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.

There is currently no consensus on how best to parameterize the large volume of data produced in measuring the magnetic field (B), temperature (T) and strain (ε) dependence of the engineering critical current density (JE(B, T, ε)) for A15 superconducting strands. For the volume pinning force (FP) and the upper critical field BC2(T, ε), we propose given b = B/BC2(T, ε) and t = T/TC(ε) where TC(ε) is the critical temperature. FP (or JE(B, T, ε)) includes three strain-dependent variables α(ε), BC2(0, ε) and TC(ε) and four constants, n, p, q and v. The form is different to that proposed by Summers et al by a factor T2C(ε). We suggest that the form is sufficiently general to describe superconductors whether the electron–phonon coupling is weak or strong and find that α(ε) is proportional to where Δ(ε) is the superconducting gap and γ(ε) is the Sommerfeld constant. Comprehensive JE(B, T, ε) data are presented for a modified jelly-roll (MJR) Nb3Sn conductor that are consistent with the form proposed with n ≈ 5/2, p = ½, q = 2 and v = 1.374. Hence the scaling law proposed leads to a critical current density for the MJR Nb3Sn given by Comparison with data in the literature suggests that α(ε) ≈ 3 × 10−3μ0γ(ε). Furthermore, the volume pinning force (FP(S/C)) within the Nb3Sn superconducting filaments alone can be described in terms of superconducting parameters in the form where κ(T, ε) is the Ginzburg–Landau parameter.

The engineering critical current density (J E ) and the index of transition, N (where E = αJ N ), of a Nb 3 Al multifilamentary strand, mass-produced as a part of the Fusion programme, have been characterized as a function of field (B), temperature (T ) and strain (ε) in the ranges B 15 T, 4.2 K T 16 K and −1.79% ε +0.67%. Complementary resistivity measurements were taken to determine the upper critical field (B C2 (T , ε)) and the critical temperature (T C (ε)) directly. The upper critical field defined at 5%ρ N , 50%ρ N or 95%ρ N , is described by the empirical relation B ρ N C2 (T , ε) = B ρ N C2 (0, ε) 1 − T T ρ N C (ε) ν . The upper critical field at zero 0953-2048/02/070991+20$30.00 © 2002 IOP Publishing Ltd Printed in the UK b 1 2where the Ginzburg-Landau (GL) parameter κ is given by the relation, γ is the Sommerfeld constant and t = T/T C (ε). At an applied field equal to the upper critical field found from fitting the Kramer dependence (i.e. at B C2 (T , ε)), the critical current is non-zero and we suggest that the current flow is percolative. The functional form of F P implies that in high fields the grain boundary pinning does not limit J E , this is consistent with J E -microstructure correlations in other superconducting materials.

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.

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A probe for investigating the eects of temperature, strain, and magnetic eld on transport critical currents in superconducting wires and tapes.', Review of scientic instruments., 71 (12). pp. 4521-4530.

Systematic variable temperature measurements of the transport critical current density (Jc) tolerance to strain (ε), performed on a bronze processed niobium-tin multifilamentary wire in high magnetic fields up to 15 T, are reported. The results show that Bc2*(T,ε), the field at which the pinning force density (Fp) extrapolates to zero, can be written as Bc2*(0,ε)g[T/Tc*(ε)], where g is a function of the reduced temperature T/Tc*(ε) and Tc*(ε) is the temperature at which Bc2* extrapolates to zero. We propose a magnetic field, temperature, and strain scaling law for Fp which unifies Ekin’s strain scaling law and the Fietz–Webb variable temperature scaling law. It is of the form Fp=Jc×B=A(ε)[Bc2*(T,ε)]nbp(1-b)q, where n, p, and q are constants, A(ε) is a function of strain alone, and b is the reduced field B/Bc2*.

We provide evidence that a single mechanism-flux flow along channels-can explain the functional form of the critical current density (J c) in the low temperature superconductor Nb 3 Sn and in the high temperature superconductors (HTS) YBa 2 Cu 3 O 7-δ (YBCO) and (Bi,Pb) 2 Sr 2 Ca n-1 Cu n O x (BiSCCO) in low and high magnetic fields. In this paper, we show that standard flux pinning theories, used for the last four decades to describe J c in low temperature superconductors (LTS), cannot explain the strain dependence of J c in YBCO because J c is a function of strain but the average superconducting properties are not. We conclude that in the polycrystalline samples presented here, the channels are grain boundaries that are narrow and metallic in Nb 3 Sn and YBCO but wide and semiconducting in BiSCCO. Strain alters J c by changing the superconducting properties of the grains in Nb 3 Sn but by changing the grain boundaries in YBCO.