Forces between arrays of magnets and superconductors

An analytic Fourier method is used to calculate magnetic fields and forces between magnet arrays for a number of arrangements, with particular application to magnetic levitation by superconductors. It is shown that the maximum clearance between a levitated magnet and superconductor is about 24 cm. Using sinusoidal current sheets the attenuation of the effect of inhomgeneities in a magnet by adding a thin permeable sheet is found. By adding further harmonics the forces and stiffnesses for two-dimensional arrays of magnets are calculated. The advantage of this method is that the effects of magnet shape, strength, size and distance to the superconductor are separated which allows us to draw general conclusions about the best design.