Wide frequency-range acceleration using second harmonic RF bucket in fixed field accelerators

We propose a novel acceleration scheme for fixed-field accelerators (FFAs), in which RF buckets with harmonic numbers $h = 1$ and $h = 2$ are time-sequenced to form a single, continuous acceleration path. This approach completes acceleration in two RF frequency sweeps, thereby reducing the total frequency sweep range and shortening the repetition period. The feasibility of this method is demonstrated through longitudinal simulations based on parameters of the FFA at the Institute for Integrated Radiation and Nuclear Science, Kyoto University (KURNS). We also establish operational conditions under which the second harmonic rf bucket remains stable and practically usable.