Inconsistencies between extrapolated and actual critical fields in Nb ₃ Sn wires as demonstrated by direct measurements of H _c2 , H* and T _c

Scaling of the pinning force (F _p ) with temperature, field and strain for Nb ₃ Sn wires is widely discussed but important issues are still unresolved, for example whether empirical engineering-oriented scaling functions can be replaced by more microscopic, physics-based models, which take account of the fact that F _p becomes zero at an irreversibility field (H*) less than the upper critical field (H _c2 ). In the present work we compare earlier extensive measurements of the critical current density (J _c ) of an ITER-benchmark bronze wire to new measurements of H* and H _c2 . Our study was also made in different strain states. We observe that the Kramer extrapolations, which are based on transport data taken up to 13 T, significantly overestimate the low temperature, high field behaviour and also underestimate the critical temperature (T _c ) at zero field. An attempt is made to connect measured H _c2 (T, ε) data on this practical conductor to microscopic theory. We also discuss the inevitable differences that occur between fully penetrated J _c data which average over all the A15 layers and small current-density probes of the H _c2 transition which are characteristics of the best part of the layer. We connect in this way the large-scale 'average' characteristics J _c (H, T, ε) to small current 'best' characteristics of H _c2 (T, ε).