Calculation of the hysteretic force between a superconductor and a magnet

The magnetic levitation forces exerted on a high-temperature superconducting (HTS) disk by a cylindrical permanent magnet (PM) are calculated from first principles for superconductors with finite thickness. The current j(p,z) and field B(p,z) profiles in the HTS in the nonuniform magnetic field generated by the PM are derived. The levitation force depends nonlinearly on the critical current density jc and on the thickness of the HTS. The flux creep is described by a current-voltage law E( j)=Ec( j/ jc)n, from which we show that the levitation force depends on the speed at which the PM approaches or recedes from the HTS, which accounts for the experimentally observed force creep phenomenon. The stiffness of the system is derived by calculating minor force loops. The numerical results reproduce many of the features observed in experiments.