A Variational Approach to the Macroscopic Electrodynamics of Anisotropic Hard Superconductors
نویسنده
چکیده
Abstract. 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 Γ-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.
منابع مشابه
A VARIATIONAL APPROACH TO THE EXISTENCE OF INFINITELY MANY SOLUTIONS FOR DIFFERENCE EQUATIONS
The existence of infinitely many solutions for an anisotropic discrete non-linear problem with variable exponent according to p(k)–Laplacian operator with Dirichlet boundary value condition, under appropriate behaviors of the non-linear term, is investigated. The technical approach is based on a local minimum theorem for differentiable functionals due to Ricceri. We point out a theorem as a spe...
متن کاملQuantum terahertz electrodynamics and macroscopic quantum tunneling in layered superconductors.
We derive a quantum field theory of Josephson plasma waves (JPWs) in layered superconductors, which describes two types of interacting JPW bosonic quanta (one heavy and one lighter). We propose a mechanism of enhancement of macroscopic quantum tunneling (MQT) in stacks of intrinsic Josephson junctions. Because of the long-range interaction between junctions in layered superconductors, the calcu...
متن کاملThermal Mechanisms of Stable Macroscopic Penetration of Applied Currents in High Temperature Superconductors and their Instability Conditions
Macroscopic mechanisms of applied current penetration in high-Tc superconductors are discussed to understand the basic physical trends, which are characteristic for the stable and unstable formation of the thermo-electrodynamics states of high-Tc superconductors placed in DC external magnetic field. The performed analysis shows that the definition of the current stability conditions of high-Tc ...
متن کاملElectric field in hard superconductors with arbitrary cross section and general critical current law
The induced electric field E(x) during magnetic flux entry in superconductors with arbitrary cross section Ω and general critical current law, has been evaluated by integration along the vortex penetration paths. Nontrivial flux motion streamlines are obtained from a variational statement of the critical state, which takes the form of an optimization problem on the finite element dis-cretizatio...
متن کاملQuantum-classical crossover in electrodynamics
A classical field theory is proposed for the electric current and the electromagnetic field interpolating between microscopic and macroscopic domains. It represents a generalization of the density functional for the dynamics of the current and the electromagnetic field in the quantum side of the crossover and reproduces standard classical electrodynamics on the other side. The effective action ...
متن کامل