The stator shape is really weird, and it doesn't make sense how it would connect into anything else; is it just wired to the beamline? -- in which case, why does it need to be so beefy? Or does the beamline go through it, somehow, in which case why is the axis solid?
The beefiness suggests high speed, if nothing else.
I wonder if the stator shape has to do with the transition from cyclotron to synchrotron resonance? -- as velocity increases into the relativistic regime, the relationship between frequency and energy changes, and a tuning component like this could be used to keep it in sync. The stator would then be cut to get just the right frequency as the particles speed up, and maybe it's stepped to keep particles confined on a desired orbit, or maybe the magnets vary in a complementary way. It would be repeating quickly, because particles are injected from a smaller cyclotron, accelerated to relativistic energies here, then accelerated further in the main beamline (or a third one before the main, I forget), and the time taken is nearly light speed around a modest sized chamber or beamline: modestly fast for electronics, but bleedingly fast for mechanics!
Tim
(Ed: I took my time, typing that while distracted, so I didn't see the above posts before sending. It looks like at least some of my suspicions were correct.)