Beam Dynamics in NS-FFAG EMMA with Dynamical Maps

The Non-Scaling Fixed Field Alternating Gradient accelerator EMMA has a compact linear lattice, in which the effects of magnet fringe fields need to be modelled carefully. A numerical magnetic field map can be generated from magnet measurements or magnet design software. We have developed a technique that produces from the numerical field map, a dynamical map for a particle travelling in a full EMMA cell, for a given reference energy, without acceleration. Since the beam dynamics change with energy, a set of maps have been produced with various reference energies between 10 MeV and 20 MeV. For each reference energy, the simulated tune and time of flight have been compared with results in Zgoubi tracking directly through numerical field map. The range of validity of a single map has been investigated by tracking particles with large energy deviation: the results can be used to implement a model of acceleration based on dynamical maps.