Method for solution of the interaction between superconductor and permanent magnet

A method for calculating the interaction between a superconductor and a permanent magnet for various initial cooling conditions is proposed. The exact solutions are obtained for the point magnetic dipole over a flat nonideal type-II superconductor. The distinction of the method from the frozen-image method is in the using of the vertical and horizontal movement images that create the same magnetic field distribution outside the superconductor as the trapped fluxes do when the permanent magnet moves vertically and horizontally, respectively. The vertical and lateral forces that are obtained by the method agree with the previous measurements qualitatively. Comparing with the frozen-image method, the method can give the lateral force in zero field cooling and the hysteresis in the vertical and lateral forces. The two characteristics cannot be obtained by the frozen-image method. In this case, the vertical stiffness during vertical traverses and the lateral and cross stiffnesses during lateral traverses are obtained by the analytic expressions of vertical and lateral forces. Those stiffness expressions can reflect the effect of cooling conditions and movement history.