The Importance of Non-Linearities in Modern Proton Synchrotrons

The first step in designing an accelerator or storage ring is to choose an optimum pattern of focusing and bending magnets, the lattice. At this stage, non-linearities in the guide field are ignored. It is assumed that the bending magnets are identical and have a pure dipole field. Gradient magnets or quadrupoles have radial field shapes which have a constant slope, unperturbed by higher-order multipole terms. Before going too far in fixing parameters, the practical difficulties in designing the magnets must be considered and the tolerances which can be reasonably written into the engineering specification determined. Estimates must be made of the non-linear departures from pure dipole or gradient field shape, and of the statistical fluctuation of these errors around the ring at each field level. (6 refs).