high-voltage transformer

Isn't that wire insulation only good for 4kV? I guess 11kV isn't enough to cause breakdown between windings.

The primary is near ground, and the secondary at HV. The coil voltages are low. I'm relying on the plastic bobbin for winding insulation from the ferrite core. The Sylgard protects all the other paths. The PCB will have a slot between coil sections, and it'll get a coat of urethane.

Common-mode chokes are often lossy; does your test include a thermometer? And, are you testing at low-load as well as high-load? Magnetization modulation in the core means that low-output-current is where the core losses are dominant. High-output-current testing will find the copper resistive losses to be the main effect.

Test it to breakdown!

We only need 0.5 watt, the losses are a fraction of that. The primary goal was to find a commercial part, with excess bobbin plastic, suitable to further HV hardening.

I was worried about the 8mm pin-to-pin clearance, and the inadequate hardening of my setup, compared to the end-use installation. I added teflon sleeves to the exposed pins.

Then I started increasing the voltage towards 11kV. But it snapped anyway, at 10kV. Everything is still fine, zero uA leakage, but I'm going to finish with a four day soak test at 8.5kV, to convince myself it'll be fine for use at 6kV.

The scheme should be good to higher voltages, with a choke having more pin clearance, like my original part's 12mm.

X-ray low power tube power supply

If by "snapped" you mean it started arcing then it is definitely not suitable for 6kV working voltage. There is a huge difference between working voltage and max dielectric withstand. Easily one order of magnitude.

Damage introduced by HV testing (such as hipot) is cumulative which is why we are time-limited in medical for such tests.

If I needed a LV supply up on a HV rail I'd look at series resonant structured with a massive isolation barrier. Simular to how electric toothbrushes such as Philips Sonicare are charged.

The arc was external to the transformer, across the thin exposed pins, acting as sharp points. I can harden them in the final product.

I made a serious HV transformer, similar to a TV flyback, and used it at 20kV, but I'm looking for a more simple approach. I think it'll work out OK.

Just be careful. Sometimes HV stuff will initially work, for a while. Then the barrier gradually breaks down until there is a loud bang. Or you arrive at your lab and wonder why there are three fire trucks :-)