Screening magnetic fields by superconductors: 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. This approach was validated by comparing the induction field calculated to the one measured above MgB2 disks of different diameters, at 20 K and for applied fields lower than 0.4 T. 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. We conclude by showing on a cup-shape geometry how one can design a magnetic shield satisfying a specific constraint