Critical current scaling and the pivot-point in Nb₃Sn strands

Abstract

Detailed measurements are provided of the engineering critical current density (J c) and the index of transition (n-value) of two different types of advanced ITER Nb 3 Sn superconducting strand for fusion applications. The samples consist of one internal-tin strand (OST) and two bronze-route strands (BEAS I and BEAS II-reacted using different heat treatments). Tests on different sections of these wires show that prior to applying strain, J c is homogeneous to better than 2% along the length of each strand. J c data have been characterized as a function of magnetic field (B ≤ 14.5 T), temperature (4.2 K ≤ T ≤ 12 K) and applied axial strain (−1% ≤ ε A ≤ 0.8%). Strain-cycling tests demonstrate that the variable strain J c data are reversible to better than 2% when the applied axial strain is in the range of −1% ≤ ε A ≤ 0.5%. The wires are damaged when the intrinsic strain (ε I) is ε I ≥ 0.55% and ε I ≥ 0.23% for the OST and BEAS strands, respectively. The strain dependences of the normalized J c for each type of strand are similar to those of prototype strands of similar design measured in 2005 and 2008 to about 2% which makes them candidate strands for a round-robin interlaboratory comparison. The J c data are described by Durham, ITER and Josephson-junction parameterizations to an accuracy of about 4%. For all of these scaling laws, the percentage difference between the data and the parameterization is larger when J c is small, caused by high B, T or |ε I |. The n-values can be described by a modified power law of the form n = 1 + rI s c , where r and s are approximately constant and I c is the critical current. It has long been known that pivot-points (or cross-overs) in J c occur at high magnetic field and temperature. Changing the magnetic field or temperature from one side of the pivot-point to the other changes the highest J c sample to the lowest J c sample and vice versa. The pivot-point follows the B-T phase boundary associated with the upper critical field and is usually attributed to the different tin content profiles and pinning properties of internal-tin and bronze-route strands. We report that the strain dependence of the pivot-point in these strands is quite different from that of the upper critical field and suggest that its origin in optimized high tin content strands is the proximity of the tetragonal Nb 3 Sn phase, which has low superconducting critical parameters.

Weakly-Emergent Strain-Dependent Properties of High Field Superconductors

“…In this canonical description the parameter ε peak specifies the optimum strain state, or equivalently the optimum atomic spacings in the material, for peak superconducting critical parameters such as T c , and therefore should not depend on B and T . Given the very good scaling of F p , it has also been assumed since then that all the material responds to an applied strain in a similar manner and hence measurements of J c provided averaged properties 6,7,15 . However even now, although Nb 3 Sn is to be used in the multi-billion dollar ITER fusion tokamak 36 and the LHC high-luminosity upgrade 37 , uniaxial strain dependent single crystal data (for Nb 3 Sn 38 or any A15 material 39 ) remain very limited.…”

The Biaxial Strain Dependence of <italic>J</italic>C of a (RE)BCO Coated Conductor at 77 K in Low Fields

“…where 0 is the electric field criterion usually taken to be 10 or 100 μVm -1 , 0 1 is the electric field and / is A or B. 1 of domain type / can be calculated using the engineering scaling law [6,[19][20][21][22][23] ,1 = 4% 56,1 , 7( 89 :(-(1 − 9) ; ,1 6 (1 − < 6 ) 6 .…”

Coupled Thermal and Electromagnetic Analysis of the NAFASSY Magnet

“…The self-field and the inductive coupling among CEs are taken into account. The CEs may develop a longitudinal electric field, that in the present case is computed with the Durham scaling law for the OST strand [4], assuming a total axial strain ε = −0.70%, including the intrinsic thermal pre-compression. This value is conservative compared to the typical performance degradation when passing from the individual strand to the jacketed cable [5].…”