PPT Slide
Longitudinal capture at low frequency
The velocity spread of ?/? (p = 100 - 500 MeV/c) leaving the production section is 0.28. In a 1.25 T solenoid decay channel the captured beam radius is 30 cm.
Accept that we shall use solenoid focussing through to somewhere along the linac, say to ~800 MeV/c, and that the linac should have a reasonably high frequency - preferably MHz. Note that the target is immersed and so the solenoid focussing is not of the familiar type.
Then, because of transverse aperture limitations in the linac, to avoid high-field solenoids (e.g. 10 T) going into and along along the channel to 800 MeV/c we must reduce both the momentum spread and the transverse beam emittance. This means: phase rotation and transverse cooling (wedges for emittance exchange can probably be avoided in the neutrino factory).
There is rapid bunch lengthening downstream from the target due to both the velocity spread and the low-pitch helical trajectories - ?z = 1 m at the entry to the first phase-rotation cavity.
So let’s do phase rotation on a grand scale, using the inherent large velocity spread to generate good momentum/phase correlation over bunch lengths of many meters, and then add some ionization cooling before the linac.
Needs low frequencies - down to 30 MHz.