A general scaling relation for the critical current density in Nb₃Sn

Abstract

We review the scaling relations for the critical current density (J c ) in Nb 3 Sn wires and include recent findings on the variation of the upper critical field (H c2 ) with temperature (T ) and A15 composition. Measurements of H c2 (T ) in inevitably inhomogeneous wires, as well as analysis of literature results, have shown that all available H c2 (T ) data can be accurately described by a single relation from the microscopic theory. This relation also holds for inhomogeneity averaged, effective, H * c2 (T ) results and can be approximated by H c2 (t)/H c2 (0) = 1t 1.52 , with t = T /T c . Knowing H * c2 (T ) implies that J c (T ) is also known. We highlight deficiencies in the Summers/Ekin relations, which are not able to account for the correct J c (T ) dependence. Available J c (H) results indicate that the magnetic field dependence for all wires from 0 H = 1 T up to about 80% of the maximum H c2 can be described with Kramer's flux shear model, if nonlinearities in Kramer plots when approaching the maximum H c2 are attributed to A15 inhomogeneities. The strain ( ) dependence is introduced through a temperature and strain dependent H * c2 (T , ) and Ginzburg-Landau (GL) parameter 1 (T , ) and a strain dependent critical temperature T c ( ). This is more consistent than the usual Ekin unification of strain and temperature dependence, which uses two separate and different dependences on H * c2 (T ) and H * c2 ( ). Using a correct temperature dependence and accounting for the A15 inhomogeneities leads to the remarkably simple relation