Reduction of the integrated odd multipoles in periodic magnets

Integrated multipoles may perturb the beam dynamics in accelerators. In particular in periodic magnets, as undulators and wigglers, only the odd orders in the U.S. notation have to be considered, because the other ones compensate themselves in each period of the magnet. In the past, several methods have been considered to reduce them, but, if their effects on the beam are very strong, because of the small particles energy and mass, and in long period magnets, a different solution has to be explored. The method proposed in this article consists in compensating the contribution to the integral of the region between the poles with the one of the pole regions in each semiperiod of the magnet. It will be shown that this condition can be achieved by displacing the magnetic axis in each semiperiod of the magnet. To demonstrate the validity of this approach, it has been applied and optimized on a real wiggler.