The strain and temperature scaling law for the critical current density of a jelly-roll Nb3Al strand in high magnetic fields

The engineering critical current density ( J E ) and the index of transition, N (where E = α J N ), of a Nb 3 Al multifilamentary strand, mass-produced as a part of the Fusion programme, have been characterized as a function of field ( B ), temperature ( T ) and strain (ε) in the ranges B ≤ 15 T, 4.2 K ≤ T ≤ 16 K and −1.79% ≤ ε ≤ +0.67%. Complementary resistivity measurements were taken to determine the upper critical field ( B C2 ( T , ε)) and the critical temperature ( T C (ε)) directly. The upper critical field defined at 5%ρ N , 50%ρ N or 95%ρ N , is described by the empirical relation B C2 ρ N ( T , ε) = B C2 ρ N (0, ε)[1 −( T / T C ρ N (ε)) ν ]. The upper critical field at zero Kelvin and the critical temperature are linearly related where B C2 ρ N (0, ε) ≈ 3.6 T C ρ N (ε) − 29.9, although strictly B C2 ρ N (0, ε) is a double-valued function of T C ρ N (ε). J E was confirmed to be reversible at least in the range −0.23% < ε < 0.67%. The J E data have been parameterized using the volume pinning force ( F P ) where F P = J E × B = A (ε) B C2 n ( T , ε) b p (1 − b ) q and b = B / B C2 ( T , ε). A (ε) is taken to be a function of strain otherwise the maximum value of F P (found by varying the field) was a double-valued function of B C2 when the temperature was fixed and the strain varied. To achieve a very high accuracy for the parameterization required by magnet engineers (∼1 A), the data were divided into three temperature–strain ranges, B C2 ( T , ε) described by the empirical relation and the constants p, q, n and ν and the strain-dependent variables A (ε), B C2 (0, ε) and T C (ε) treated as free-parameters and determined in each range. A single scaling law that describes most of the J E data has also been found by constraining B C2 ( T , ε) using the resistivity data at 5%ρ N where ν = 1.25, n = 2.18, p = 0.39 and q = 2.16. When B C2 ( T , ε) is constrained at 50%ρ N or 95%ρ N , the scaling law breaks down such that p and q are strong functions of temperature and q is also a strong function of strain. Good scaling provides support for identifying B C2 5%ρ N ( T , ε) as the characteristic (or average) upper critical field of the bulk material. The J E data are also consistent with a scaling law that incorporates fundamental constants alone, of the Kramer-like form where the Ginzburg–Landau (GL) parameter κ is given by the relation γ is the Sommerfeld constant and t = T / T C (ε). At an applied field equal to the upper critical field found from fitting the Kramer dependence (i.e. at B C2 ( T , ε)), the critical current is non-zero and we suggest that the current flow is percolative. The functional form of F P implies that in high fields the grain boundary pinning does not limit J E , this is consistent with J E -microstructure correlations in other superconducting materials.