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We present a model for the variation of the upper critical field H c2 with Sn content in A15-type Nb-Sn wires, within the Ginzburg-Landau-Abrikosov-Gor’kov (GLAG) theory frame. H c2 at the vicinity of the critical temperature T c is related quantitatively to the electrical resistivity ρ, specific heat capacity coefficient γ and T c. H c2 versus tin content is theoretically formulated within the GLAG theory, and generally reproduces the experiment results. As Sn content gradually approaches the stoichiometry, A15-type Nb-Sn undergoes a transition from the dirty limit to clean limit, split by the phase transformation boundary. The H-T phase boundary and pinning force show different behaviors in the cubic and tetragonal phase. We dipict the dependence of the composition gradient on the superconducting properties variation in the A15 layer, as well as the curved tail at vicinity of H c2 in the Kramer plot of the Nb3Sn wire. This helps understanding of the inhomogeneous-composition inducing discrepancy between the results by the state-of-art scaling laws and experiments.

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We introduce a critical-state model incorporating the anisotropy of flux-line pinning to analyze the critical states developing in an anisotropic biaxial superconducting slab exposed to a uniform perpendicular magnetic field and to two crossed in-plane magnetic fields which are applied successively. The theory is an extension of the anisotropic collective pinning theory developed by Mikitik and Brandt. The anisotropic flux-line pinning enters into the critical states by generating the angular dependence of the critical current density and by deviating the direction of the electric field from the current in the plane perpendicular to the vortex line. Comparing to the isotropic case, the anisotropic flux pinning strongly influences the magnetic response in the slab. We also apply the critical-state model to predict the underlying physical phenomenon of a field-cooled slab in a rotating magnetic field. IntroductionThe critical-state model in Type-II superconductors is first introduced by Bean [1, 2]. The component J ⊥ of the current density J perpendicular to the magnetic induction B is restricted to the threshold c J ⊥ for flux depinning, c J J ⊥ ⊥ = . The vortex moves whenever the driving Lorentz L f J B ⊥ = exceeds the average pinning force c p f J B ⊥ = ,thus causing a local flux-transport electric field [3]. As it only contains physics of flux pinning, Bean model solves the critical states in a symmetric superconductor exposed to an external magnetic field that is applied along the symmetry axis [1] [4, 5] [6] [7-9]. The Bean critical states also describe the most cases of practical interest, such as in superconducting magnets where the self-field is generally perpendicular to the local current flow [10] and in HTS ac power cables [11]. If J is not perpendicular to the magnetic field H ( 0 µ = B H is a good approximation for high-κ superconductors [12]), as expected in the samples with nonsymmetrical geometry or excited by the magnetic field that varies in both magnitude and direction [13-16], the vortex lines may tilt each other. To avoid flux-line cutting, there is † Current address:a maximum gradient of the tilt angle α such that the component J  of J along H is constrained to the threshold c J  . The fundamental physics is the local helical instability in a vortex with a sufficiently large J  [17-19]. Flux-line cutting explains the first onset of a nonvanishing parallel component E  of the electric field at c J J ≥   [20]. This is put into the generalized double-critical-state model (GDCSM) by Clem and the coauthors [21-23], accounting for both flux cutting and flux transport in the critical states. Assuming uncoupled flux transport and flux cutting, GDCSM sketches a rectangular of c ( , ) J J J ⊥  in the J J ⊥ −  plane. GDCSM successfully predicts the experimental magnetic response of high-temperature superconducting plates [24] and YBCO thin film [25] in which B is inclined with J . In practical applications, this theory allows to calculate the AC loss in power transmission cables with second gene...

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