Inhomogeneities in Magnetic Field Due to Variations of Lamination Gap Heights

It is difficult and expensive to maintain stringent tolerances on the variation in gap heights of dipole magnet lamination. Using the perturbation technique of K. Halbach, whereby one approximates a deformation of a magnet pole tip by a change of the scalar potential on the undeformed pole, we have calculated the tolerance necessary to achieve a given homogeneity of the magnetic field. Tolerances may be significantly relaxed if a systematic shuffling scheme is used to minimize the lamination variations averaged over a distance small compared to the gap height. Results of our calculations are compared with data from field measurements on the bending magnets for the NSLS 700 MeV Ring, for which laminations were carefully shuffled, and for the corresponding prototype magnet which was not shuffled. We conclude that for magnets used in storage rings, very tight gap height tolerances are not necessary, because field variations are reduced by shuffling and significantly cancel out when integrated over the magnet.