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Open Access Publications from the University of California

A general scaling relation for the critical current density in Nb3Sn

  • Author(s): Godeke, A.
  • Haken, B. ten
  • Kate, H.H.J. ten
  • Larbalestier, D.C.
  • et al.

We review the scaling relations for the critical current density (Jc) in Nb3Sn wires and include recent findings on the variation of the upper critical field (Hc2) with temperature (T) and A15 composition. Measurements of Hc2(T) in inevitably inhomogeneous wires, as well as analysis of literature results, have shown that all available Hc2(T) data can be accurately described by a single relation from the microscopic theory. This relation also holds for inhomogeneity averaged, effective, Hc2*(T) results and can be approximated by Hc2(t)=Hc2(0) = 1-t1.52, with t = T=Tc.Knowing Hc2*(T) implies that also Jc(T) is known. We highlight deficiencies in the Summers/Ekin relations, which are not able to account for the correct Jc(T) dependence. Available Jc(H) results indicate that the magnetic field dependence for all wires from mu0H = 1 T up to about 80 percent of the maximum Hc2 can be described with Kramer's flux shear model, if non-linearities in Kramer plots when approaching the maximum Hc2 are attributed to A15 inhomogeneities. The strain (e) dependence is introduced through a temperature and strain dependent Hc2*(T,e) and Ginzburg-Landau parameter kappa1(T,e) and a strain dependent critical temperature Tc(e). This is more consistent than the usual Ekin unification of strain and temperature dependence, which uses two separate and different dependencies on Hc2*(T) and Hc2*(e). Using a correct temperature dependence and accounting for the A15 inhomogeneities leads to the remarkable simple relation Jc(H,T,e)= (C/mu0H)s(e)(1-t1.52)(1-t2)h0.5(1-h)2, where C is a constant, s(e) represents the normalized strain dependence of Hc2*(0) andh = H/Hc2*(T,e). Finally, a new relation for s(e) 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 withrespect to Jc scaling in Nb3Sn and is therefore of importance to the applied community, who use scaling relations to analyze magnet performance from wire results.

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