Regarding the Ikako Chibinidze video:

First I agree with verpies thoughts on the flyback transformer.

I'd like to add that we should be able to rule in or rule out normal transformer induction of the RF  output coil with a bit of reverse engineering if we could get a handle on the following:

1) What is the actual power dissipation in the bulb?

2) What is the size of the gap (voltage breakdown)

3) What is the value of the discharge capacitor i.e how many pulses per second of what energy magnitude are required to transfer the required power to light the lamp?

Then we could take a closer look at the flyback transformer. Modern flybacks from TV sets are designed with multiple secondary windings to handle the power for the entire set. The high voltage winding is much lighter duty, designed to maintain anode potential on the CRT being lost by electron emission from the cathode.
Can this winding really support the power dissipated in the lamp?

The ferrites (as noted by verpies) are designed for flyback operation not forward push pull operation. But I doubt the HV secondary can handle enough current to provide 200 Watts or more of power. I could be wrong but would like to attempt to disqualify normal transformer induction in the RF output coil.

We might guess from the video  that the two 80 turn windings are bifilar and presumably wound in the same direction. This would put the dots at one end of the coil form for these wires. Let us assume the dot wires feed the transformer. This would create a null output for ordinary induction as the pulse voltage would effectively cancel (not counting the smaller winding with the capacitor).
 

Food for thought and summary:
If the two 80 turn windings are in series connection (properly phased for normal induction) then all we have is a RF transformer being pinged at the spark gap frequency. This could probably light the bulb shown, but the spark in the gap does not look intense enough to carry that wattage considering the turns ratio 3:160. The flyback transformer HV winding alone may not be designed to carry the power being demonstrated. If anyone can estimate the gap distance, we would have a good idea how high the capacitor is charging before discharge in the gap. We can then calculate the energy per pulse (if we knew the cap value) and get the approximate necessary pulse repetition rate to sustain the lamp at some reasonable level of brightness as shown in the video.

If none of this adds up, we have something unknown and  interesting going on in the RF output coil. Keep a rad meter handy.


 

I have to disagree with you about the Royer oscillator not being appropriate to drive modern rectified flyback transformers. I've made all kinds of flyback drivers and the Royer oscillator is the easiest and best to use in my experience,

I welcome  your disagreement followed with rigorous thinking.
I don't deny that modern rectified flyback transformers (RFBT) work when the primary is supplied by Royer Oscillator, I just claim that they do not work efficiently when the primary of such transformer is supplied with AC.  The main reason for it is that an RFBT is not really a transformer.

An AC driving signal is less than perfect because it's sinusoidal, not because it's AC.

When I wrote AC I meant just that - a current waveform that reverses polarity.  I did not synonimize AC with a sine waveform.

A square pulse works better because of the fast risetime.

Yes, di/dt is important for the operation of RFBTs.

The "AC" or "pulsed DC" nature of the current in the primary is unimportant to the voltage rise in the secondary even if the secondary is rectified; it is the rate of change of the current that is the determining factor.

Yes, di/dt is important to the magitude of EMF but which di/dt do you mean?  The rising edge or the falling edge ?
They are the same for sine or square waveforms, but for others they are not.

I think you can prove this to yourself by using the offset function on a FG. Set up a transformer with the secondary feeding a diode, just as in a flyback.

In my case, I am feeding a resistive load through a HV diode connected in series to the secondary winding (the diode conducts during the falling edge of the primary current).

Stimulate the primary with a true sine wave, AC, symmetrical about the zero baseline. Then use the offset function to raise the signal up until it's all above the baseline, or lower it until it's all below the baseline. What happens to the output voltage of the secondary?

Across the load, the voltage amplitude is 5V on the rising edge and 790V on the falling edge of the primary current.

...the rest later

Watching the manual switching sequence carefully shows that the croc earth lead is needed for lamp illumination. At one point the switch on the transformer is operated and the lamp does not light. The guy then realises that he has the earth lead disconnected. When re-connected and the switch is operated again, the lamp lights. This device does not seem to work like the Tungus device that appears not to need the earth lead to self-run.

  Good to see all these discussions, on the self runners.
  One device is using the spark gap, the other is not.  Spark gaps are noisy, cheap and practical, but are they really needed?  Both devices output somewhat similar power, but one does not make any noise, at all, and may even use a convenient store bought driver circuit, plus a couple of Fets and caps and diodes. Nothing too fancy to replicate.  Just thinking out loud...
   Where did this last Romanov diagram come from, as it is different than any previous ones.
Also where did the simple two NPN transistor diagram come from, if I may ask?

  Where did this last Romanov diagram come from, as it is different than any previous ones.
Also where did the simple two NPN transistor diagram come from, if I may ask?

It comes as second part from http://www.youtube.com/watch?v=Sbb_kSgvzoo and http://www.youtube.com/watch?v=ZRfWTlbFy1k for example of processes isolation in air core transformer from input.

   @ T-1000, thanks for the link, I'll check on it.

   @Vortex1:  This may not all work like a regular electric circuit would, if magnetic resonance is the "secret" behind the effect generation, possibly at the expense of the normal known electrical coil induction practices.
   As HV/HF and/or magnetic flux, on the outside of the wires (skin effect) may not burn them out, or work in the same way.
  One of the first TPU circuit devices Steven Marks made could be picked it up, while holding and touching it, yet not get shocked, at the same time showing a very hefty blue/white spark when shorting out the two output wires that read several hundred volts output. Yet, the bulbs and the rest of the circuit were getting very hot.  As are these devices (having possible heat issues, core noise and vibrations), that we are looking into now.
 May be related, and may not be...

   @ T-1000, thanks for the link, I'll check on it.

   @Vortex1:  This may not all work like a regular electric circuit would, if magnetic resonance is the "secret" behind the effect generation, possibly at the expense of the normal known electrical coil induction practices.
   As HV/HF and/or magnetic flux, on the outside of the wires (skin effect) may not burn them out, or work in the same way.
  One of the first TPU circuit devices Steven Marks made could be picked it up, while holding and touching it, yet not get shocked, at the same time showing a very hefty blue/white spark when shorting out the two output wires that read several hundred volts output. Yet, the bulbs and the rest of the circuit were getting very hot.  As are these devices (having possible heat issues, core noise and vibrations), that we are looking into now.
 May be related, and may not be...

Messy build with long straggly wiring runs may also be a factor here.

  There does appear to be a number of components that are found in all these different cases. Coils, and caps, are usually present, and a feed back path to most if not all self runners. The load is also very important, but not in the normal way, but in a way that allows this unknown input source to increased the output, to a degree, but with what looks like some limiting factor. 
  There is the issue of this unknown input source, which must always come from somewhere, as overunity does not exist, unless you believe in the ¨Big Bang¨.
Maybe it´s due to nuclear decay, or maybe not, but, who can really say that this output is not causing the decay, if radioactivity is actually found, instead of the other way around.

  Wesley is working hard on all of this, with some new information on his rad tests, which is very good for those of us who can´t afford to go that route.