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 (epsilon) dependence of the engineering critical current density (J(E)(B, T, epsilon)) for A 15 superconducting strands. For the volume pinning force (F-p) and the upper critical field B-C2(T, epsilon), we propose F-P = J(E)(B, T, epsilon) x B = alpha(epsilon)[T-C(epsilon)(1-t(2))](2) x [B-C2(T, epsilon)](n-2)/(2piPhi(0))(1/2)mu(0) b(p)(1-b)(q) and B-C2(T, epsilon) = B-C2(0, epsilon)[1-t(p)] given b = B/B-C2(T, epsilon) and t = T/T-C(epsilon) where T-C(epsilon) is the critical temperature. F-p (or J(E)(B, T, epsilon)) includes three strain-dependent variables alpha(epsilon), B-C2 (0,epsilon) and T-C(epsilon) and four constants, n, p, q and v. The form is different to that proposed by Summers et al by a factor T-C(2) (epsilon). We suggest that the form is sufficiently general to describe superconductors whether the electron-phonon coupling is weak or strong and find that alpha(epsilon) is proportional to mu(0)gamma(epsilon)/[1 - 1/5(2Delta(epsilon)/k(B)T(C)(epsilon) - 3.53)] where Delta(epsilon) is the superconducting gap and gamma(epsilon) is the Sommerfeld constant. Comprehensive J(E)(B, T, epsilon) data are presented for a modified jelly-roll (MJR) Nb3Sn conductor that are consistent with the form proposed with n approximate to5/2, p = 1/2, q = 2 and v = 1.374. Hence the scaling law proposed leads to a critical current density for the MJR Nb3Sn given by J(E)(B, T, epsilon) approximate to alpha(epsilon)/(2piPhi(0))(1/2)mu(0) [T-C(epsilon)(1 - t(2))]B-2(C2)-1/2(T, epsilon)b(-1/2)(1 - b)(2). Comparison with data in the literature suggests that alpha(epsilon) approximate to 3 x 10(-3)mu(0)gamma(epsilon). Furthermore, the volume pinning force (F-P(S/C)) within the Nb3Sn superconducting filaments alone can be described in terms of superconducting parameters in the form F-P(S/C) approximate to 1/100 B-C2(5/2)(T, epsilon)/(2piPhi(0))(1/2)mu(0)x(2)(T, epsilon) b(1/2)(1 - b)(2) where K(T, c) is the Ginzburg-Landau parameter.