Comprehensive measurements are reported of the critical current density (J C) of internal-tin and bronze-route Nb 3 Sn superconducting wires as a function of magnetic field (B 23 T), temperature (4.2 K T 12 K) and axial strain (−1.6% ε I 0.40%). Electric field-temperature characteristics are shown to be equivalent to the standard electric field-current density characteristics to within an experimental uncertainty of ∼20 mK, implying that J C can be described using thermodynamic variables. We report a new universal relation between normalized effective upper critical field (B * C2 (0)) and strain that is valid over a large strain range for Nb 3 Sn wires characterized by high upper critical fields. A power-law relation between B * C2 (0, ε I) and T * C (ε I) (the effective critical temperature) is observed with an exponent of ∼2.2 for high-upper-critical-field Nb 3 Sn compared to the value 3 for binary Nb 3 Sn. These data are consistent with microscopic theoretical predictions and suggest that uniaxial strain predominantly affects the phononic rather than the electronic properties of the material. The standard Summers scaling law predicts a weaker strain dependence than is observed. We propose a scaling law for J C (B, T , ε I) based on microscopic theory and phenomenological scaling that is sufficiently general to describe materials with different impurity scattering rates and electron-phonon coupling strengths. It parametrizes complete datasets with a typical accuracy of ∼4%, and provides reasonable predictions for the J C (B, T , ε I) surface from partial datasets.

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) at 10 µV m−1 and the index (n) characterized over the range 10–100 µV m−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%≤εI≤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+rICs, where r 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,ε) 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.

The relationship between the n-value and critical current (I C) is investigated for six different ITER-candidate Nb 3 Sn wires characterized as a function of magnetic field (B 28 T), temperature (4.2 K T 12 K) and intrinsic axial strain (−1% ε I +0.4%). For the five wires exhibiting intrinsic behaviour, n(I C) can be parameterized by a modified power law of the form n = 1 + r I s C , where s is a constant with a value of 0.41 ± 0.03. The parameter r decreases as the magnitude of the intrinsic strain increases and is a relatively weak function of temperature. For one of the wires, the n-value saturates at high critical currents (low magnetic fields), characteristic of extrinsic filament nonuniformities.

The use of helical (Walters) springs is an effective technique for measuring the critical current density (J C ) of superconducting wires in high fields as a function of both compressive and tensile axial strains. We report J C versus strain measurements for Nb 3 Sn wires on a number of helical springs of different materials and geometries, together with results from finite element analysis (FEA) of these systems. The critical current density, n-value and effective upper critical field data are universal functions of intrinsic strain (to within ±5%) for measurements on four different spring materials. The strains on the wire due to the differential thermal contraction of the spring are equivalent to the applied mechanical strains and hence only produce a change in the parameter ε M (the applied strain at the peak in J C ). Variable-strain J C data for springs having turns with rectangular and tee-shaped cross-sections (and hence different transverse strain gradients across the wire) show good agreement when the strain-gauge calibration data are corrected to give the strain at the midpoint of the wire. The correction factors can be obtained from FEA or analytical calculations. Experimental and FEA results show that the applied strain varies periodically along the wire with an amplitude that depends on the spring material and geometry. We suggest that Ti-6Al-4V springs with an integer number of turns and optimized tee-shaped cross-sections enable highly accurate measurements of the intrinsic properties of superconducting wires.

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