A general scaling relation for the critical current density in Nb 3 Sn

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 , 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 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 κ 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 , where C is a constant, s ( ) represents the normalized strain dependence of H c2 * (0) and h = H / H c2 * ( T , ). Finally, a new relation for s ( ) is proposed, which is an asymmetric version of our earlier deviatoric strain model and based on the first, second and third strain invariants. The new scaling relation solves a number of much debated issues with respect to J c scaling in Nb 3 Sn and is therefore of importance to the applied community, who use scaling relations to analyse magnet performance from wire results.