A variational approach to the macroscopic electrodynamics of anisotropic hard superconductors

Details A variational approach to the macroscopic electrodynamics of anisotropic hard superconductors A variational approach to the macroscopic electrodynamics of anisotropic hard superconductors

2006-12-20

arxiv.org/abs/math/0612597v1

Mathematics

Analysis of PDEs

24 pages, 15 figures

Scientific paper

We consider the 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 the 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.

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