A scaling law for the critical current of Nb3Sn stands based on strong-coupling theory of superconductivity

We study the transition temperature Tc, the thermodynamic critical field Bc, and the upper critical field Bc2 of Nb3Sn with Eliashberg theory of strongly coupled superconductors using the Einstein spectrum α2(ω)F(ω)=λ⟨ω2⟩1∕2δ(ω−⟨ω2⟩1∕2). The strain dependences of λ(e) and ⟨ω2⟩1∕2(e) are introduced from the empirical strain dependence of Tc(e) for three model cases. It is found that the empirical relation Tc(e)∕Tc(0)=[Bc2(4.2K,e)∕Bc2(4.2K,0)]1∕w (w≈3) is mainly due to the low-energy-phonon mode softening. We derive analytic expressions for the strain and temperature dependences of Bc(T,e) and Bc2(T,e) and the Ginzburg-Landau parameter κ(T,e) from the numerical calculation results. The Summers refinement on the temperature dependence of κ(T) shows deviation from our calculation results. We propose a unified scaling law of flux pinning in Nb3Sn strands in the form of the Kramer model with the analytic expressions of Bc2(T,e) and κ(T,e) derived in this work. It is shown that the proposed scaling law gives a r...

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