Angular Dependence of Lateral and Levitation Forces in Asymmetric Small Magnet/Superconducting Systems

The dipole-dipole interaction model is used to calculate the angular dependence of lateral and levitation forces on a small permanent magnet and a cylindrical superconductor in the Meissner state lying laterally off the symmetric axis of the cylinder. Under the assumption that the lateral displacement of the magnet is small compared with the physical dimensions of the system, we obtain analytical expressions for the lateral and levitation forces as functions of geometrical parameters of the superconductor as well as the height, the lateral displacement and the orientation of magnetic moment of the magnet. The effect of thickness and radius of the superconductor on the levitation force is similar to that for a symmetric magnet/superconducting cylinder system, but within the range of lateral displacement. The splitting in the levitation force increases with the increasing angle of orientation of the magnetic moment of the magnet. For a given lateral displacement of the magnet, the lateral force vanishes when the magnetic moment is perpendicular to the surface of the superconductor and has a maximum value when the moment is parallel to the surface. For a given orientation of the magnetic moment, the lateral force has a linear relationship with the lateral displacement. The stability of the magnet above the superconducting cylinder is discussed in detail.

Vibrations in Magnet/Superconductor Levitation Systems

The problem of a small magnet levitating above a very thin superconducting disc in the Meissner state is analysed. The dipole-dipole interaction model is employed to derive analytical expressions for the interaction energy, levitation force, magnetic stiffness and frequency of small vibrations about the equilibrium position in two different configurations, i.e. with the magnetic moment parallel and perpendicular to the superconductor. The results show that the frequency of small vibrations decreases with the increasing levitation height for a particular radius of the superconducting disc, which is in good agreement with the experimental results. However, the frequency increases monotonically up to saturation by increasing the radius of the disc for a particular height of the magnet. In addition, the frequency of vibrations is higher when the system is in the vertical configuration than that when the system is in the horizontal configuration.

Effects of Magnet Size and Geometry on Magnetic Levitation Force

We obtain analytical relations for the levitation force as a function of dimensions of the superconductor-magnet system. The force has been calculated on the basis of the dipole-dipole interaction model. The effect of thickness of the superconductor on the levitation force is investigated. The results show that the influence of geometry and thickness of the magnet becomes significantly large at small levitation distances. Furthermore, approximating the permanent magnet as a point dipole results in an inaccurate estimation of the levitation force.