The unified strain and temperature scaling law for the pinning force density of bronze-route Nb 3Sn wires in high magnetic fields

Abstract

Detailed measurements of the critical current density ( J c) 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 F p (B,T,ε)=J c ×B=A(ε)[B c2 ∗(T,ε)] nb p(1−b) q , where A( ε) is a function of strain alone, B c2 ∗ is the effective upper critical field at which F p extrapolates to zero, b=B/B c2 ∗ is the reduced magnetic field and n, p and q are constants. It is demonstrated that were A(ε)(B c2 ∗) n replaced by F(T)(B c2 ∗) 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 B c2 ∗(T,ε)=B c2 ∗(0,ε)(1−(T/T c ∗(ε)) ν) , where ν is a constant and T c ∗(ε) is the effective critical temperature at which B c2 ∗ at a given strain extrapolates to zero. The strain dependence of the ratio B c2 ∗(0,ε)/T c ∗(ε) and the slope (− ∂B c2 ∗(T,ε)/ ∂T) T=T c ∗(ε) is reported. The data presented are useful for cryocooled high field magnets and for identifying the mechanisms that determine J c in niobium–tin superconducting wires.