What i'm saying i repeat than,
In the problem, in witch you connect two capacitors of the same size and half the energy disappear, in my opinion it happens because the charge don't succeed to completely pass from one capacitor to the other, basically when the capacitor reach the other voltage you are pushing from both sides and when there is no difference, as there is no inertia it will get damped and stop pushing. (like the vacuum break i proposed). Probably there is a kind of small oscillation when energy disappear cause just connecting a capacitor into the other the current will not have enough inertia again to keep flowing till the 2° capacitor is full or better till the first is completely discharged.
I just said that charging a capacitor with 10kv 1ma and charge a capacitor with 100v 100ma will give two different joule energies. So following the same principle, conservation of charge, but using resonance, you than are able to charge the capacitor and by transformer coupling action to than discharge it completely into the other smaller one raising the joule energy. Basically i'm talking of charging 2 capacitors with the same charge however in the smaller capacitor, the voltage will be greater to compensate to the accommodation of the same charge.
The important is that the capacitor completely discharge into the smaller other, or at least partially, cause as we are coupling it magnetically and as we can have a Q factor of maybe 100 on the primary, the energy witch was not transferred will still be there for some time for other interactions.
So
A nice 50khz inverter and res tank just like was proposed by don L smith, mckain, stan, tesla... having the capacitors hand made attached to, and thus tuned by the coupling of the two bobbins. Another transformer can be connected to the second tank to extract the energy. Whenever you multiply the energy you can than lose some energy converting the voltage however to keep over unity attention must be paid on this energy transformation to not exceed in the energy disappear.
The key formulas are
EnergyC= 1/2*v^2*c
EnergyL=1/2*i^2*L
Q=V*C
C=Q/V
V=Q/C
As every cycle produces energy, the amount of produced energy will increase with the frequency, or increasing the difference between the inductors and capacitors.
100 times difference like 100nf to 1nf would provide a 100 times bigger energy and voltage, however this gain seems to much and technically should provide only 10x gain.
Here i remember that stan talked about 3 times 5 times transformer ratio up to 30...
So a 3 transformer ratio would represent 9x greater energy already. Would be good for a first shoot.
Maybe a 1mh and 10nf cap coupled to 10mh coils and a and a 1nf cap at 50khz.... Or 10mh with 10nf and 1mh with 100nf at 15,5khz
Or times 10x squared
10mh inductor with 1nf and a 100uh with a 100nf 50khz still...
many possibilities,...