Design of Dipole Magnet with Circular Iron Shield

Complex variable function theory is used to formulate the magnetostatic problem of a rectangular current block of uniform current density located within a circular region bounded by infinite permeability iron. The magnetic field from the superposition of several blocks arranged to exhibit dipole symmetry is calculated using a generalization of Cauchy´s integral formula. Subsequent multipole expansion yields expressions for the multipole coefficients which through the use of variable metric minimization permits block arrangements to be found for rather pure dipole fields. Application is made to superconducting dipoles for both a pancake arrangement and a shell arrangement of the individual blocks.