Unified scaling law for flux pinning in practical superconductors: I. Separability postulate, raw scaling data and parameterization at moderate strains

Abstract

The unified strain-and-temperature scaling law underlies the many pinning-force-model expressions proposed to parameterize the dependence of the critical current I c on magnetic field B, temperature T and applied axial strain ε in superconductors for high-field magnet design. Increasingly, these expressions have been evaluated by use of multiparameter simultaneous fits, without the use of scaling. In this review, we reintroduce the unified scaling law on which the recent parameterizations are based, as well as the power of raw scaling data for parameter consistency, extrapolation capability and data-based model evaluation.The unified scaling law (USL) for the flux-pinning force per unit conductor length F P [≡I c (B, T, ε)B] in practical high-field superconductors is expressed bywhere K (t, ε 0 ) is a temperature-and-strain dependent prefactor. The scaling variables are: reduced magnetic field b ≡ B/B * c2 (t, ε 0 ) with B * c2 (t, ε 0 ) an effective upper critical field; reduced temperature t ≡ T /T * c (ε 0 ) with T * c (ε 0 ) an effective strain-dependent critical temperature; and intrinsic axial strain ε 0 ≡ ε − ε m defined as zero at the strain ε m , where I c is maximum. The scaling parameters p and q are constants, which is a necessary (but not sufficient) condition for scaling. The strain dependences of T * c and B * c2 are correlated as) is also designated as s(ε 0 ) in the recent literature). It is shown that, when raw scaling data are used to determine the scaling parameter w, it has a constant value w ≈ 3.0 ± 0.1 in a wide range of Nb 3 Sn superconductors. This is significant, because w is the only scaling parameter that requires very large data matrices of I c (B, T, ε) to determine its value. Unified scaling has been demonstrated in a number of different superconducting materials, including Nb 3 Sn, Nb 3 Al and more recently, the fundamentally distinct MgB 2 and Bi-2223 material systems. * This article is based in part on the presentation 'Unified strain-and-temperature scaling law: separable parameter set' given at the Mechanical and Electromagnetic Properties of Composite Superconductors Conference (Princeton, NJ, Aug. 2007). Trade names are used for identification purposes only and do not imply endorsement by NIST. Contribution of US Government, not subject to US copyright.

Maximum Entropy Distributions Describing Critical Currents in Superconductors

“…The retention of the same , with temperature scaling, if it applies, shows that temperature is not altering any important relative length scales, or pinning potentials that determine the shape of F(b). In contrast it is known that changes in microstructure will alter the fitting parameters , for some superconductors [1,20] and between different superconductors there are considerable variations.…”

“…Various explanations have been offered for this, but without consensus. The same shape implies that data over multiple conditions can be scaled to a common curve, a useful property for constructing empirical models used in engineering of devices [20].…”

“…This procedure is also known to apply to LTS data as a function of temperature and strain [20]. At different angles the accommodation of the vortices to the pinning landscape in a Bi-2223 wire must be very different as it is a highly anisotropic material and the wire is well textured.…”

Magnetic irreversibility and pinning force density in the Mo100− Re alloy superconductors

“…A detailed analysis of F p (H) in terms of the size, spacing and nature of the pinning centers, and the nature of their interaction with the flux lines has been done by Dew-Hughes [27], and we have presented a similar analysis in a recent work [21]. To investigate into the flux line pinning mechanisms in the present alloys using DewHughes model, we have used a normalized field h, where h ¼ l 0 H l 0 H Ã , H ⁄ being the field at which the (approximately) linearly falling portion of the F p versus l 0 H curves (in the higher H side) extrapolate to F p = 0 [24,28]. We have found that the F p ðhÞ curves for the present alloys cannot be fitted by any of the functions of form F p 1h p ð1 À hÞ q , where the values of p and q depend on the details of the pinning mechanism, as prescribed by Dew-Hughes [24,27].…”

The Influence of Ex Situ MgB2Barrier and HIP on the IcAnisotropy in Double Core MgB2/Cu Wires

“…This wire has had low anisotropy in a range from 3 to 5%. The scaled pinning force on magnetic field of our Cu shield wires determines dominant of pinning mechanism as the grain boundary mechanism [9,10]. The evaluated from scaling process parameter p is close to 0.5 and appropriate q parameter is almost equal to 2 -all suggested the dominant grains boundary pinning (Fig.…”