FFAG Ring of magnets, like synchrotron, not solid like cyclotron Fixed field magnets, like cyclotron, not variable like synchrotron Can work at relativistic energies with swept RF. Rep rate driven by RF acceleration, not magnet cycling, hence fast acceleration High duty cycle may be possible. Depends on longitudinal dynamics

nsFFAG Bending by dipoles, focussing by quadrupoles As beam momentum rises, dipole field rises so bending power the same Focussing power stays the same if and only if quadrupole field rises proportional to momentum. Then optics stays the same This is ‘scaling’ Easy to achieve with synchrotron: dipoles and quadrupoles have same current. Severely constrains geometry of FFAG fields, B ~ r k

nsFFAG: will it work Optics changes during the acceleration cycle: focussing and bending are not linked Tune changes during cycle. (Number of betatron oscillations per turn) Normally integer tune = death due to resonances: lattice imperfection tweaks beam at same point on every cycle But in the rapid acceleration cycle of an FFAG this should not matter. Maybe…