Optimization of the Quadrupoles for the Collector Ring of FAIR

The Collector Ring (CR) is a part of the challenging international project Facility for Anti-proton and Ion Research (FAIR) started in Darmstadt, Germany. The ion optics of the CR includes quadrupole magnets with an elliptical aperture and embedded octupole correction coils. To fulfill the requirements of the field quality in the magnet aperture, it is necessary to find an optimal pole tip shape as well as an optimal configuration of the coil system. We used a specially developed optimization procedure for designing the magnet cross-section. This procedure is based on a representation of the pole border line by a superposition of hyperbolic functions corresponding to different Fourier components of the magnetic field expansion. The goal function of the optimization minimizes amplitudes of the undesired field harmonics, and the Newton-Raphson method is applied to find a solution of the problem. We combined the described optimization procedure with the finite element method of the magnetic field computation and applied the developed algorithm as well as the corresponding computer program for optimizing the pole tip shape and the configuration of the coil system in the quadrupole magnets of the FAIR CR.