Magnetic field calculations for a large aperture narrow quadrupole

In the design of high-intensity proton synchrotrons and accumulator rings, quadrupole magnets of narrower size in one of the transverse dimensions are often needed to accommodate the compact ring geometry, the various injection and extraction devices, and the large vacuum chamber aperture. The stringent limit on tolerable beam loss further demands a good magnetic field quality to minimize beam resonances caused by higher-order magnetic multipoles. In this paper, we present results from magnetic field calculations performed on 2D and 3D models of a large-aperture narrow-quadrupoles that is suitable for a high intensity, low beam-loss accumulator rings. The pole face of the quadrupole has been optimized to minimize the integrated field of the first three allowed multipoles (12pole, 20pole and 28pole). The ratio of each integrated magnetic-multipole-strength to the integrated magnetic-quadrupole-strength at a radius of 85% of the quad´s pole-tip-radius is less than 2×10^-4. Results from the calculations performed on the two-dimensional and three-dimensional models of the narrow quad are presented.