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)Ba₂Cu₃O_7-δ (REBCO) coated conductor, and a low temperature superconductor (LTS), a Nb₃Sn 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 Nb₃Sn conductors and that for the LTS Nb₃Sn conductor, the emergent behaviour is not consistent with the long-standing canonical explanation for J_c(ε).