Optimization of the Sextupole Magnets With Trim Coils for the Collector Ring of the FAIR Project

The collector ring (CR) is a part of the challenging international project facility for antiproton and ion research started in Darmstadt, Germany. The ion optics of the CR includes sextupole magnets with embedded dipole 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 consists of two steps. The first one 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 optimization procedure based on the Newton-Raphson descend algorithm minimizes amplitudes of the undesired field harmonics. At the second step of the magnet design procedure, the parameters of the dipole winding are optimized to provide the required field characteristics in the magnet aperture.