Critical current scaling laws for advanced Nb₃Sn superconducting strands for fusion applications with six free parameters

Abstract

This paper presents comprehensive measurements on three advanced ITER internal-tin Nb3Sn strands manufactured by Oxford Superconducting Technology (OST), Outokumpu Superconductors (OKSC) and Luvata Italy (OCSI) for fusion applications. The engineering critical current density (JC )a t 10μ Vm −1 and the index (n) characterized over the range 10‐100 μ Vm −1 are presented as a function of magnetic field (B 15 T in Durham and B 28 T at the European high-field laboratory in Grenoble), temperature (2.35 K T 14 K) and intrinsic strain (−1.1% eI 0.5%). Consistency tests show that the variable strain JC data are homogeneous (±5%) along the length of the strand, and that there is a good agreement between different samples measured in Durham and in other laboratories (at zero applied strain). Limited strain cycling (fatigue) tests demonstrate that there is no significant degradation in the critical current density in the strands due to cyclic mechanical loads. JC is accurately described by the scaling law that was derived using microscopic and phenomenological theoretical analysis and n is described by the modified power law of the form n = 1 + rI s C ,w herer and s are approximately constant. Using variable strain high magnetic field data at 2.35 K for the OCSI sample, it is demonstrated that these laws can be extended to describe data below 4.2 K. For these advanced strands, thirteen, nine and six free parameter fits to the data are considered. When thirteen or nine free parameters are used, the scaling laws fit the data very accurately. The accuracy with which the scaling law derived from fitting data taken at 4.2 K alone fits all the variable temperature data if calculated errors in fitting JC are shown to be primarily determined by uncertainties in TC. It is shown that six free parameter fits can successfully be used when, as with these advanced strands, the strain dependence of the normalized effective upper critical field at zero temperature is accurately known—this approach may provide the basis for comparing partial JC(B, T ,e )data on other similar strands from different laboratories. The extensive data presented here are also parametrized using an ITER scaling law recently proposed for characterizing Nb3Sn strands and the strengths and weaknesses of that approach are discussed.