Longitudinal emittance blowup in fixed field alternating gradient muon accelerators

The fixed field alternating gradient (FFAG) accelerator is proposed as a muon accelerator because of its large aperture and no need of magnet ramping. In particular, the nonscaling type of FFAG has been studied because of its simple magnets and its unique acceleration method using the path out of the rf bucket. A recent 6D tracking study reveals, however, that the time of flight difference due to transverse amplitude causes the longitudinal emittance blowup which limits the transverse acceptance. This is a serious problem for an accelerator that is expected to accelerate a muon beam with huge transverse emittance. Two methods of curing the problem are examined by particle tracking. One is higher rf voltage and the other is higher harmonic rf in addition to the fundamental one. A 50% increase of rf voltage suppresses the emittance blowup. Second and third harmonic rf also improve the final momentum spread. Both methods work fine in a single FFAG system. However, a few percent of particle loss is inevitable when two FFAG are cascaded.