Analysis of the interaction between magnet and superconducting ring in the mixed state

Abstract

The interaction between a small permanent magnet and a superconducting ring in the mixed state has been analyzed using a phenomenological model of the supercurrents known as the J_s + J_v model. The trapped magnetic field has been described by a constant surface current density J_s circulating the inner and outer surfaces of the superconducting ring as well as a volume current density J_v flowing within the entire volume of the ring. Under field-cooled (FC) condition, the results showed that the interaction energy between the magnet and the superconducting ring has the minimum value when the magnet is located at the center of the ring indicating the existence of a stable equilibrium position. The axial force versus the distance of the magnet from the center of the ring showed that the magnitude of the force is zero at the center while maximum when the magnet is just at the borders of the ring. The results are found to be in agreement with the experimental and theoretical results reported previously in literature.