Calculation of the interaction forces between superconductor and permanent magnet using equivalent current loops in zero field cooling

The levitation between high temperature superconductors (HTSs) and permanent magnets (PMs) has been applied to the flywheel energy storage systems and magnetic bearing systems for the last nearly twenty years. The interaction forces acting on the levitating body are calculated by the modified frozen-image method. The magnetic dipoles are equivalent to Amperian current loops. The current intensity in loops changes linearly when the PM moves. Under the zero field cooling condition, the expression of vertical force is obtained when the PM traverses vertically, and when the PM traverses horizontally, the expressions of vertical and horizontal forces are obtained. Those expressions of vertical and horizontal forces are gained by calculating the forces between current loops and using superposition theorem of vector. The calculations agree well with the previous experimental data, which means that the deductions of the expressions are reliable.