@fcb:
Superconductors is not an option. Litz wire would be an option for a commercial embodiment, fine copper/silver tubing with water cooling will be the experimental prototype's embodiment due to cooling requirements. Due to the low required duty cycle, I may even be able to get away with Litz. It needs experimentation. A commercial embodiment can be fixed-frequency so many issues disappear.
My experimental prototype is already the absolute smallest I can make it, due to an absolute requirement of 1 CM3 minimal volume. I can go to 20 KV though, to have a small value cap and a Helmholtz coil with just a couple windings and still achieve a high resonance freq. A commercial embodiment would better use a lower voltage.