Smooth double critical state theory for type-II superconductors

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