsight a blunder, since most coilers know, that e.g. omitting a breakout point, can cause a DRSSTC to arc not at all. I think, the model is basically sound, as its calculations include much of the physics of the charge carriers involved, although in a quantitatively much simplified way. It definitely needs some fine tuning.
That doesn't really answer your question, but if you try it out and it fails (or not), that will add some guide for refinement.  ;)

Offline Hydron

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Re: A dynamical arc model v2
« Reply #8 on: July 04, 2019, 11:59:11 PM »
@Hydron:
I didn't mention that in the post, but I'm certainly eagerly awaiting new data. Do you have any specifics about your big coils primary tank? My simulations predict a somewhat larger current there as your OCD setting, so I am a bit puzzled. Your new data on primary and secondary base currents would definitely be helpful. The breakout points also play a big role. I've taken the extension of your point from the video. I hope I got that right. (7.6cm?) I believe, the length of the rod plays a significant role wrt to the voltages of the top load.

See here for the new data I mentioned:
https://highvoltageforum.net/index.php?topic=117.msg4628#msg4628

These come with accurately measured coil parameters (see javatc load file) - note that the tank cap should be the same value as with the 2014 data, however the primary tap definitely changed.
I may be able to work out where the tap was for the 2014 data from photos + my later physical measurements - I will let you know if I can.

As mentioned in the thread, I may have another shot at data collection this month - would you have any suggestions on which is more valuable data to get from second channel of the non-floating ("primary") scope - choices are bridge output voltage or secondary-base current (primary current is a given for the first channel).

Offline Hydron

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Re: A dynamical arc model v2
« Reply #9 on: July 27, 2019, 12:44:55 PM »
As mentioned in the thread, I may have another shot at data collection this month - would you have any suggestions on which is more valuable data to get from second channel of the non-floating ("primary") scope - choices are bridge output voltage or secondary-base current (primary current is a given for the first channel).
I'm sad to report that my plan to get more data was foiled - this time by my scope dying :(. While it is an easy fix I couldn't get it going in time to grab any new data - a shame as I had access to the coil in winter for once and likely won't have another chance for a fair while.

Offline Uspring

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Re: A dynamical arc model v2
« Reply #10 on: December 11, 2019, 05:28:46 PM »
If theory and experiment don't agree, too bad for the theory, right?
I promised some explanations for the model, so here it goes.

When I applied my older version of the arc model to Hydrons data, the arc currents came out about a factor 3 too large. One major difference in the experiments was, that Hydrons coil frequency is about 70kHz, which is roughly half of that of mine. The other difference was the power of Hydrons coil, it being capable of putting out > 2m arcs as compared to about 1m arcs of my coil. Hydrons lower power measurements where similar in arc currents to mine, but even there the difference to the calculated currents persisted. So my first impulse was to look for frequency dependent and not power related effects.

The models are based on an equivalent circuit made of a string of resistances and capacitors illustrated below.



The resistors simulate the arc resistance and the caps the effect of space charges. The resistance I've taken to depend on the energy put into it, considering the electrical power dissipation and a conductive heat flow to the surrounding air. To model the arc as a resistor might be somewhat doubtful, but it seems to work in some circumstances, e.g. as shown in the recent measurement by davekni for his Jacobs ladder. The current seems nearly proportional to the voltage for the duration of a cycle.

Such a purely resistive model has an interesting scaling property. Irregardless of the dependency of resistance to the power dissipated in it, the current should only depend on f * V^2. Comparing my coil with twice the frequency of Hydrons, this would imply, that I get the same current at sqrt(1/2) the voltage of Hydrons coil for my coil. That turns out to to be false. Actually the scaling property applies only to steady state situations, such as in QCW coils, but it still should work roughly for shorter bursts. Another failure is, that the resistive model cannot account for the peaked currents in ground strikes. It is much too sluggish for this.

The conductivity of an arc arises from its free charge carriers, namely ions and electrons. Ions, due to their mass being several magnitudes higher than those of electrons, move slowly and don't contribute much to the conductivity. Free electrons are created by 2 effects: In hot plasmas gas molecules will hit each other fast enough to knock electrons off them. That requires temperatures of 4000K or higher. The other effect requires a strong electric field, which will accelerate spurios electrons against air drag fast enough to knock off additional electrons from air molecules. This will lead to an avalanche of electrons. In TC arcs both effects occur, heat generated electrons near the breakout point, field generated ones near the tip of the arc.

Heat does also play a role at much lower temperatures than those, which turn air into a plasma. The heat will cause air to expand, which makes it thinner. So the drag, braking electrons, will be reduced and the voltage required for a breakdown is reduced also. This leads to the often observed retrace of arc paths between TC bursts. It's a bit of an open question, whether DSSSTC arcs grow slow enough in girth as to allow for the expansion of air. The sideway growth should be lower than the speed of sound. I believe this to be mostly the case. Marx generator arcs are much faster and correspondingly much louder than TC arcs. QCW coils are comparatively quiet, as their slow growth won't compress air as much.

For an estimate of the number of electrons n, or rather their density, I've used the equation

dn/dt = c1 + h(T) + n * f(V) - c2 * n

c1 is the background generation rate for electrons e.g. by UV radiation, natural radioactivity or cosmic rays.
h(T) is a temperature T dependent function, which accounts for the generation of electrons by heat. T is calculated from dissipated energy. f(V) describes the electron multiplication effect due to the electric field.
The last term c2 * n removes free electrons. The dominating effect is the attachment of electrons to neutral air molecules. This makes these electrons basically immobile and prevents them to contribute to conductivity. The conductivity I've taken to be proportional to the number of electrons n.

The LTSpice circuitry solving the above equation improved the fit between theory and experiment only a bit. I'd tried a lot of different parameters and functions and finally more or less gave up. A year later I had an idea.

In the analysis of the data from my coil I wanted to subtract from the measured current the current due to the capacitance of the breakout rod. It was pretty long and I made a current measurement at low voltages without breakout occuring. I actually could establish a few pF capacitance and I corrected for this. I tried to do the same for Hydrons low voltage measurement, but I couldn't see any current due to the breakout rod, just a bit of corona current. From a picture of his coil I estimated the rod capacitance, but the current due to that was missing. The reason for this is the proximity of that rod to the top load. The rod is engulfed by the toroid field and only a tiny bit of charge is needed to bring it up to the toroid voltage. So its effective capacitance is much less than that of a rod floating in free air far away. TC arcs experience the same effect. A space charge near the toroid will be at a much higher voltage, than one far away. I added this effect to the model by moving up the ground connection of the capacitor chain to the potential generated by the toroid. For simplicity I used a spherical potential.

The difference that made was tremendous. I was finally able to make a fit to both my older data and Hydrons measurement using the same set of paramaters, except of course, the toroid and breakout rod sizes. Much better reproduced was also the voltage at which breakout occurred. On hindsight a pretty obvious result, since every DRSSTC builder knows about the importance of such a rod.



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Re: A dynamical arc model v2
« Reply #10 on: December 11, 2019, 05:28:46 PM »

 


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davekni
December 08, 2019, 06:50:11 AM
post Re: CW multiplier resistor string suggestions
[Voltage Multipliers]
plasma
December 08, 2019, 12:00:00 AM

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