3-D New Calculation Principle of Levitation Force Between Permanent Magnet and Hard Type-II Superconductor Using Integral Approach

A new contribution is given for the calculation of interaction forces between the permanent magnet (PM) and a hard type-II superconductor (SC) used as a classical levitation system. The forces and also mutual inductances are developed via Green's functions using an Amperian model, assuming a cuboidal thin coil for PM and a superposition of closed loops of rectangular cross section of the SC. In the superconductor, the critical current (J
_c
) is known, but the variable penetration thickness of J
_c
is given from external magnetic fields by Bean's critical-state models. All the analytical results are obtained with a dynamic representation of all penetration thicknesses of J
_c
depending on applied external magnetic field variations. The most important parts are the original mathematical process of considering current penetration in superconductors and the new analytical development of vertical forces between PM and SC, realized after several analytical integral calculations. The results have been evaluated for vertical displacements of a PM above the SC, proving the accuracy of our analytical model compared with those realized by Flux3D finite-element method software.