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 ΔB(θ, B₀)/B₀ = [B_y(real)(B₀, θ) _y(ideal)(θ)]/B_y(ideal)(θ) with all flux densities taken for different azimuthal angles θ 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 B₀ 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 θ for pole-tip flux densities ≤1.5 T.