Calculations on high field magnets with iron yokes and rectangular coils

Most studies on high-field bending magnets for superconducting synchrotrons or high energy beam transport in the last years concentrated on designs with a circular aperture and cos θ current distribution which is approximated by blocks of windings of stepwise decreasing current density. An alternative solution consists in the design of a magnet with square or rhomb shaped aperture which has the property that rectangular coils with only 2 steps of current density represent its exact solution. There exist also solutions with the same current density in all coils. The multipole field distortions of this class of magnets are studied in order to find suitable shapes of the outer iron shield.