The unified strain and temperature scaling law for the pinning force density of bronze-route Nb 3Sn wires in high magnetic fields
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 ( ∊) 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,∊)=J c×B=A(∊)[B c2∗(T,∊)] nb p(1-b) q, where A( ∊) is a function of strain alone, B c2∗ is the effective upper critical field at which Fp 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(∊)(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,∊)=B c2∗(0,∊)(1-(T/T c∗(∊)) ν) , where ν is a constant and T c∗(∊) 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,∊)/T c∗(∊) and the slope (- ∂B c2∗(T,∊)/ ∂T) T=T c∗(∊) 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.