Smooth double critical state theory for type-II superconductors

Abstract

Several aspects of the general theory for the critical states of a vortex lattice and themagnetic flux dynamics in type-II superconductors are examined by a direct variationaloptimization method and widespread physical principles. Our method allows us to unify anumber of conventional models describing the complex vortex configurations in the criticalstate regime. Special attention is given to the discussion of the relation between the fluxline cutting mechanism and the depinning threshold limitation. This is done byusing a smooth double critical state concept which incorporates the so-calledisotropic, elliptical, T and CT models as well-defined limits of our general treatment.Starting from different initial configurations for a superconducting slab in a 3Dmagnetic field, we show that the predictions of the theory range from the collapse tozero of transverse magnetic moments in the isotropic model, to nearly force-freeconfigurations in which paramagnetic values can arbitrarily increase with the applied fieldfor magnetically anisotropic current–voltage laws. Noteworthily, the differencesbetween the several model predictions are minimal for the low applied field regime.