Exactly right it is a gapped core. Once I git's a scope on I'll see.

But the voltage doubler they using is full wave doubler. Which means
they taking the positive and negative waves to get 4000 or so volts
DC
Now the positive half they use a .0082 mfd for a filter and the
negative half they use a .0056 mfd filter both at 3000wvdc.


my guess is the quasi-push pull output is due to the leakage energy
recovery circuit. HV flyback transformers usually have very high
leakage inductance (the part of the magnetizng inductance not coupled
to the secondary is leakage inductance) because distance between
windings is a major cause of poor coupling and you need distance for
isolation.

The leakage energy sloshes about in the primary causing all sorts of
mischief. This circuit recovers it and dumps it back into the primary.
It's unusual since the leakage energy is usually dumped back into the
bulk storage capacitor on the primary side if it's recovered by a clamp
winding or active clamp circuit.

A soft switching topology often uses the leakage inductance to reduce
transistion losses in the switch. Sometimes a discrete inductor is
added in series with the transformer primary to add to it. Another
bonus for the lousy coupling of the HV flyback transformer... no
discrete inductor needed. I think of this as electronic ju-jitsu.

The energy per half cycle (on the secondary) won't be equal so juggling
the capacitor values helps equalize the voltage stress.

Eh! I might be completely wrong. Simulating it would be the thing
but it's too much like work work and I'd need the transformer parameters.

At least that's how I think it works... Please let me know when you've
scoped the waveforms.