Critical current scaling laws for advancedNb3Sn superconducting strands for fusion applications with six free parameters

Abstract

This paper presents comprehensive measurements on three advanced ITER internal-tinNb3Sn strands manufactured by Oxford Superconducting Technology (OST), Outokumpu Superconductors(OKSC) and Luvata Italy (OCSI) for fusion applications. The engineering critical current density(JC) at10 µV m−1 and the index(n) characterized overthe range 10–100 µV m−1 are presented as a function of magnetic field(B≤15 T inDurham and B≤28 T at the European high-field laboratory in Grenoble), temperature(2.35 K≤T≤14 K) andintrinsic strain (−1.1%≤εI≤0.5%). Consistency tests show that the variable strainJC data arehomogeneous (± 5%) along the length of the strand, and that there is a good agreement between differentsamples measured in Durham and in other laboratories (at zero applied strain).Limited strain cycling (fatigue) tests demonstrate that there is no significantdegradation in the critical current density in the strands due to cyclic mechanical loads.JC is accurately described by the scaling law that was derivedusing microscopic and phenomenological theoretical analysis andn is described by the modified power law of the formn = 1+rICs,where r and s are approximately constant. Using variable strain high magnetic field data at 2.35 K for theOCSI sample, it is demonstrated that these laws can be extended to describe data below4.2 K. For these advanced strands, thirteen, nine and six free parameter fits to the data areconsidered. When thirteen or nine free parameters are used, the scaling laws fit the datavery accurately. The accuracy with which the scaling law derived from fitting data taken at4.2 K alone fits all the variable temperature data if calculated errors in fittingJC are shown to be primarily determined by uncertainties inTC. It is shown that six free parameter fits can successfully be used when, as with these advancedstrands, the strain dependence of the normalized effective upper critical field at zerotemperature is accurately known—this approach may provide the basis for comparing partialJC(B,T,ε) data on other similar strands from different laboratories. The extensive data presented hereare also parametrized using an ITER scaling law recently proposed for characterizingNb3Sn strands and the strengths and weaknesses of that approach are discussed.