Screening magnetic fields by a superconducting disk: a simple model

We introduce a simple approach to evaluate the magnetic field distribution around superconducting samples, based on the London equations; the elementary variable is the vector potential. This procedure has no adjustable parameters, only the sample geometry and the London length, $λ$, determine the solution. The calculated field reproduces quantitatively the measured induction field above MgB$_2$ disks of different diameters, at 20K and for applied fields lower than 0.4T. The model can be applied if the flux line penetration inside the sample can be neglected when calculating the induction field distribution outside the superconductor. Finally we show on a cup-shape geometry how one can design a magnetic shield satisfying a specific constraint.

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