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

Published

Author(s)

John (Jack) W. Ekin

Abstract

The unified strain-and-temperature scaling law underlies the many pinning-force model expressions proposed to parameterize the dependence of the critical current Ic on magnetic field B, temperature T, and axial strain ε 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 parameteri-zations are based, as well as the power of raw scaling data that is being lost for model evalua-tion, consistent parameter values, and the potential for simpler measurements for engineering purposes. The unified scaling law (USL) for the flux pinning density FP [{defined as}Ic(B,T,ε) × B] in practical high-field superconductors is expressed by FP = K(t,ε0) f(b) = K(t,ε0) bp(1–b)q , with the following functions and variables: reduced temperature t {defined as} T/Tc*0), strain-dependent critical temperature Tc*0), reduced magnetic field b {defined as} B/Bc2*(t,ε0), effective upper critical field Bc2*(t,ε0), and intrinsic axial strain ε0 {defined as} ε–εm defined as zero at the strain εm where Ic is maximum. The scaling parameters p and q are constants, which is a necessary (but not sufficient) condition for scaling. The strain dependences of Tc* and Bc2* are correlated as tc0) = [bc20)]1/w, where tc0) {defined as} Tc*0)/Tc*0=0) denotes...
Citation
Superconductor Science and Technology
Volume
23
Issue
8

Keywords

critical current, Nb3Sn, scaling law, strain effect, superconductivity, unified scaling law

Citation

W., J. (2010), Unified scaling law for flux pinning in practical superconductors: I. Separability postulate, raw scaling data and parameterization at moderate strains, Superconductor Science and Technology, [online], https://doi.org/10.1088/0953-2048/23/8/083001 (Accessed February 24, 2024)
Created July 13, 2010, Updated November 10, 2018