There are two reasons why to keep PS looped back into input - the tuning involves it as part of circuit and it also will compensate power required for series resonance. The power draw from the battery is your losses and that what I was asking about - how much? Also when you have it looped the lighting of the bulb also has interest on how much power it take in that condition.

Also I was working in background with Oleg's DC-DC step-up converter and Tesla driver circuits. There are possibly intentional errors in original schematics and after fixing them all I hooked up small Tesla coil. It worked but the IRFP460 mosfet is no good for driving Tesla transformer primary at 1MHz+ range. The gate-source junction consumes about 100mA there which show inefficiency of that MOSFET. That also cause almost short circuit when hooked up with DC-DC converter. Will try other MOSFETs to find best one.

The DC-DC converter transformer details which was missing in Olegs schematics: I made 24+24T primary on small transformer with 1mm diameter magnet wire and the secondary was around 0.25mm for target voltage of about 130V. It gets up to 145V DC in in open end and drops to 87V with 15W 220V microwave bulb.
 
Cheers!

That's medium easy for me to draw

But what we need of our pll is to change this frequency every time according to any change that happens inside inductor's line. What is your opinion about that? Where do we have ti inter-vain? Any block diag. would be very helpful.

The PLL should be operating in blocking oscillator mode on the current peak in the series resonance.
So when there is maximum current on positive half-cycle the PLL will switch off MOSFET and flip to another half. Then the PLL should do same with on the peak of current in the negative half-cycle.
In this way it will chop low frequency square wave duty cycle to the best matching length and will make frequency shift to the best matching resonant frequency of the series resonance.
Then the signal on the PLL flip-flop time goes to the Tesla coil driver which will fire up signal to the Tesla coil.
There is an issue as well - due changing resonant frequency on the PLL the Tesla coil driver have to change its frequency to the resonant harmonic. This make manual tuning hard to achieve due changing conditions and instability of system operation. So to solve that the both frequency generators have to be synchronized. akula tried 2 PLL but that appeared to be "mission impossible" to get proper operation. My idea is from different approach - by applying frequency multiplier instead of manual frequency generator for the Tesla coil this problem go away instantly due locking of 2 frequencies on resonant harmonics all the time.

Here is Ruslan's video about mode of operation: https://youtu.be/NHpUE6oqt7k?t=9m27s

Is is still taking 5A with PS looped when you have same voltage from battery over diode and looped PS?
For Oleg circuits - will share modified version after the whole system will be functioning in proper mode.

I also saw a similar effect as was mentioned here of hearing the PWM driver circuit making funny whining/hissing noises
when I was touching the frequency adjust pot at certain frequency settings, and the little light bulb would go a lot
brighter when that happened. This only happened when the spark gap was activated. It seems HV spikes/noise
is probably being coupled into the PWM driver circuit when I touch the freq adjust pot, with my body acting as
an antenna of sorts, and this is making the PWM driver circuit act unstable.  My Digital ammeter showed an
increase in current draw to the PWM driver when this was happening and the light bulb got a lot brighter.