The strain-dependence of the critical current density in the high-field superconductor Nb(_3)Sn

Abstract

Measurements of the critical current density (J_c) of Nb(_3)Sn superconducting wires were performed as a function of magnetic field (B ≤ 23 T), temperature (4.2 K ≤ T ≤ 12 K), and axial strain (-1.6% ≤ ɛ ≤ 0.7%). Data are presented for wires measured on helical strain springs of different materials and geometries, together with results from finite element analysis (FEA) of these systems. It is demonstrated that the differential thermal contraction of the spring only affects the behaviour of the wire via a change in the parameter ɛ(_M) (the applied strain at the peak), and that the data for different spring geometries show good agreement when the strain is calculated at the midpoint of the wire using FEA. Strain cycling measurement show that the critical current density and n-value behave reversibly for applied strains up to 0.3% (-500 cycles), increase irreversibly for strains up to 0.6% (-1000 cycles in total), and decrease irreversibly at higher strains (˃0.75%). Comparisons of electric field-temperature characteristics (as measured for the ITER model coils) with the standard electric field-current density characteristics show agreement to within an experimental uncertainty of-20 mK. Comprehensive J(_c)(B, T, ɛ(_1)) data are presented for two ITER Nb(_3)Sn wires, which are characterised by high effective upper critical fields [B(_c2)(0)]. A new universal relation between normalised [B(_c2)(0)]and strain is reported, which shows a stronger strain-dependence than previous data for binary Nb(_3)Sn. A power-law relation between B(_c2)(0, ɛ,) and T(_c)( ɛ,) (the effective critical temperature) is observed with an exponent of -2.2, compared to the value > 3 for binary Nb(_3)Sn. This is in agreement with microscopic theory, which predicts a power law with an exponent that is lower for dirtier materials, and also shows that the uniaxial strain effects are predominantly due to changes in the phonon properties. A new general scaling law is proposed that parameterises complete J(_c)(B,T, ɛ) datasets with a typical accuracy of -4%, and also provides reasonable predictions from partial datasets.