Tests of advanced Nb 3 Sn strands

Tests of advanced Nb 3 Sn strands David M.J. Taylor and Damian P. Hampshire Superconductivity Group, Physics Department, Durham University, Durham DH1 3LE, UK ontract. No.: EFDA/3-1126. ritical urrent Density (1 8 Am 2 ) 8 Temperature (K) 4 6 6 4 8 2 1. -.25 -.5 -.75-1. 7 9 11 13 Magnetic Field (T) The four-dimensional J ( BT,,ε I ) surface for the OST strand

ii AKNOWLEDGEMENTS The authors acknowledge the help and support of N. Mitchell, E. Salpietro, A. Portone, A. Vostner and E. Mossang and the very helpful discussions with R. Zanino. We also acknowledge the many discussions we have had with those in the community including: D. Bessette, D. Bruzzone, N. heggour, J. Duchateau, J. Ekin, W H Fietz, H. Fillunger, B. Karlemo, P. Komarek, R. Maix, N Martovetsky, J. Minervini, A. Nyilas, A Nijhuis, A. Portone, K. Osamura, L. Savoldi Richard, J. Schultz and A. Ulbricht.

iii EXTENDED ABSTRAT This report presents work carried out under EFDA contract 3-1126, comprising a comprehensive characterisation of the advanced ITER Nb 3 Sn strands manufactured by OST and Outokumpu (OKS). The data are required for reliable full-size conductor design. omprehensive measurements are reported of the engineering critical current density (J ) at 1 μvm 1 as a function of magnetic field (B 28 T), temperature (4.2 T 14 K) and intrinsic strain ( 1.1% ε I.2%). The n-value in the range 1 1 μvm 1 was also measured over the same range of parameter space. onsistency tests show that the variable-strain J data are homogeneous (±5%) along the length of the strand, and that there is good agreement between different samples measured in Durham and in other laboratories (at zero applied strain). A scaling-law parameterization is presented that provides an accurate fit (±2 A) to the measured J ( ) B, T, ε data. This scaling law is fully consistent with work on previous-generation ITER-candidate conductors for example, showing a similar intrinsic strain-dependence for the normalised effective upper critical field and the normalised critical current density (although the advanced strands have I higher by a factor of ~2). In addition, critical temperature (and upper critical field) data, generally defined at.5 A and 1 μvm 1, are presented as a function of field and strain. Short strain-cycling (fatigue) tests demonstrate that there is no significant degradation in the critical current density in the strands due to cyclic mechanical loads. Accompanying this report is a spreadsheet that contains tabulations of the J and n-value data, as well as the scaling-law parameterisation of J ( B, T, ε ).

iv TABLE OF ONTENTS 1 INTRODUTION... 1 2 EXPERIMENTAL PROEDURE... 2 3 RESULTS AND ANALYSIS... 6 3.1 onsistency tests... 6 3.2 ritical current density data and parameterisation... 9 3.3 n-value results... 15 3.4 ritical temperature results... 16 3.5 Strain-cycling results... 19 4 REFERENES... 21

1 1 INTRODUTION The critical current density (J ) of Nb 3 Sn strands depends on magnetic field (B), temperature (T) and strain (ε) 1-7, with uniaxial strain generally accepted as the most important component. 8-1 The design of large-scale magnets such as for the International Thermonuclear Experimental Reactor 11 requires accurate J ( ) B, T, ε data for the component Nb 3 Sn strands, as well as scaling-law parameterisations to interpolate/extrapolate the data 2,7,12. A number of model coils were recently tested for ITER 13-15, motivating the investigation of advanced Nb 3 Sn strands with higher critical current densities as candidates for the ITER conductors. The full characterisation of these advanced strands requires facilities capable of performing variable-field, temperature and strain critical current density measurement 2,16. The group at Durham University has such a facility, and have been involved in a number of previous strand characterisation tasks (e.g. EFDA contracts -515, 2-662, 3-113) 17-19. In this report, we present the results of J ( B, T, ε ) measurements, as well as n-value, critical temperature and strain-cycling (fatigue) data, for the advanced Nb 3 Sn strands manufactured by OST and Outokumpu (OKS). There is currently no consensus on the best approach to parameterising J ( B T ),, ε data. In previous work 12,18, we showed that the standard Summers Scaling Law 7,2 was not accurate for a number of ITER-candidate conductors and proposed a new scaling law based on comprehensive experimental data and theoretical considerations this new scaling law is also used to parameterise the J ( ) B, T, ε data presented here. The remainder of this report is structured as follows: Section 2 outlines the experimental procedure, while Section 3 presents the experimental results, analysis and discussion. Section 3.1 presents the results of a number of consistency tests addressing homogeneity and intersample and interlaboratory comparisons; Section 3.2 presents the J ( B T ),, ε data and the scaling-law parameterization for the two strands; Section 3.3 presents n-value data and Section 3.4 presents critical temperature and upper critical field data; finally, the results of limited strain-cycling (fatigue) tests are presented in Section 3.5.

2 2 EXPERIMENTAL PROEDURE Measurements were performed on two types of advanced Nb 3 Sn strands: OST [billet 7567-2 (back end), received June 24] and Outokumpu (OKS) [billet NT681 (outer), received Oct. 24]. The wires were chrome plated, mounted on oxidised stainless steel mandrels and then heat-treated under argon in a three-zone furnace using the schedules shown in Table 1. The wires were then etched in hydrochloric acid to remove the chrome and transferred to nickel-plated Ti 6Al 4V helical springs, to which they were attached by copper plating and soldering. The helical springs used for both strands have the same optimised tee-shaped cross-section 21,22 ; the OST strand was measured on a spring with four-and-a-half turns (see Figure 1), while the OKS strand was measured on a four-turn spring. Table 1 Heat-treatment schedules for the OST and OKS strands. OST strand Ramp at 1 /h to 21 and hold for 5 h Ramp at 1 /h to 34 and hold for 25 h Ramp at 1 /h to 45 and hold for 25 h Ramp at 1 /h to 575 and hold for 1 h Ramp at 1 /h to 65 and hold for 1 h OKS strand Ramp at 1 /h to 185 and hold for 24 h Ramp at 5 /h to 46 and hold for 48 h Ramp at 5 /h to 575 and hold for 1 h Ramp at 5 /h to 65 and hold for 175 h Ramp at 25 /h to room temperature Ramp at 1 /h to room temperature The Durham strain probe 16,21 (see Figure 2) was used to carry out voltage current (V I) measurements on the strands as a function of magnetic field (B), temperature (T) and applied axial strain (ε Α ). The spring is twisted to apply the strain to the wire via concentric shafts: the inner shaft connects a worm-wheel system at the top of the probe to the top of the spring, and the outer shaft is connected to the bottom of the spring via an outer can. For measurements at 4.2 K, the outer can contains a number of holes to admit liquid helium from the surrounding bath, whereas for variable-temperature measurements, the outer can forms a vacuum space around the sample with a copper

3 Figure 1 Photograph of a superconducting strand mounted on a tee-shaped spring (diameter: 22 mm). gasket and knife edge seal between the can and the outer shaft. In this case, the temperature is controlled via three independent ernox thermometers and constantan wire heaters 23. The voltage across a section of the wire (typical length: ~2 mm) was measured using a nanovolt amplifier and a digital voltmeter. J measurements were performed at constant temperature with a slowly-increasing current; zero-field T measurements were performed at a small constant current with a slowly-increasing temperature. One sample of the OST strand and one sample of the OKS strand were measured at the European high-field laboratory in Grenoble, using a similar experimental procedure for both strands. J measurements were first performed using the variable-temperature enclosure at temperatures of 6, 8, 1 and 12 K and at applied strains up to +.3% and down to.8% (the OKS strand was also measured at 14 K). Additional J measurements at 4.2 K were also performed on the OST strand during the first tensile applied strain cycle. ritical temperature measurements were then performed for applied strains between.8% and +.3%, in zero magnetic field using a D current of.1 A for the OST strand and.5 A for the OKS strand (see Section 3.4). The strain was then set to zero and the probe warmed to room temperature so that the 4.2 K enclosure could be fitted. Variable-field J measurements were then performed at 4.2 K at applied strains up to +.3% and down to 1%. Finally the wire was subject to a small number (five) of

4 ( ) Figure 2 Schematic diagrams of the top and bottom parts of the J B, T, ε probe (reproduced from heggour and Hampshire 16 ). strain cycles up to +.4% and down to.8% applied strain, during which a number of additional J measurements were performed. In addition, a second OKS sample was measured at a temperature of 4.2 K, in magnetic fields up to 15 T in Durham, where the experimental conditions enable currents up to ~45 A to be used. A subset of the data obtained for the OST strand at temperatures above 4.2 K and compressive applied strains below.39% was later found to be unreliable (inconsistent with the rest of the dataset and any reasonable scaling-law parameterisation). Reversibility measurements (see Section 3.5) demonstrate that this was not due to damage to the strand; the possible explanation was a short-circuit of the current leads in the probe. In addition, the data obtained at compressive applied strains for the second OKS sample (measured in Durham) have been discarded, as two sections of the strand exhibited irreversible changes in J after straining to 1.%. None of the data obtained at compressive applied strains can be demonstrated to be reversible and hence are not reliable. In contrast, the J data at zero applied strain was found to be reversible to within ~.5% after tensile strains were applied to the strand. Furthermore, the compressivestrain data for the second OKS sample did not agree with the equivalent data obtained

5 on the first OKS sample (measured in Grenoble). The irreversible changes observed were possibly indicative of a breakage within the strand or in the bonding between the strand and the spring. This report presents critical current (I ) and engineering critical current density (J ) data defined at an electric-field criterion of 1 μvm 1, where the latter is calculated by dividing the critical current by the total cross-sectional area of the wire (5.153 1 7 m 2 ). J was calculated using the value of current in the wire alone, obtained by subtracting the current in the normal shunt (typically 5 ma) from the total current 24. However, the critical temperature data and the interpolated upper critical field data (see Section 3.4) are obtained using the total current (i.e. including the shunt current). 5 4 Data discarded B = 8 T 3 2 1 15 T OKS strand Sample 2-1. -.8 -.6 -.4 -.2..2 Applied Strain (%) Figure 3 ritical current versus applied strain data for the second OKS strand (measured in Durham) at 4.2 K and half-integer values of magnetic fields. The symbols show the measured data; the dashed lines are guides to the eye. Data at compressive applied strains (enclosed by the rectangle) were discarded and not used in the analysis. This was because irreversible changes in J were observed for two different sections of the strand after straining to 1.%. Data are considered unreliable if they are not reversible. The only data considered reliable from the second sample were the tensile strain data where after tensile strain measurements, J at zero applied strain agreed with the original measurement to within ~.5%. Note that for the first OKS strand, measurements presented and used in the parameterisation for J in high fields were reversible after both tensile and compressive measurements.

6 3 RESULTS AND ANALYSIS 3.1 onsistency tests Figure 4 shows electric field current data obtained for four different sections of the OKS strand at 4.2 K and zero applied strain (before any strain cycling). Each section is ~2 mm long and separated from neighbouring sections by ~15 mm. It can be seen that this wire has homogeneous properties for example, the critical currents at 1 μvm 1 agree to within ~1% for each section. omparable levels of agreement were observed for all the samples investigated prior to strains being applied. Figure 5 shows variable-strain critical current data at 4.2 K for two different sections of the OST and OKS strands. The I values are seen to agree typically to within ±5%. The different sections have values of ε M (the applied strain at the peak) that vary by ~.4% (OST) and ~.2% (OKS). Figure 6 compares I and n-value data obtained on the two different OKS samples (measured in Durham and Grenoble) at 4.2 K and zero applied strain. In both cases, the data lie on a single curve, demonstrating that the data for the two samples are consistent. Figure 7 shows a comparison of our data for the OST strand with the manufacturer s data at 4.2 K and zero applied strain. The critical currents and n-values again show a good level of agreement. Figure 7 also confirms the accuracy of the extrapolation to low fields (high currents) made using the scaling-law parameterisation (see section 3.2).

7 25 Electric field (μvm 1 ) 2 15 1 OKS strand Zero applied strain B = 14 T Tap A Tap B Tap Tap D 5 5 1 15 2 25 urrent (A) Figure 4 Plots of electric field versus current for four different sections of the OKS strand at 4.2 K, 14 T and zero applied strain (before any strain cycling). The symbols show the measured data (every fourth data point is plotted). 25 (a) 12 (b) 2 15 1 OST Tap 1 Tap 2 B = 14 T 16 T 1 8 6 4 OKS Tap 1 Tap 2 B = 17 T 18 T 5 2-1.2-1. -.8 -.6 -.4 -.2..2.4 Applied Strain (%) -1. -.8 -.6 -.4 -.2..2.4 Applied Strain (%) Figure 5 Homogeneity of the critical current as a function of applied strain at 4.2 K and different magnetic fields for (a) the OST and (b) the OKS strands. The symbols show the measured J data (at 1 μvm 1 ) for two different sections of the wire; the dashed lines are guides to the eye.

8 4 35 35 3 25 2 15 1 OKS strand Zero applied strain n-value (dimensionless) 3 25 2 15 1 5 8 1 12 14 16 18 2 22 24 26 Magnetic Field (T) 5 OKS Sample 1 OKS Sample 2 Scaling-law fit 8 1 12 14 16 18 2 22 24 26 Magnetic Field (T) Figure 6 Intersample comparisons of the critical current (main graph) and n-value (inset) of the OKS strand at zero applied strain and 4.2 K as a function of magnetic field. The symbols show the measured data for the two OKS samples; the solid line shows the scaling-law fit for J (Equations (1) (5) and Table 3); the dashed line in the inset is a guide to the eye. 4 35 35 3 25 2 15 1 5 OST strand Zero applied strain Manufacturer Durham Scaling-law fit n-value (dimensionless) 3 25 2 15 1 5 1 12 14 16 18 2 22 24 26 1 12 14 16 18 2 22 24 26 Magnetic Field (T) Magnetic Field (T) Figure 7 Interlaboratory comparisons of the critical current (main graph) and n-value (inset) of the OST strand at zero applied strain and 4.2 K as a function of magnetic field. The symbols show data measured by the manufacturer 25 and in Durham; the line shows the scaling-law fit for J (Equations (1) (5) and Table 2).

9 3.2 ritical current density data and parameterisation The J ( B, T, ε ) data at 1μVm 1 are parameterised using the scaling law described previously 12,26, which involves the following relations: 2 3 (,, ) ( ) * ( )( 1 2 ) * (, ) n p ε ε ε ε 1 ( 1 ) J B T I = A I T I t B2 T I b b (1) (, ε ) (, ε )( 1 ) B T = B t ν (2) * * 2 I 2 I q ( ) ( ) (, ) ( ) 1 u 1 w * * I 2 I = = * * 2 ( I) ( ) A ε B ε T ε A B, T (3) B (, ε ) (,) * 2 I 2 3 4 = 1+ c2ε * I + c3εi + c4εi 2 B, (4) ε = ε ε, (5) I A M where J is the engineering critical current density (the critical current divided by the total cross-sectional-area of the wire), ε A is the applied strain, ε I is the intrinsic strain, ε M is the applied strain at the peak, * T is the effective critical temperature, * t = T T is the reduced temperature, B * 2 is the effective upper critical field and * b= B B 2 is the reduced field. The optimum values of the scaling-law parameters are shown in Table 2 for the OST strand and Table 3 for the OKS strand. Highly accurate parameterisations are obtained for the complete J ( ) B, T, ε datasets the root-mean-square differences between the measured and calculated values of I are ~1.5 A (OST strand) and ~2 A (OKS strand), compared to the average I values of ~4 45 A. The scaling-law parameterisations are compared graphically with the measured data in Figure 8 through to Figure 12.

1 Table 2 Scaling law parameters for the OST strand [billet 7567-2 (back end), received June 24]. Intrinsic strain is in units of percent and the calculated J is the engineering critical current density in units of Am 2. p q n ν w u ε M (%).9631 2.229 2.532 1.518 2.423.1155.1371 A ( ) (Am 2 T 3 n K 2 ) T ( ) * (K) ( ) * B 2, (T) c 2 c 3 c 4 4.291 1 7 16.71 29.72.7816.6318.1732 Table 3 Scaling law parameters for the OKS strand [billet NT681 (outer), received Oct. 24]. Intrinsic strain is in units of percent and the calculated J is the engineering critical current density in units of Am 2. p q n ν w u ε M (%).4556 1.723 2.642 1.318 2.43.811.154 A ( ) (Am 2 T 3 n K 2 ) T ( ) * (K) ( ) * B 2, (T) c 2 c 3 c 4 1.379 1 7 17.22 29.41 1.768 1.1514.4125 5 4 OST Strand 3 2 B = 9 T 1 22 T -1. -.8 -.6 -.4 -.2..2 Figure 8 The critical current of the OST strand as a function of intrinsic strain at 4.2 K. The symbols show the measured data at an electric field criterion of 1 μvm 1 ; the lines show the scaling-law fits (Equations (1) (5) and Table 2).

11 16 14 12 1 8 6 4 2 (a) OST strand T = 6 K B = 14 T 22 T 25 2 15 1 5 (b) T = 8 K B = 1 T 19 T -1. -.8 -.6 -.4 -.2..2-1. -.8 -.6 -.4 -.2..2 18 16 14 12 1 8 6 4 2 (c) T = 1 K B = 8 T 15 T 2 15 1 5 (d) T = 12 K B = 4 T 11 T -1. -.8 -.6 -.4 -.2..2-1. -.8 -.6 -.4 -.2..2 Figure 9 The critical current of the OST strand as a function of intrinsic strain at 6, 8, 1 and 12 K. The symbols show the measured data at an electric field criterion of 1 μvm 1 ; the lines show the scaling-law fits (Equations (1) (5) and Table 2). 2 OST strand (a) 1 OST strand (b).52% intrinsic strain.52% intrinsic strain 15 1 5 12 T 13 T 14 T 15 T 16 T 17 T 18 T 1 1 8 K 6 K 1 K 4 5 6 7 8 9 1 1 12 K 5 1 15 2 Temperature (K) Magnetic Field (T) Figure 1 The critical current of the OST strand at.52% intrinsic strain (a) as a function of temperature at different magnetic fields and (b) as a function of field at different temperatures. The symbols show the measured data at an electric field criterion of 1 μvm 1 ; the lines show the scaling-law fits (Equations (1) (5) and Table 2).

12 4 OKS Strand 3 2 1 B = 1 T 24 T -1. -.8 -.6 -.4 -.2..2 Figure 11 The critical current of the OKS strand as a function of intrinsic strain at 4.2 K. The symbols show the measured data at an electric field criterion of 1 μvm 1 ; the lines show the scaling-law fits (Equations (1) (5) and Table 3). 15 1 5 (a) OKS strand T = 6 K B = 12 T 15 1 5 (b) T = 8 K B = 9 T 22 T -1. -.8 -.6 -.4 -.2..2 19 T -1. -.8 -.6 -.4 -.2..2 2 15 1 5 (c) T = 1 K B = 5 T 3 25 2 15 1 5 (d) T = 12 K B = 2 T 15 T -1. -.8 -.6 -.4 -.2..2 11 T -1. -.8 -.6 -.4 -.2..2 Figure 12 The critical current of the OKS strand as a function of intrinsic strain at 6, 8, 1 and 12 K. The symbols show the measured data at an electric field criterion of 1 μvm 1 ; the lines show the scaling-law fits (Equations (1) (5) and Table 3).

13 8 (a) OKS strand.7% intrinsic strain (b) OKS strand.7% intrinsic strain 6 4 2 13 T 14 T 15 T 16 T 17 T 1 1 1 K 8 K 6 K 4 5 6 7 8 1 12 K 5 1 15 2 Temperature (K) Magnetic Field (T) Figure 13 The critical current of the OKS strand at.59% intrinsic strain (a) as a function of temperature at different magnetic fields and (b) as a function of field at different temperatures. The symbols show the measured data at an electric field criterion of 1 μvm 1 ; the lines show the scaling-law fits (Equations (1) (5) and Table 2). Figure 14(a) shows a comparison of the critical current of the OST and OKS advanced strands with a previous-generation (Vac) ITER strand. It can be seen that the critical currents at 14 T, 4.2 K and zero intrinsic strain are larger by typically a factor of ~2 in the advanced strands. Figure 14(b) shows the same data but with the critical currents normalised to their values at zero intrinsic strain. The strain-dependence of the normalised values of I is seen to be similar for all three wires, showing that the factor ~2 increase in I for the advanced strands occurs at all value of applied strain (at 4.2 K and 14 T). Figure 15 shows the normalised values of effective upper critical field at T = for the OST and OKS strands, compared with previous data for four different ternary Nb3Sn strands 12. These data provide further evidence for an approximately universal * relation for normalised B (, ε ) in ternary Nb 3 Sn, which can be parameterised by a 2 I polynomial function 12. We note that this relation is significantly different from that used in the standard Summers Scaling Law 7,2 (Summers law was derived from data on Nb 3 Sn strands characterised by low upper critical field values, and exhibits a weaker strain-dependence).

14 1. 2 OST OKS Vac 15 1 5 B =14 T Normalised ritical urrent.8.6.4.2 B =14 T OST OKS Vac I,MAX (A) 216 193 93. -1.2-1. -.8 -.6 -.4 -.2..2.4-1.2-1. -.8 -.6 -.4 -.2..2.4 Figure 14 A comparison of (a) the critical current and (b) the normalised critical current of the OST, OKS and Vac strands as a function of intrinsic strain at 4.2 K and 14 T. Normalised effective upper critical field at T = 1..9.8.7.6 MJR Vac EM-LMI Fur Universal fit OST OKS -1.5-1. -.5..5 Figure 15 The normalized effective upper critical field at T = as a function of intrinsic strain for the OST and OKS strands, compared with previous data for four different ternary Nb 3 Sn strands and a universal fit described previously 12.

15 3.3 n-value results Figure 16 and Figure 17 show examples of the n-value data (for the electric-field range 1 1 μvm 1 ) that were obtained for the OST and OKS strands. The n-value is defined via the following relation: E J n, (6) where E is the electric field and J is the (engineering) current density. A tabulation of the J ( B, T, ε ) and (,,ε ) report 27. n B T data can be found in the spreadsheet that accompanies this 3 OST Strand 25 B = 15 T n-value (dimensionless) 2 15 1 18 T 21 T 5-1. -.8 -.6 -.4 -.2..2 Intrinsic strain (%) Figure 16 The n-value of the OST strand (for the electric-field range 1 1 μvm 1 ) as a function of intrinsic strain at 4.2 K and different magnetic fields. The symbols show the measured data; the dashed lines are guides to the eye.

16 2 18 16 OKS strand T = 8 K n-value (dimensionless) 14 12 1 8 6 B = 13 T 4 2 -.8 -.6 -.4 -.2..2 Intrinsic stain (%) 19 T Figure 17 The n-value of the OKS strand (for the electric-field range 1 1 μvm 1 ) as a function of intrinsic strain at 8 K and different magnetic fields. The symbols show the measured data; the dashed lines are guides to the eye. 3.4 ritical temperature results Figure 18 shows the normalised resistivity as a function of temperature for the OST and OKS strands in zero magnetic field. Zero-field critical temperature data [ T ρ ] are shown in Figure 19. For the OST strand, T ρ was measured using the recommended current of.1 A, but the normal-state resistivity is such that an electric-field of 1 μvm 1 is never reached hence T ρ was defined at 2 μvm 1. For the OKS, a current of.5 A and an electric-field criterion of 1 μvm 1 was used. Figure 19 also shows a comparison between the normalised values of critical temperature obtained from resistivity measurements [ T ρ ] and the scaling-law parameterization [ T ], showing the lower strainsensitivity of T ρ in relation to T. Although in-field resistivity measurements were not ρ performed, the values of critical temperature [ T ( B) field [ B ρ 2 ( T) ] or, equivalently, upper-critical ] were determined by interpolating the J data at constant temperature and strain to find the value of magnetic field where J =.1 A, which is equal to defined at 1 μvm 1 and.1 A (as discussed previously 12 ). The values of ( ) obtained [together with the T ρ data] are shown in Figure 2 and in Tables 4 and 5. B ρ 2 B ρ 2 ( T) ( T) thus

17 Normalised Resistivity 1..8.6.4.2 Intrinsic Strain -.91% -.81% -.72% -.62% -.52% -.33% -.23% -.14% -.4%.6%.15% OST Strand B = Normalised Resistivity 1..8.6.4.2 Intrinsic Strain -.9% -.7% -.49% -.28% -.11% -.3%.8%.18% OKS Strand B =. (a). (b) 14 15 16 17 18 14 15 16 17 18 Temperature (K) Temperature (K) Figure 18 The normalized resistivity as a function of temperature for (a) the OST strand and (b) the OKS strand at different applied strains at zero field. The symbols show the measured data; the lines are guides to the eye. 17.5 OST OKS ritical Temperature (K) 17. 16.5 16. 15.5 Zero applied field Normalised T 1..95.9 OST (Scaling law) OKS (Scaling law).85-1. -.8 -.6 -.4 -.2..2.4 15. -1. -.8 -.6 -.4 -.2..2.4 Figure 19 The critical temperature of the OST and OKS strands as a function of intrinsic strain at zero field. T ρ was measured at.1 A and 2 μvm 1 for the OST strand, and.5 A and 1 μvm 1 for the OKS strand. The symbols show the measured data; the lines are guides to the eye. The inset shows the normalized critical temperature as a function of intrinsic strain, compared with the scaling-law values of T.

18 Upper ritical Field (T) 25 2 15 1 5 Intrinsic Strain.15%.6% -.4% -.14% -.33% -.52% Upper ritical Field (T) 25 2 15 1 5 Intrinsic Strain.18%.8% -.3% -.11% -.28% -.49% -.7% -.9% (a) OST Strand (b) OKS Strand 4 6 8 1 12 14 16 4 6 8 1 12 14 16 18 Temperature (K) Temperature (K) Figure 2 The upper critical field as a function of temperature (equivalent to the critical temperature as a function of field) for (a) the OST and (b) the OKS strands. T ρ was measured at.1 A and 2 μvm 1 for the OST strand, and.5 A and 1 μvm 1 for the OKS strand; B ρ 2 was obtained at.5 A and 1 μvm 1 for both strands via an interpolation of the J data. Table 4 The upper critical field [ B ρ 2 ] at different temperatures and intrinsic strains and the critical temperature [ T ρ ] at different intrinsic strains for the OST strand. T ρ was measured at.1 A and 2 μvm 1 and B ρ 2 was obtained at.5 A and 1 μvm 1 via an interpolation of the J data. Intrinsic B ρ (T) 2 [T (K)] Strain (%) 4.2 6 8 1 12 T ρ (K).15 22.41 19.18 15.29 11.3 17.11.6 24.98 19.85 11.56 17.27.4 25.2 2.5 11.63 17.27.14 25.1 22.92 19.57 15.72 11.32 17.2.23 17.6.33 23.84 18.37 1.29 16.87.52 22.18 19.96 16.82 13.8 8.95 16.44.62 16.21.72 2.3 15.95.81 15.68.91 18.76 15.4

19 Table 5 The upper critical field [ B ρ 2 ] at different temperatures and intrinsic strains and the critical temperature [ T ρ ] at different intrinsic strains for the OKS strand. was measured at.5 A and 1 μvm 1 and B ρ was obtained at.5 A and 1 μvm 1 2 via an interpolation of the J data. T ρ Intrinsic B ρ (T) 2 [T (K)] Strain (%) 4.2 6 8 1 12 14 T ρ (K).18 23.52 21.26 18.1 14.41 1.42 6.2 17.11.8 24.46 22.54 19.33 15.58 11.44 7.15 17.34.3 24.97 22.87 19.67 15.92 11.75 7.29 17.41.11 24.8 22.56 19.37 15.64 11.48 7.13 17.37.28 23.6 21.15 18.2 14.33 1.3 6.6 17..49 21.76 19.27 16.24 12.75 8.86 4.79 16.52.7 19.91 17.53 14.59 11.18 7.45 3.54 16.8.9 18.19 15.98 13.16 9.8 6.27 2.52 15.52 3.5 Strain-cycling results The strands were subject to a number of strain cycles during the course of the detailed I measurements and in the subsequent limited fatigue tests (see Section 2). Figure 21 shows variable-strain I data for the OST and OKS strands at two different stages in the strain cycling procedure. For the OST strand, the first dataset was obtained at the beginning of the experiment; for the OKS strand, the first data set was obtained in the second full strain cycle. For both strands, the second dataset [cycle 3 (increasing)] was obtained after the detailed I measurements had been performed, on the first leg of the fatigue-test cycles. The data show a reasonable level of agreement, with typical deviations of ±5%. Table 6 shows the values of critical current at 22 T, 4.2 K and zero applied strain at various stages throughout the experiment. The set of 5 strain cycles from +.4% to.8% applied strain did not have a significant effect on I for either wires.

2 2 18 (a) 14 (b) 16 12 OKS 14 12 1 8 6 4 2 OST B = 22 T ycle 1 (increasing) ycle 3 (increasing) 1 8 6 4 2 B = 22 T ycle 2 (decreasing) ycle 3 (increasing)..5.1.15.2.25.3.35 -.3 -.2 -.1..1.2.3.4 Applied Strain (%) Applied Strain (%) Figure 21 The critical current of the OKS and OST strands at 4.2 K and 22 T with different strain cycling histories. The symbols show the measured data; the dashed lines are guides to the eye. Table 6 The critical current of the OST and OKS strands at 22 T, 4.2 K and zero applied strain after various strain cycles. Applied strain history (%) J( 22 T,4.2 K, ε A = ) (A) OST OKS No strain cycles 14.1 +.3.8 +.3 16. 11.6 +.3 14.5 1.7 1 15.2 1.7 5 ( +.4.8 ) 15.4 11.7

21 4 REFERENES 1 2 3 4 5 6 7 8 9 1 11 12 13 14 15 16 17 18 19 2 21 22 23 J. W. Ekin, ryogenics 2, 611 (198). B. ten Haken, A. Godeke, and H. H. J. ten Kate, J. Appl. Phys. 85, 3247 (1999). N. heggour and D. P. Hampshire, J. Appl. Phys. 86, 552 (1999). S. A. Keys and D. P. Hampshire, Supercond. Sci. Tech. 16, 197 (23). D. P. Hampshire, H. Jones, and E. W. J. Mitchell, IEEE Trans. Magn. 21, 289 (1984). A. Martínez and J. L. Duchateau, ryogenics 37, 865 (1997). L. T. Summers, M. W. Guinan, J. R. Miller, and P. A. Hahn, IEEE Trans. Magn. 27, 241 (1991). D. O. Welch, Adv. ryo. Eng. 26, 48 (198). A. Godeke, B. ten Haken, and H. H. J. ten Kate, Physica 372-376, 1295 (22). K.. Lim, J. D. Thompson, and G. W. Webb, Phys. Rev. B 27, 2781 (1983). R. Aymar, Fusion Eng. Des. 55, 17 (21). D. M. J. Taylor and D. P. Hampshire, - The scaling law for the strain-dependence of the critical current density in Nb Sn superconducting wires - Supercond. Sci. Tech 18 (25) S241-S252 3 R. Zanino, N. Mitchell, and L. Savoldi-Richard, ryogenics 43, 179 (23). R. Zanino and L. Savoldi-Richard, ryogenics 43, 79 (23). N. Mitchell, Fusion Eng. Des. 66-8, 971 (23). N. heggour and D. P. Hampshire, Rev. Sci. Instrum. 71, 4521 (2). D. P. Hampshire, D. J. Taylor, P. Foley, and S. A. Keys, University of Durham Report No. DurS61 (21). D. M. J. Taylor, P. Foley, H. Niu, and D. P. Hampshire, Durham University Report No. EFDA/3-113 (24). D. M. J. Taylor and D. P. Hampshire, Physica 41, 4 (23). ITER, Design Requirements and Guidelines Level 1 (Annex) (22). D. M. J. Taylor and D. P. Hampshire, Supercond. Sci. Tech. 18, 356 (25).. R. Walters, I. M. Davidson, and G. E. Tuck, ryogenics 26, 46 (1986). B. L. Brandt, D. W. Liu, and L. G. Rubin, Rev. Sci. Instrum. 7, 14 (1999).

22 24 25 26 27 S. A. Keys and D. P. Hampshire, in Handbook of Superconducting Materials; Vol. 2, edited by D. ardwell and D. Ginley (IOP Publishing, Bristol, 23), p. 1297. J. A. Parrell (private communication). D. M. J. Taylor, P. Foley, H. Niu, and D. P. Hampshire, Durham University Report No. EFDA/3-113 (Appendix) (24). D. P. Hampshire, www.dur.ac.uk/superconductivity.durham/publications.html (25).