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Fixed-field Alternating Gradient (FFAG) accelerators offer the potential ofhigh-quality, moderate energy ion beams at low cost. Modeling of thesestructures is challenging with conventional beam tracking codes because of thelarge radial excursions of the beam and the significance of fringe fieldeffects. Numerous tune resonances are crossed during the acceleration, whichwould lead to beam instability and loss in a storage ring. In a non-scalingFFAG, the hope is that these resonances can be crossed sufficiently rapidly toprevent beam loss. Simulations are required to see if this is indeed the case.Here we simulate a non-scaling FFAG which accelerates protons from 31 to 250MeV. We assume only that the bending magnets have mid-plane symmetry, withspecified vertical bending field in the mid-plane (y=0). The magnetic field canbe obtained everywhere using a power series expansion, and we developmathematical tools for calculating this expansion to arbitrary order when thelongitudinal field profile is given by an Enge function. We compare the use ofa conventional hard-edge fringe with a more accurate, soft-edge fringe fieldmodel. The tune 1/3 resonance is the strongest, and crossing it in thehard-edge fringe model results in a 21% loss of the beam. Using the soft-edgefringe model the beam loss is less than 6%.

Fringe field simulations of a non-scaling FFAG accelerator