Fundamental Limit of Nonscaling Fixed-Field Alternating-Gradient Accelerators

Systematic nonlinear space-charge resonances may cause substantial emittance growth in the nonscaling fixed-field alternating-gradient (FFAG) accelerators. To avoid systematic nonlinear space-charge resonances, the phase advance of each nonscaling FFAG cell must avoid pi/2 and pi/3. Using multiparticle numerical simulations, we empirically obtain a minimum tune ramp rate vs the systematic 4th order space-charge resonance strength. We also find that the emittance growth obeys a simple scaling property when the betatron tunes cross the linear half-integer and sum resonances.