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

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 ( J E ( B , T , ε)) for A15 superconducting strands. For the volume pinning force ( F P ) and the upper critical field B C2 ( T , ε), we propose given b = B / B C2 ( T , ε) and t = T / T C (ε) where T C (ε) is the critical temperature. F P (or J E ( B , T , ε)) includes three strain-dependent variables α(ε), B C2 (0, ε) and T C (ε) and four constants, n , p , q and v . The form is different to that proposed by Summers et al by a factor T 2 C (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 to where Δ(ε) is the superconducting gap and γ(ε) is the Sommerfeld constant. Comprehensive J E ( B , T , ε) data are presented for a modified jelly-roll (MJR) Nb 3 Sn 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 Nb 3 Sn given by Comparison with data in the literature suggests that α(ε) ≈ 3 × 10 −3 μ 0 γ(ε). Furthermore, the volume pinning force (F P(S/C) ) within the Nb 3 Sn superconducting filaments alone can be described in terms of superconducting parameters in the form where κ( T , ε) is the Ginzburg–Landau parameter.