Design of an iron dominated quadrupole magnet with a high pole-tip flux density

Designing steel-dominated high-field quadrupoles one finds that saturation effects cause a considerable reduction in field quality, i.e., an increase in /spl Delta/B(/spl theta/, B/sub 0/)/B/sub 0/ = [B/sub y(real)/(B/sub 0/, /spl theta/) /sub y(ideal)/(/spl theta/)]/B/sub y(ideal)/(/spl theta/) with all flux densities taken for different azimuthal angles /spl theta/ along a circle of radius r within the quadrupole aperture. Some improvements can be achieved by additional corrective-coils the current through which is not a constant percentage of the current through the main coils but a percentage that varies with the maximal pole-tip flux density B/sub 0/ in the quadrupole. A considerably greater improvement can be obtained, however, when voids are formed inside the magnet poles close to their tips. Using such voids field qualities of a few hundredth of 1% can be achieved over all azimuthal angles /spl theta/ for pole-tip flux densities /spl les/1.5 T.