The idea that is keeping me thinking is that when the C1 is charged during pulse on for sake of simplicity, the C2 is forced by the bifilar coil and arrange to keep at the same potential. But when polarity reverses the C2 could be extrapolated by 3 capacitors in series being the middle one charged reversely! what this tell me is that if you have negative voltage potential in that middle it sums up with source voltage to charge up C2 completely, but thats not all. A capacitor is a mean for storing charge, but this storage is limited by some factors, like size, dielectric constant, and thickness. The thickness dictates the electric field as direct function of the potential difference.

when you are charging a capacitor what is happening is that you add one electron at a time, and for every electron you add it gains a voltage potential. The sum of all the electrons times the voltage they had to fight to enter the capacitor equals the energy in that give capacitor.

Now lets look at the very instant of the point where C2 plates are at the same potential than c1 plates and the voltage reverses in the coil. What happens is that the coil is going to charge C2 but charging C2 means to discharge C1 too. But the point is that the electrons coming out of the coil are actually attracted to get into that capacitor.. by the electric flux formed..

is necessary to do further mathematical analysis to complete this theory, here is going to be possible chose the parameters knowing the parameters to change to improve the performance.