One way to add in scaled primary current:  Add a third primary CT output stage (or entire third CT) with its own adjustable burden resistor (or fixed burden resistor followed by POT to reduce voltage)...

That's a very neat way to measure the top voltage. You can even measure the arc current when you scope primary and secondary current:

I_arc = I_sec + L_sec*C*d²I_sec/dt² + M*C*d²I_pri/dt²

L_sec, M and C are the secondary inductance, the mutual inductance and the top load capacitance respectively.
The main problem is, that the first 2 terms are large and almost cancel each other, so that the result is susceptible to measurement errors when the arc current is small. But the measurement is much simpler than having electronics on the top load.

Quote

There should be 3, the upper and lower ones the poles.

Uspring:  Is that a typo?  Should be 2 peaks, the two poles.

Yes, there are 3 ZCS frequencies but only 2 current peaks.

Steve Ward has built a 160 kW QCWDRSSTC: https://www.flickr.com/photos/kickermagnet/15705193211/
It creates 11 feet arcs, runs at around 350 kHz with 20 ms burst length. Steve mentioned, that arc length and branching didn't live up to his expectations. I think, that probably the branches contribute to the lower than expected total length. He experimented a bit with a higher frequency and found, that this seemed to reduce branching.
Another experience he made, is, that under the severe arc loading the upper pole ceases to exist. His explanation was along the lines of this post: https://highvoltageforum.net/index.php?topic=113.msg15012#msg15012 . He observed a decline in primary current followed by a jump down in frequency to the remaining lower pole. He was able to avoid this by increasing the coupling.

The primary winding looks like a lossy inductive load to the bridge. Lossy, because energy is drawn by the secondary coil. The MMC is added in order to cancel out the inductive part of the primary impedance. This has 2 advantages:
1. You can achieve zero current switching
2. You can input much more current for a given input voltage, since the reactive part of the input impedance is cancelled. So you can have both many primary turns and large primary currents, whcih produce a strong field to drive the secondary.
What kind of feedback are you using?

I'm also puzzled about the temperature and/or humidity depencies of the arc curvatures. Particularly, because these quantities are scalars and don't directly imply vectorial effects, such as arc directions. But they might modulate other effects. I will speculate a bit:
Candidates for arc direction causes are the ambient electric and magnetic fields. Slowly growing arcs are particularly susceptible to these.Consider e.g. a 2 m long arc grown in 20 ms, such as from Davids coil. It lengthens at about 100 m/s or about 0.1 mm per half cycle of its frequency.
Now suppose, the arc bends with a 1 m radius of curvature. That implies, that for each 0.1 mm step, the angle of the arcs direction has to change by 0.1mm / 1 m = 0.0001 radians. The direction of the electric field near the tip is straight ahead, changed a tiny bit by some externally caused surrounding field. The straight ahead compnent of the field is in magnitude near the breakdown field of air, i.e. 30 kV/cm. But to change this field in direction by 0.0001 radians, an external field of strength of only 0.0001*30 kV/cm = 3 V/cm is necessary. This kind of QCW arc is really a field probe.

The strongest fields surrounding the TC are the top load electric field and the primary and secondary coil magnetic field. The primary and secondary coil magnetic field lines can only cause azimuthal or spiralling direction components, which don't seem to happen. From the videos it is a bit difficult to tell.

The top load electric field is definitely strong enough to influence the direction of the arc, but shouldn't it cause the arc to seek a direction away from it?
I've run a simulation of the arc with my arc model. In the diagrams below the voltages of the top load (red) and along the arc (green) are displayed. In the first diagram the arc voltage near the breakout point is shown. In the second diagram the arc voltage near the tiip is displayed.





The arc resembles a phase shifting transmission line. The phase shift in the second diagram between the voltages is near to 180 degrees, so there the top load will bend the arc towards it. As from the statements above, this tendency is small and will cause only a slight bending, the major directional influence still being the arcs charge right behind the tip, which will tend to keep it straight.

Davids setup is nearly axially symmetric, so the arc has to have a reason to go anywhere except straight up. The effect I've described works only, if the arc is already off axis, since an external field can only bend the arc, if it is not parallel to it. I believe this might be caused by the initial bump in the primary current as shown here: https://highvoltageforum.net/index.php?topic=1950.msg17719#msg17719
This is different than in the diagram https://highvoltageforum.net/index.php?topic=2397.msg18480#msg18480, where the bump is much smaller. The bump might be causing a jump start of the arc, which will give it a more random initial direction from where it can bend from. This is very speculative, but might explain the observed straighter arcs seen with the new driver.
Another difference might arise from the ambient temperature. A higher temperature will lower the air density and thus reduce the breakdown voltage. That will change some arc properties but I'm not sure how that affects arc curvature.

Edit: replaced the first diagram with a corrected version (the original one was taken with a wrong time range)

I would have liked to check arc power against power transferred from primary to secondary by
P = ω * M * Ipri * Isec * sin(phi)
Primary current seems to be logged only as averages. Do you have a non averaged record of the primary current?

I think the 90 degree turn of the ground arc is a branch. The main arc probably died out quickly and was missed by the vdeo. Ground arcs loose their branches from the main channel when ground is hit due to the loss of voltage.
Wrt rectification: Was the foil grounded?

A very nice measurement and afaik the first one of this kind obtained from a QCW DRSSTC.
The mutual capacitances between secondary, top and arc are indeed hard to handle. JavaTC doesn't do too bad of a job calculating top load to secondary effects. You can e.g. compare secondary top and bottom currents.
The very flat secondary voltage curve is strange.
Are the values in your zip file raw data or did you already subtract arc current from top load current to get net top current?

I didn't see exactly what the arc  hit for this capture.

It hit a diode 

Thank you for the schematic.
I've checked my equations and found a problem with them. I started from energy stored in the tanks and have now realised, that this is a wildly varying quantity due to the large coupling. Also the energy content is a dubious quantity, since much of the field is shared by the tanks, so that energy cannot be attributed separately to them. Anyway, after corrections I can confirm your values. (It's hard to argue against measurements)

I'm wondering a bit about the energy loss in the primary. I would have put the resistance causing the loss in series with the coil. That is because the coil voltage is the sum of the drop along the resistance and the induced voltage. Did you make a primary Q measurement before installing the secondary?
For a 50% loss the series copper resistance would have to be about 0.4 ohms. That seems much more, than can be accounted for by skin depth of your copper foil, assuming the current is distributed evenly across its width (maybe a cm or so). MMC ESR would have to be added to this. But perhaps current density varies across the width of the band. I haven't looked in detail at this. Did you consider using stranded wire?

Regarding curvy arcs: Perhaps Mads is right, that the top loads field doesn't matter much. If you're interested in that, you could try a very long breakout rod (perhaps 1m) or place it off center or point it at an angle. Adding extra capacitance to the top likely won't affect tuning very much, since the coupling is so large.

I'd like to get a stable 15 torr globe working for use as a permanent display. So far as I can tell people are getting the 15 torr toroid to run without a kicker coil to start ionization.

You might have an impedance matching problem with lower pressure. Ignition will require less voltage, but possibly the toroids resistance will be higher compared to your previous experiments due to the lower pressure. That might require extra turns to get enough power into the toroid to heat it up to plasma temperatures.