• Y. Giboudot
  Brunel University, Middlesex
• F. Méot
  CEA, Gif-sur-Yvette

The Non Scaling FFAG EMMA lattice allows a important displacement of the magnets in the radial direction. From this peculiarity, interesting studies of beam dynamics can be performed comparing simulated and experimental results. Being able to study a specific resonance, choosing a certain set of parameters for the lattice is really challenging. Simulations have been done integrating particle trajectories with Zgoubi through Magnetic Field Map created with OPERA. From a chosen tune evolution, one can find the corresponding magnets' configuration required by interpolating between a various sets of Field Map. Relative position and strength of the magnets are degrees of freedom. However, summing field maps requires a special care since the real magnetic field created by two magnets is not obviously linearly dependent on each single magnet. For this reason, frequently used hard edge and fringe field models may not be accurate enough. This linearity of the magnetic field has been studied directly through OPERA finite element method solutions and further on with Zgoubi tracking results.

• Y. Giboudot, A. Khan
  Brunel University, Middlesex
• T.R. Edgecock
  STFC/RAL, Chilton, Didcot, Oxon
• A. Wolski
  The University of Liverpool, Liverpool

The unconventional size and the possibility of transverse displacement of the magnets in the EMMA non-scaling FFAG motivates 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, using (for example) OPERA, or ZGOUBI. However, by obtaining an analytical description of the magnetic field (by fitting a Fourier-Bessel series to the numerical data) and using a differential algebra code, such as COSY, 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 allows different configurations of the lattice, in terms of magnet positions, to be represented very easily using a set of dynamical maps, with interpolation between the coefficients in different maps*.

*yoel.giboudot@stfc.ac.uk