What I want to look at specifically is the phase/frequency shift of the secondary current in relation to its self

Basically my running theory is that the frequency at the end of the burst should be much lower than when it started

Making the power ramp longer even by 5ms or so doesn’t make the sparks longer, rather chubbier. This principle of power per time is important

0.2 ohms, that I estimated by wire diameter, length and skin effect for BSVis coil.

it seems, that you need a loss resistance of about 1 Ohm to explain, what he observed. But that is a lot more than I get by a simple estimate from his wire thickness etc.

Increasing coupling can be problematic due to flashovers, though.

BSVi, can we have some more photo's of the whole primary tank circuit, please?

Have you try adding more capacitance I.E. energy storage for your bridge to convert

If this is for the large coupling case, I would assume the cap voltage drop during the burst to be considerably larger for the low coupling, since there is an increased current draw. It might be just large enough to stifle spark growth at some time during the burst.

Any info on the caps? What is the dielectric? Do they get hot?

Those brown capacitors are definitely a series string, Teravolt. I'm pretty certain that is the MMC. The other end of the series string goes to the primary coil, I assume, and that red wire with the toroidal inductors around it is the return wire from the primary coil, but I'm only guessing.

There will be smoke, fire and burnt components long before the thermal resistance rise of the wiring becomes significant. Also, if wiring resistance was significant enough to limit performance with lower coupling, the dissipation in the wiring would lead to complete destruction in a short time.

No, unfortinutaley, I don't have access to another big capacitor. I have to get another one or two. I agree that 80v voltage drop is signifacant, throught. But voltage drop decrease logariphimcally with capacitance, so to decrease it much, you need really BIG primary bus capacitor.

It's good idea to take measuremet of this voltage drop with lower couping. I'll do this.

Now consider a lossy primary. Current will also increase here with lower coupling, increasing power input, but also energy is burned in the tank. If tank loss resistance is large enough, power output decreases, even though power input increases. That will be at the point, where about 50% of power input is burned up in the primary. This does not really make sense to me, since the coil performs too well to be that lossy. So I don't think, that less spark length with lower coupling can be explained by this alone.

I think the secondary resistance and impedance plays a role here too. The EMF driving the secondary sees more leakage inductance in the secondary, which has nearly as much impedance as the arc has, so wouldnt this cause a reduction in power as well and help explain the sensitivity to K?

...The same spark looks like a smaller load to the 40p coil and consequently the inverter can drive more power into the system and make bigger plasma because the source impedance is effectively smaller.

Bigger coils have higher energizing costs, and i think its really quite significant in terms of primary current during operation. Figuring out the right amount of energy storage for your tesla coil design i think is key to optimizing its efficiency. Seems obvious, and overlooked.