In general, for small air gaps, is A_L * I_sat constant when increasing the air gap? I know stored energy goes up, because energy goes as I^2. But I don't need that here.
In other news, I've measured the largest cores I have on hand...
Powdered iron (yellow, one side white): 178nH/T^2, >200At saturation
2" o.d. blue or green toroid: 3.3uH/T^2, 20 or 10At saturation respectively Big flyback core (black ferrite, like 4" tall, 1" dia. limbs): 6uH/ T^2, 20At saturation
The latter looks like it could actually work, since about 7 turns of
1/4" copper tubing would get me 300uH inductance (secondary). At
10kHz, that's 18.47 ohms X_L, which would draw 2.7A at 50Vrms. 2.7A *
7T = 18.9 At, which is just shy of saturation. Maybe it'll saturate noticably on the peaks, or on startup transients, but 10kHz is a design minimum, too (it will run at 20kHz most of the time, and can start as high as 50kHz easily enough).
Now, that's a real core, with a fairly long magnetic path and cross- section of maybe a square inch (give or take.. I'll measure it in more detail some time). That's about equivalent to the largest toroid Amidon sells (although that has maybe half the path length and no gaps, which might get a higher A_L * I_sat product, I don't know). It does look like I'll need a fairly large toroid either way, probably 4 or 5" across, maybe 6. I don't think it has to be ankle sized, but a few square inches cross section would be a good start. It still appears to be special order, or at least non-Amidon-stocked material.
Tim