The unified strain and temperature scaling law for the pinning force density of bronze-route Nb3Sn wires in high magnetic fields Original Research Article

Detailed measurements of the critical current density (Jc) of a bronze-route niobium–tin wire are presented for magnetic fields (B) up to 15 T as a function of temperature (T) from 6 K up to 16 K in the strain (ε) range between −0.7% and +0.7%. The data for this technological wire are described by a unified strain and temperature scaling law for the pinning force density of the form Fp(B,T,ε)=Jc×B=A(ε)[Bc2∗(T,ε)]nbp(1−b)q, where A(ε) is a function of strain alone, Bc2∗ is the effective upper critical field at which Fp extrapolates to zero, b=B/Bc2∗ is the reduced magnetic field and n, p and q are constants. It is demonstrated that were A(ε)(Bc2∗)n replaced by F(T)(Bc2∗)m where F(T) is a function of temperature alone, the strain index m is a strong function of temperature and strain, and in high compression m=n. The effective upper critical field can be parameterized using the expression Bc2∗(T,ε)=Bc2∗(0,ε)(1−(T/Tc∗(ε))ν), where ν is a constant and Tc∗(ε) is the effective critical temperature at which Bc2∗ at a given strain extrapolates to zero. The strain dependence of the ratio Bc2∗(0,ε)/Tc∗(ε) and the slope (−∂Bc2∗(T,ε)/∂T)T=Tc∗(ε) is reported. The data presented are useful for cryocooled high field magnets and for identifying the mechanisms that determine Jc in niobium–tin superconducting wires.