Ok, Gentleman I gave up to try to sleep and I made new coil. I used the main coil as a base with those small alterations we discussed:
Changes- 45 degree on the primary angle, that I achieved by cutting shorter tube. The length is now 46mm instead of 70mm.
- I made it a bit tidy, so cut the edge in at every 10 degrees, you will have wire 36 holding gaps on each side. (altogether 72) It makes the winding process 5 minutes on the primary!
- The turnes on the secondary. It was 36 on the completed coil (I didn't post pic on that, only with 3 turn on the same tube) now it is 3 again.
- The gaps between the secondary turns, they were tight now there is 10mm gap. (the most important found)
- The secondary diameter, it was 0.74mm, now 1.40.
What didn't change- The diameter and wall thickness of the tube (80mm and 2mm).
- The diameter of the primary wire. (0.40mm)
- The materials:
solid copper, paper tube.
- My curiosity: still cant sleep.
Test environmentInput parameters 500kHz/50% square wave, 31VDC, 0.8A. 3x IGBTs in parallel. Rated 1200V/74A/500W per each.
ConclusionsPositive results
- The output peak became just beautiful. Rises on an exponential curve and symmetrically falls dow. If you make 3 channels of it you will get the "JET-turbine effect" SM said, so we can decrease the input current as well and the IGBT's will not heat as they only need to pile movement on a wire that already has some electron flow triggered by the previous channel.
- RF noise components disappeared after the peak as I wanted, no rectifier bridge needed anymore to clean up the negative range.
- Output peak goes to 153V. No significant drop on it after connecting the 250V/50W halogene light bulb. Only a few volts.
- IGBTs are doing better due to the lack of noise components.
Negative results
- Primary wire is still heating, so time to increase the channels to 3 and change it to a bigger on the next device if still an issue. (The next size I'v got handy is 0.74mm.)
- Voltage is too low to make light on the bulb, so need to increase the secondary turnes and decrease the gaps. e.g fully wound secondary from top to bottom with 2x bigger gaps than the diameter (~3mm).
- Need more spikes to fill the gaps, so the next milestone is the 3 channel and a syncronised driving circuitry. (I have professional equipment with 12 CH pulse generator and an own PC software to create any kind of bit pattern)
Is that a left handed wind on the primary I see?
I don't know what handed that is.

But it only changes the polarity of the secondary.
Also have you tried a lesser or greater angle on the primary winds? And if so what did you see?
Yes but I also changed some other parameters as well, so we don't know about the result of it. Now the standard is 45 degree and will remain as it seems perform well. But it is a useful idea, later we can try to change it.
If this is indeed a source of such a huge power then two questions arise:
1. The design is very simple. Why has nobody observed this effect during billions of experiments before? People have successfully developed and applied technology for extracting power from a controlled nuclear chain reaction and missed this simple and clean path? Unbelievable.
The design is naturally very simple and indeed the primary winding technique is still in use within CRT TVs as an electron accelerator. This is what I use it for.

To find simple things is always difficult.
2. Where the hell the energy comes from? What are we dealing with?
The energy is very likely from cosmic background but I will talk about it in a video lecture as it is not easy to understand in writing. I will have to make charts to make it understandable as it is.
Tomorrow I'll try this design... I just can't believe it until I see the bulb glowing on my table.
I hope so.

Keep an eye on the updates as I am trying to make it simpler and cheaper to duplicate.
What would happen if it was wound in a right handed manner?
Would change the polarity on the secondary output.

What would happen or be experienced if one was left handed and another was right handed and those were stacked and inter connected?
I presume that you'd get very bad results. Remember it is not only a switching power supply, but also an electron accelerator. It is a very important thing you have to keep always in mind.
Imagine the secondary as hose pipe where you want to make a liquid flowing. If its in an untidy pile and you open high pressure water on it it's going to wave to the neighbors.

In our case it would cause unexpected collisions, rather than a smooth flow. In other words you need to make the electron flow as smooth as possible. You can only do it if you avoid primary-primary and secondary-secondary wires crossing or touching each other.
You create this smooth electron flow with the primary is a spinning manner. You spin up the electrons as vortex and yet it will automatically flow much faster and much more electrons you'd expect at a normal transformer.
I wonder whether there is any flyback diode used to protect the FET(s) against the large voltage occurring at the drains right after switching off the primary coil....
Naturally not as I want that energy to be harvested on the secondary side and not on the primary PSU.

So Need to adjust the winding parameters to make the flow in the secondary as smooth as possible.
The description of the output power is still vague.
Not really as top IGBTs don't cook from nothing, especially not in 3 sec with molten solder and zinc plating on the back side. (I will post photos of that)
It's not said that the output is > 1KW. It says 'it moves > 1KW'. Probably to the switching fet(s), instead of the output.
Yes, presently it is true but I am on it to get that out on the output.
I'll have some more patience to see what exactly the input / output configuration is.
My task list is presently so long that probably that will be the last thing we do when I finish the demo device in a few days to Stefan and make it selfrunning.