Acceleration stages for a muon collider

Using muons in high energy colliders has an advantage in that the muons emit negligible synchrotron radiation, but has the disadvantage that the lifetime of the muons is very short. The latter requires that the muons be accelerated as rapidly as possible to prevent particle loss. The former allows one to loop back and pass through the same linac multiple times, thereby achieving potentially significant cost advantages. Some of the acceleration systems will use recirculating linacs to achieve the reuse of the accelerating structures. However, the large longitudinal beam emittances make it difficult to simultaneously achieve large gradients by using high frequency RF and design an arc with a sufficient energy acceptance. The current state of the design for the acceleration stages for a muon collider is presented, with emphasis on systems accelerating to 70 GeV per beam. Known difficulties will be described as will their possible solutions. In particular, the use of an FFAG-like lattice for the arcs of a recirculating linac is described which accepts a beam with a very large energy spread over a wide range of energies, allowing a single are to be used instead of multiple arcs.