[kalee20]

I've come across small avionics fans, 400Hz induction motors, a couple of inches in diameter, but they've always been 3-phase. Naturally, they run mighty fast!

As Russel says though, this wouldn't explain the capacitor.

I'd be surprised if there was a need for a single-phase 400Hz fan. If 400Hz is available it would normally be 3-phase, from a 3-phase generator. A balanced 3-phase system is constant power, whereas a single-phase system isn't: the load imposed by the generator on the engine varies from zero to maximum twice each cycle, which gives rise to torsional vibration meaning bigger flywheels and possibly torsional dampers are needed, which is all extra weight. So, even if only low power, 3-phase generation is best.