A Fast Analytical Method to Compute the Radial Flux Density Distribution in the Airgap of a Superconducting Inductor

An original topology of superconducting rotating machine propose to use the diamagnetism of high temperature superconducting (HTS) bulk. Here, YBCO bulks allow to shield the magnetic field created by two solenoids supplied by dc currents in contra-directions. The obtained airgap field is multipolar as in conventional ac machines. A quick analytical method is developed here to compute the magnetic field distribution. It is based on the determination of the modulating function associated with the radial flux density distribution resulting from the introduction of the superconducting bulks. A first step allows the calculation of the modulating function by a 2D analytical method (using the resolution of Laplace´s and Poisson´s equations by the separation of variables technique). The later is used in a second step together with the field produced by the two solenoids to calculate the radial flux density distribution in the airgap of the considered inductor. Comparisons to experiments and to 3D FE results show the validity of the proposed approach with the benefit of low computation time.