Analytic Models for the Calculation of the Iron Yoke Contribution in Superconducting Accelerator Magnets

The superconducting coil of an accelerator magnet is usually surrounded by magnetic material, the iron yoke, in order to enhance the field in the aperture and to reduce the fringe field outside the magnet. For the calculation of the magnetic field of such superconducting magnets, numerical methods, typically FEM are used. Nevertheless, analytic solutions of simplified geometries are still needed in order to cross-check numerically obtained results and gain deeper understanding of the underlying principles. For the calculation of the effect of the iron yoke on the field distribution and field quality of superconducting coils as a first approximation a circular hollow cylinder of high permeable material could be used.