A Variational Approach to the Macroscopic Electrodynamics of Anisotropic Hard Superconductors

We consider Bean's critical state model for anisotropic superconductors. A variational problem solved by the quasi-static evolution of the internal magnetic field is obtained as the Gamma-limit of functionals arising from Maxwell's equations combined with a power law for the dissipation. Moreover, the quasi-static approximation of the internal electric field is recovered, using a first order necessary condition. If the sample is a long cylinder subjected to an axial uniform external field, the macroscopic electrodynamics is explicitly determined.