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 Meissner-effect, i.e. the repulsion of external magnetic fields within the superconductor. In experiments, an interesting behavior of the levitated magnet can be observed: it might start to oscillate with increasing amplitude 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.

A new thermo-magnetic wheel

“…Several authors have discussed dynamical models for the levitated and oscillating magnet above a superconducting plate [10][11][12]. Here we propose a model to describe the experimental results for an oscillating and rotating magnet at room temperature.…”

“…What is the equation of motion for the angular displacement φ between 0 and 2π ? These questions have also been examined for a levitated magnet above a superconducting plate in a vertical temperature gradient by solving the respective differential equations by means of finite element simulations [12]. The following explanations are based on a simple physical model, which is supported by experimental results that were not available at the time when superconducting levitation was examined.…”

“…To our knowledge, this effect, which occurs at room temperature, without superconductivity and low temperatures, has not been reported before. For a cylindrical magnet above a superconducting plate, however, this behaviour has been observed by several authors [7][8][9][10] and described by a mathematical model based on physical equations and finite element simulations [11,12].…”