Particle Tracking Studies Using Dynamical Map Created from Finite Element Solution of the EMMA Cell

The possibility of transverse displacement of the magnets in the EMMA non-scaling FFAG [1] and the unconventional size of the accelerator motivate a careful study of particle behavior within the EMMA ring. The magnetic field map of the doublet cell is computed using a Finite Element Method solver; particle motion through the field can then be found by numerical integration. However, by obtaining an analytical description of the magnetic field and using a differential algebra code to integrate the equations of motion, it is possible to produce a dynamical map in Taylor form. This has the advantage that, after once computing the dynamical map, multi-turn tracking is far more efficient than repeatedly performing numerical integrations. Also, the dynamical map is smaller (in terms of computer memory) than the full magnetic field map; this should allow different configurations of the lattice to be represented very easily using a set of dynamical maps, with interpolation between the coefficients in different maps.