Analysis of Rapid Betatron Resonance Crossing

The reduction of transverse and longitudinal cooling requirements, the increased number of beam circulations, and the reduced cost, as compared to RLAs, are arguments to adopt the linear-field FFAG as the acceleration stage of a Neutrino Factory[1]. Because of the large range of central momenta, ± 50% δp/p, and negative uncorrected chromaticity, the non-scaling FFAG will cross many integer and half-integer betatron resonances during the 10-20 turns acceleration. There is the expectation that if driving terms are small enough and crossing is fast enough, then there is insufficient time for the betatron amplitudes to grow. The conventional theory of resonance crossing[2, 3, 4] is applied to slow acceleration, over 100s or 1000s of turns. This paper examines whether the rapid parameter changes encountered in the multi-GeV FFAGs, or few-MeV electron model, are compatible with simple theory.