I dont like the charge curve
- it has large spikes, maybe solvable with some small caps
- it is wobly. Why? probably, due to the interaction with the resonant coil. might remove the diode parallel to the coil, and give it 2 diodes, as mentioned before, but doubt if this will work, as the coil is connected to the middle of the 2 series caps, where the voltage is 1/2 -V
So the diodes only open up when 1/2 -V is reached. no solution.

I now use a diode in parallel of the coil, seems to work. Another option, is a Diode in series. But this should be 2 diodes, giving another 2 hickups for the impulse...

maybe add a diode between cap and pulse transformer to prevent oscillations

Going to do something different
remove the diode from the center impulsed coil, and let it resonate via the series parallel concept.
The inductive negative spike of coil 1 will still be captured in a capacitor.
But the second coil is to be resonated. then, at the right time (???) the charged capacitor , will be discharged into the resonant coil.
This charged capacitor should be in series.

If the resonance is reversed, the inductive spike happens at max positive voltage. the max negative voltage of the resonant sine then is at the start of the pulse of the first coil. This should be the right time, to discharge the capacitor into the resonant coil, increasing its voltage, and therefor increasing its magnetic field.

The third coil should still be tuned to the center coil for max output.

Cool idea.  If after the cap arcs it immediately returns to being a capacitor again, this might just be a method to abruptly shutoff the discharge the way Mr. Tesla recommends.  Give it a shot for sure.  Maybe even try homemade capacitors with different types of dielectric, different thickness and  shapes.  You might just find something that works even better than a magnetically quenched spark gap.

Yes Matt, and we know what Nelson does. overcharge the cap with negative voltage. he said it was not as destructive as a positive voltage overcharge.
But I rather use a mosfet for now to be able to control the process and learn from it.

already made the setup and played around a bit. interesting results.

got the series charging /disruptive discharged cap now between the resonant coil and ground.

still wonder if its ther right side. have already seen amplification of the res sine, but then there was no disruptive discharge.

still many factors to play with. so many variables, but the goal is again  clear.
series parallel resonance, with a disruptive discharge into it.