Smoothing of Magnetic Fields for Superconducting Bearings by Multilayers

Losses in magnetic bearings, whether conventional or superconducting, are caused by any magnetic inhomogeneities in the direction of motion. These can be smoothed by inserting a permeable sheet between the magnet and superconductor. However, this will also have the effect of reducing the field of the main magnet, which supplies the levitating force. Drawing on the parallel with shielding, where shields with air-gaps are more effective than solid shields of the same thickness (Rucker in Philos. Mag. 37:95, 1894), the same principle can be applied to smoothing layers. Analytic solutions are easy to obtain by using an anisotropic permeability in the smoothing layer. An air gap makes the normal permeability about unity while maintaining the parallel smoothing permeability which shorts out small wavelength inhomogeneities. For inhomogeneities which are mainly in the direction of motion we can striate the layer so that the in plane permeability is also inhomogeneous. The results are applied to a magnet track made of permanent magnets joined together with an effective gap of 0.1 mm. A suitable ferromagnetic layer can reduce the dip in field by a factor of 53 while only reducing the main field by 3 %.