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Calculation of the Forces Applied to a Superconductor in Levitation in an Inhomogeneous Magnetic Field

Stable levitation of systems consisting of a magnetic source and a superconductor is actively investigated due to the promising applications of this technology. While huge efforts have been made for modeling these setups with numerical simulations, analytical models, in spite of their use being limited to devices with a high degree of symmetry, can bring precious information on certain characteristics of levitating systems. Summarizing our previous work in the field, we present the mean-field model that we have proposed to reproduce the interactions between a magnetic source and a superconductor. We show that the model provides an estimation of the surface critical current density of the shielding currents flowing in the superconductor and an estimation of the thickness, t, of the layer carrying the currents. We emphasize that the calculated values of t are an increasing function of temperature, which tend toward the Meissner limit at low temperatures. Finally, we determine the condition that ensures stable levitation of axisymmetric systems.