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Extrapolative Scaling Expression: A Fitting Equation for Extrapolating Full Ic(B,T,ε) Data Matrixes from Limited Data



John (Jack) W. Ekin, Najib Cheggour, Loren F. Goodrich, Jolene D. Splett, Bernardo Bordini, David Richter, Luca Bottura


Scaling analysis of several thousand Nb3Sn critical-current (Ic) measurements is used to derive the extrapolative scaling expression (ESE), a global fitting equation that can quickly and accurately extrapolate (or interpolate) limited datasets to obtain full three-dimensional dependences of Ic on magnetic field (B), temperature (T), and mechanical strain (ε). Unlike non-extrapolative fitting equations, ESE is based on fundamental raw scaling data from master pinning-force curves. The results show that the ESE relation can extrapolate critical currents at fields, temperatures, and strains that are remarkably different from the fitted minimum dataset, with errors approaching typical Ic measurement errors. The scaling expression is simple and robust, providing straightforward extrapolation capability for conductor characterization and magnet design. The ESE relation offers the prospect for extrapolations in several new areas, including: • A reduction in the measurement space for full Ic(B,T,ε) characterization to about one fifth the size through the use of minimum datasets. • Combining data from separate temperature and strain apparatuses to provide flexibility in data acquisition and productive use of more limited data. • Extrapolation of full Ic(B,T,ε) datasets from as little as a single Ic(B) curve when several core parameters have been measured in similar conductors (particularly applicable to qualifying production wires). Examples are given for practical Nb3Sn conductors, including illustrations of concatenating several of these extrapolations capabilities at the same time.
IEEE Transactions on Applied Superconductivity


Superconductors, strain, scaling, critical current, niobium-tin


W., J. , Cheggour, N. , Goodrich, L. , Splett, J. , Bordini, B. , Richter, D. and Bottura, L. (2017), Extrapolative Scaling Expression: A Fitting Equation for Extrapolating Full Ic(B,T,ε) Data Matrixes from Limited Data, IEEE Transactions on Applied Superconductivity, [online], (Accessed December 7, 2023)
Created January 4, 2017, Updated October 8, 2021