Weakly-Emergent Strain-Dependent Properties of High Field Superconductors

All superconductors in high field magnets operating above 12 T are brittle and subjected to large strains because of the differential thermal contraction between component parts on cool-down and the large Lorentz forces produced in operation. The continuous scientific requirement for higher magnetic fields in superconducting energy-efficient magnets means we must understand and control the high sensitivity of critical current density J(c) to strain ε. Here we present very detailed J(c)(B, θ, T, ε) measurements on a high temperature superconductor (HTS), a (Rare−Earth)Ba(2)Cu(3)O(7−δ) (REBCO) coated conductor, and a low temperature superconductor (LTS), a Nb(3)Sn wire, that include the very widely observed inverted parabolic strain dependence for J(c)(ε). The canonical explanation for the parabolic strain dependence of J(c) in LTS wires attributes it to an angular average of an underlying intrinsic parabolic single crystal response. It assigns optimal superconducting critical parameters to the unstrained state which implies that J(c)(ε) should reach its peak value at a single strain (ε = ε(peak)), independent of field B, and temperature T. However, consistent with a new analysis, the high field measurements reported here provide a clear signature for weakly-emergent behaviour, namely ε(peak) is markedly B, (field angle θ for the HTS) and T dependent in both materials. The strain dependence of J(c) in these materials is termed weakly-emergent because it is not qualitatively similar to the strain dependence of J(c) of any of their underlying component parts, but is amenable to calculation. We conclude that J(c)(ε) is an emergent property in both REBCO and Nb(3)Sn conductors and that for the LTS Nb(3)Sn conductor, the emergent behaviour is not consistent with the long-standing canonical explanation for J(c)(ε).