A scaling law for the critical current density of weakly- and strongly-coupled superconductors, used to parameterize data from a technological Nb3Sn strand

Abstract

There is currently no consensus on how best to parameterize the large volume of data produced in measuring the magnetic field (B), temperature (T) and strain (ε) dependence of the engineering critical current density (JE(B, T, ε)) for A15 superconducting strands. For the volume pinning force (FP) and the upper critical field BC2(T, ε), we proposegiven b = B/BC2(T, ε) and t = T/TC(ε) where TC(ε) is the critical temperature. FP (or JE(B, T, ε)) includes three strain-dependent variables α(ε), BC2(0, ε) and TC(ε) and four constants, n, p, q and v. The form is different to that proposed by Summers et al by a factor T2C(ε). We suggest that the form is sufficiently general to describe superconductors whether the electron–phonon coupling is weak or strong and find that α(ε) is proportional towhere Δ(ε) is the superconducting gap and γ(ε) is the Sommerfeld constant. Comprehensive JE(B, T, ε) data are presented for a modified jelly-roll (MJR) Nb3Sn conductor that are consistent with the form proposed with n ≈ 5/2, p = ½, q = 2 and v = 1.374. Hence the scaling law proposed leads to a critical current density for the MJR Nb3Sn given byComparison with data in the literature suggests that α(ε) ≈ 3 × 10−3μ0γ(ε). Furthermore, the volume pinning force (FP(S/C)) within the Nb3Sn superconducting filaments alone can be described in terms of superconducting parameters in the formwhere κ(T, ε) is the Ginzburg–Landau parameter.