  Fixed-field Alternating Gradient (FFAG) accelerators offer the potential of
high-quality, moderate energy ion beams at low cost. Modeling of these
structures is challenging with conventional beam tracking codes because of the
large radial excursions of the beam and the significance of fringe field
effects. Numerous tune resonances are crossed during the acceleration, which
would lead to beam instability and loss in a storage ring. In a non-scaling
FFAG, the hope is that these resonances can be crossed sufficiently rapidly to
prevent 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 250
MeV. We assume only that the bending magnets have mid-plane symmetry, with
specified vertical bending field in the mid-plane (y=0). The magnetic field can
be obtained everywhere using a power series expansion, and we develop
mathematical tools for calculating this expansion to arbitrary order when the
longitudinal field profile is given by an Enge function. We compare the use of
a conventional hard-edge fringe with a more accurate, soft-edge fringe field
model. The tune 1/3 resonance is the strongest, and crossing it in the
hard-edge fringe model results in a 21% loss of the beam. Using the soft-edge
fringe model the beam loss is less than 6%.
