Muon acceleration in FFAG rings

Compared to muon acceleration in re-circulating linear accelerators, considered earlier, muon acceleration in FFAG rings holds the promise of having one arc instead of several, and a smaller number of RF cavities; i.e., using more than a few turns for acceleration from about 6 to about 20 GeV/c. We consider non-scaling FFAG machines (but with limited tune variation) that are essentially strong-focusing rings with a dispersion small enough to keep muons over the full momentum range inside the same magnet aperture. We compare several scenarios: (i) Rings with straight sections, long enough - a few metres - to house super-conducting RF cavities at about 200 MHz (and with enough space for decay of the magnetic fields in neighbouring components to a level of about 10 mGauss); (ii) Rings with shorter straight sections, just long enough about a metre to house normal-conducting RF cavities also operating at about 200 MHz; (iii) Racetrack-shaped rings with compact arcs without RF cavities, joined to long straight sections with super-conducting RF cavities by adiabatic transition sections that match between them over the wide momentum range needed; (iv) Rings with a number of super-periods (about 10) so that there are only a number of sc RF sections. In all four scenarios we consider the travel time of the muons around the ring which depends on the muon momentum and, hence, produces variable phase at the RF cavities during the acceleration process.