A procedural solution for determining the temperature dependence of transport critical current in Nb$_{3}$Sn superconducting wires using magnetization measurements

Using magnetization techniques to determine the temperature dependence of critical current in Nb$_{3}$Sn wires is attractive because of the relative ease compared with using variable-temperature transport measurements. However, there is a known mismatch in the temperature scaling characterizations when using magnetization data compared to transport data. From a practical standpoint, it is the transport properties that matter, as performance prediction, margin calculations, and other aspects of magnet designs rely on the knowledge of the amount of transport current the superconductor can carry in a magnetic field. In this paper, we will identify the underlying issues and propose a procedural solution for determining the temperature dependence of transport critical current in Nb$_{3}$Sn superconducting wires using magnetization measurements. By using one standard transport measurement at 4.2 K as an ‘anchor’, with this procedural solution it becomes possible to combine the simplicity and economy of quick magnetization measurements at different temperatures with the accurate prediction of transport properties in extrapolated temperature ranges. This study is based on experimental data using internal tin-type wire, but we also address the theoretical implications that would be generally applicable to other wire designs. The strength of our analysis is that our work leads to proposed procedures that improve the accuracy of the temperature scaling even if the assumed pinning curve shape does not fit the data as well at some temperatures, whether those temperatures are close to 4.2 K or to T $_{C}$.