Is it possible for an oscillator to do work without damping the oscillations?

[sparks]

    Is the below circuit possible.   The current transformers which are designed not to draw power from the conductors they monitor drive a load and a feedback circuit for any losses due to resistance of the conductors that act as a core for the current transformers.  Current levels in this tank could be thousands of times stronger than the input current once the tank is revved up.

[CompuTutor]

Gosh I hope I don't get stomped for my opinion on this one,
but I want to fall back on my belief that Tesla thinking
was the right way to look at it all.

I don't know the exact vernacular he would use is,
but I think it would go something like this:

With resonance,
and that which resonates with it,
there can be no gain nor loss.
For one does not see the other.

Real nice idea.
Variable cap to match the spark gap.
Full wave rectifier to feed the Op-amp feedback loop,
right off one of the current transformer's loads
with a smoothing cap to be sure.

What type of resonant HV generator
are you indicating on the right?

[sparks]

    The circle to the right is just an inductance. One designed to be operated below saturation at the anticipated high current levels.   I am trying to create a harmonic oscillator with phased input.  When the capacitor goes low enough relative to the input capacitor then in goes the pulse as fast as possible.  That way when the tank inductor discharges back into the capacitor the capacitor starts off with just a little bit more charge in it on each cycle.  Just enough to maintain the harmonic oscillations and overcome any leakage problems.  I will try to get this thing to ring at low frequency so as to avoid rf and audio losses from the primary oscillator.  The inductance to input frequency will be so far out of wack most of the input power will be go to charging the capacitor and not result in any current through the tank loop.  To avoid losses in the sparkgap I was thinking of using a bank of avalanche diodes connected in series parallel configurations depending on the voltage levels needed to operate the oscillator at the desired power level.

     I am not looking for highvoltage I'm looking for high current levels.  The conductors between the capacitor and the inductor should of course be of as little a resistance as possible so they may start looking like a Tesla coil primary while to get the current transformers to output some voltage they may start looking like Tesla coil secondaries.