Levitation force on a permanent magnet over a superconducting plane: Modified critical-state model

摘要

The authors consider a model system of a permanent magnet above a semi-infinite superconductor. They introduce a modified critical-state model, and carry out derivations of the levitation force acting on the magnet. A key feature of the modification allows the current density to be less than the critical value. The theoretical results show an exponential relationship between the force and the distance. Analytical expressions are developed for permanent magnets in the form of a point dipole, a tip of a magnetic force microscope, and a cylindrical magnet. In the latter case, the exponential relationship has been observed in numerous experiments but without previous interpretation.