The dynamics of a levitated cylindrical permanent magnet above a superconductor

Abstract

When a permanent magnet is released above a superconductor, it is levitated. This is due to the Meissner­effect, i.e. the repulsion of external magnetic fields within the superconductor. In experiments, an interesting behavior of the lev itated magnet can be observed: it might start to oscillate with increasing am plitude and some magnets even reach a continuous rotation. In this paper we develop a mathematical model for this effect and identify by analytical methods as well with finite element simulations two reasons for the described behavior of the levitated magnet. It is shown, that the oscillations of the magnet are due to inhomogeneities of the magnetization within the magnet, whereas the continuous rotations are due to temperature gradients of the surrounding air. 2000 Mathematics Sub ject Classification: 82D55, 35K05, 37N20, 74H55.