Abstract
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.
Highlights
Integrated multipoles with respect to the beam trajectory may be a source of perturbation for the beam dynamics in accelerators [1]
In particular for periodic magnets, as undulators and wigglers, only the odd orders in the U.S notation have to be considered, because the integrals of the even multipoles are equal in magnitude and opposite in sign from a pole to the following one, so that they cancel themselves in each period
All the analyses presented in this article have been done calculating the multipoles around the beam trajectory, but to prove the validity of the approach it is convenient to express these coefficients as a function of the ones calculated around the magnetic axis
Summary
Integrated multipoles with respect to the beam trajectory may be a source of perturbation for the beam dynamics in accelerators [1]. A possibility consists in adding some jaws at the extremities of the magnet to compensate a specific order integrated multipole. This solution, already successfully applied in the past [2], may be decisive if only a specific order needs a correction and a small one, so that this approach can be done without significantly modifying the other orders. The improvement of the transverse field uniformity by means of pole shims allows to reduce all the odd integrated multipoles, but only in the pole regions. III its application and optimization on a real magnet are presented
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