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[Xudong Wang](https://orcid.org/0000-0001-8717-6444), [Kiyosumi Tsuchiya](https://orcid.org/0000-0002-7514-5330), Akio Terashima, Suguru Tanabe, Nobuyuki Negishi, [Akihiro Kikuchi](https://orcid.org/0000-0002-5044-7156)

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[Critical Current Measurements of Prototype REBCO Round Cables at 77 K](https://mdr.nims.go.jp/datasets/7d83bdc7-5bb2-46fc-b634-48343fcd1f9d)

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Critical Current Measurements of Prototype REBCO Round Cables at 77 KXudong Wang, Kiyosumi Tsuchiya, Akio Terashima, Suguru Tanabe, Nobuyuki Negishi, and Akihiro Kikuchi54PoA03-12[footnoteRef:1]Submitted for review September 19, 2023This work was supported by “MEXT Development of key element technologies to improve the performance of future accelerators Program” Japan Grant Number JPJ123456 and JSPS KAKENHI Grant Numbers 19H01911. Xudong Wang, Kiyosumi Tsuchiya, and Akio Terashima are with the High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305-0801, Japan (e-mail: wanxdon@post.kek.jp).Suguru Tanabe is with the Junkosha Inc., Kasama, Ibaraki 309-1603 Japan.Nobuyuki Negishi is with the Junkosha Inc., Chiyoda, Tokyo 101-0062 Japan.Akihiro Kikuchi is with the National Institute for Materials Science (NIMS), Tsukuba, Ibaraki 305-0028, Japan.Color versions of one or more of the figures in this article are available online at http://ieeexplore.ieee.orgAbstract—High temperature superconducting (HTS) cables are necessary for next-generation high-field accelerator magnets, and various types of HTS cables have been developed worldwide. We have started the development of HTS cables in which rare-earth barium copper oxide (REBCO) coated conductors are spirally wound around a flexible multi-wire core. In this study, we constructed five sample cables with a 2-mm-wide coated conductor and a 1.8-mm-diameter multi-wire core. The transport critical current (Ic) of the coated conductors used for the sample cables was measured at 77 K and 4.2 K. At 4.2 K, the Ic was measured in a perpendicular magnetic field from 1 T to 18 T. The transport Ic and bending properties of the sample cables were characterized at 77 K. The cable Ic degraded 10-16% due to the cable construction and 10% after bending the cable with a radius of 20 mm. The cable current density (Je) at 20 T and 4.2 K was estimated as a function of the cable diameter.Index Terms—REBCO, cable, critical current, current density, high magnetic field.I. IntroductionWITH the advances in manufacturing technology of rare-earth barium copper oxide (REBCO) coated conductors, the development of high-field accelerator magnets has become more active in recent years. Since REBCO coated conductors are in tape form rather than round wires like NbTi conductors, new high current cables with coated conductors have been developing worldwide, such as Roebel cables [1, 2], twisted stacked-tape cables [3, 4], CORC® wires [5-11], and STAR® wires [12-15]. In particular, the CORC® and STAR® wires, which are small diameter round cables with a structure similar to superconducting power transmission cables in which coated conductors are spirally wound around a metal core, are expected to be applied to the future accelerator magnets. This round cable configuration provides the bending flexibility required for coil manufacturing and makes it easy to increase the current capacity through multi-layering. Considering these advantages, we started the development of the REBCO round cable using our previous research experience with the coated conductors [16-18] and a REBCO sextupole magnet [19-23]. In this study, five prototype REBCO round cables were fabricated and measured to characterize the transport critical current (Ic) and the cable current density (Je) at 20 T and 4.2 K. The bending properties of the sample cables were also measured to confirm its flexibility.  II. ExperimentsA. REBCO Coated Conductor PropertiesA 2-mm-wide coated conductor, manufactured by SuperPower Inc., was used to construct the sample cable. The specifications of the coated conductor are summarized in Table 1. As a first attempt at cable construction, this relatively thick coated conductor was chosen for ease of handling. The voltage versus current (V-I) properties of the coated conductor were measured by the standard four-probe method at 77 K and 4.2 K with a U-shape holder developed in our previous studies [16-18]. A pair of voltage taps with a conductor length of 29 mm were soldered to the center of a 120-mm-long sample. The transport Ic of the sample was determined using an electric field criterion of 1.0 µV/cm calculated by dividing the measured voltage by 29 mm. An 18 T solenoid with a 52-mm-bore was used to measure the Ic in a perpendicular magnetic field from 1 T to 18 T at 4.2 K. B. REBCO Cable PropertiesFive 300-mm-long sample cables #1 to #5, shown in Fig. 1 and summarized in Table 2, were constructed using the 2-mm-wide coated conductor and the 1.8-mm-diameter multi-wire core. The core was stranded with 37 0.26-mm-diameter wires. The coated conductors were spirally wound around the core with the superconducting layer facing to the core so that the superconducting layer was under compressive strain. The winding direction of the next layer was opposite to that of the previous layer for the multi-layer sample cables #3 to #5. There was no insulating layer between the core and the conductor layer, and between the conductor layers. The coated conductors and core were soldered together with a round terminal at the end of the cable. The round terminal was bolted to a copper block to transport the current. A pair of voltage taps with cable lengths between 110 mm to 240 mm were soldered to the center of the outermost layer of each sample cable. The cable Ic was determined using an electric field criterion of 1.0 µV/cm calculated by dividing the measured voltage by the cable length between the voltage taps. TABLE ISPECIFICATIONS OF REBCO COATED CONDUCTORParametersValuesConductor width2 mmConductor thickness0.12 mm   Substrate thickness30 µm   REBCO thickness1.6 µm   Copper thickness40 µm per sideIc (self-field, 77 K)54 A (>50 A) a a The minimum Ic was provided by SuperPower Inc.C. Cable Bending TestsThree sample cables #2 to #4 were sequentially bent to radii of 40 mm, 30 mm, and 20 mm at room temperature using glass fiber reinforced plastic (GFRP) disk holders. Fig. 2 shows the GFRP disk holders and the sample cable #2 bent to a radius of 40 mm. The transport Ic was measured first without bending, then after bending at each radius, and finally again without bending at 77 K. The voltage taps were the same as the cable Ic measurements. Fig. 1. Five REBCO sample cables #1 to #5 constructed by spirally winding a 2-mm-wide coated conductor around a 1.8-mm-diameter multi-wire core without insulation.TABLE IISPECIFICATIONS OF FIVE REBCO SAMPLE CABLESCable no.# oflayers# ofconductorsDiameter(mm)Cable length betweenvoltage taps (cm)#1112.0513 (19) a#2122.0512 (19) a#3242.2511 (19) a#4362.5013 (26) a#55113.0024 (38) aa The values in parentheses are the conductor length measured from the outermost layer of the cable between the voltage taps.Fig. 2. GFRP disk holders used for the bending test with radii of 40 mm, 30 mm, and 20 mm. The sample cable #2 was bent to a radius of 40 mm in this photo.III. Results and DiscussionA. Transport Ic of Coated ConductorFig. 3 shows the electric field versus current plots of the coated conductor at 77 K and 4.2 K. Fig. 4 shows the perpendicular magnetic field dependence of the transport Ic. The conductor Ic was 54 A in self-field at 77 K and 86 A at 18 T and 4.2 K. To extrapolate the perpendicular field dependence up to 20 T at 4.2 K, a well-known power law equation of Ic=kB-α [24, 25] was adopted using the measured Ic from 10 T to 18 T. Where, k and α are the fitting parameters. The dashed lines in the insets of Fig. 4 represent the fitting results of the conductor Ic. The lift factor defined as Ic (B, 4.2 K)/Ic (self-field, 77 K) was used to estimate the cable Ic at 20 T and 4.2 K. B. Cable Ic and Je Fig. 3. Electric field versus current plots of the coated conductor at (a) 77 K and (b) 4.2 K. The magnetic field dependence of the Ic perpendicular to the coated conductor was measured from 1 T to 18 T at 4.2 K. Fig. 4. Magnetic field dependence of the conductor Ic measured at 4.2 K. The dashed lines in the insets show the fitting curve using the power law equation.Fig. 5 shows the V-I plots of the sample cables #1 to #5 measured in self-field at 77 K. The cable Ic measured at 77 K is summarized in Table 3. Because the coated conductor is spirally wound around the core, the length of the coated conductor is longer than that of the cable between the voltage taps. As a result, the cable Ic calculated using the cable length is smaller than that calculated using the conductor length as the tap length. In Table 3, the cable Ic at 77 K shown in parentheses were calculated using the conductor length listed in parentheses of Table 2. Comparing these Ic values, the cable Ic calculated using the cable length was less than that calculated using the conductor length by several percent. Excluding this Ic difference, there was no Ic degradation for the single-layer cables #1 and #2 compared to the expected Ic as a multiple of the conductor Ic. On the other hand, the multi-layer cables #3 to #5 showed 10% to 16% Ic degradation compared to the cable #1. Considering that the compressive strain induced in the superconducting layer decreases as the cable diameter increases, this Ic degradation may be due to the self-field effect and interference at intersections between the conductor layers in the multi-layer cables, rather than due to the compressive strain during conductor winding. The maximum self-field perpendicular to the coated conductor (B//c) of the cable #5 was analyzed to be less than 0.015 T by an Opera-3D model as shown in Fig. 6. The self-field profile shows peaks around the edges of the coated conductor. This self-field effect reduces the cable Ic by up to 5% at 77 K according to our previous study [18]. As shown in Fig. 7, the non-uniform copper plating thickness on the conductor edge may cause interference between the conductor layers and induce additional strain in the superconducting layer. Therefore, dimensional uniformity of the coated conductor thickness might be important for the cable construction. Fig. 6. The self-field perpendicular to the coated conductor (B//c) of the cable #5, (a) an Opera-3D model and (b) field profile in the z-axis direction on the conductor surface of the 3rd layer and the 5th layer. The length of the 5th layer conductor in the z-axis direction is longer than that of the 3rd layer conductor because its winding pitch is longer.Fig. 7. Micrographs of the coated conductor with a nominal copper thickness of 40 µm per side. The photos on the left and right are the edge and middle of the coated conductor in the width direction.Fig. 8. Estimated cable (a) Ic and (b) Je at 20 T and 4.2 K as a function of the cable diameter. The plots are the estimated values of the sample cables #2 to #5. The lines are calculated assuming a 2-mm-wide coated conductor with a thickness of 0.12 mm or 0.05 mm. The 0.12-mm-thick coated conductor has the same configuration as listed in Table 1. The 0.05-mm-thick coated conductor has the same configuration as the 0.12-mm-thick coated conductor, except that the copper plating layer is thinner. Estimations were made taking into consideration a gap of around 0.2 mm between coated conductors in the same layer.The cable Ic and Je estimated at 4.2 K are also summarized in Table 3. The lift factors of 1.72 and 1.46 obtained from Fig. 4 are used to estimate the cable Ic at 16 T and 20 T, respectively. The cable Je was calculated by dividing the cable Ic by the cable cross-sectional area obtained from the measured cable diameter listed in Table 2. The sample cable #5, consisting of 11 2-mm-wide coated conductors, was estimated to have an Ic of 853 A at 16 T and 4.2 K, and 724 A at 20 T and 4.2 K. Fig. 8 shows the estimated cable Ic and Je at 20 T and 4.2 K as a function of the cable diameter. These estimations were made not only for the 0.12-mm-thick coated conductor tested in this study, but also for the commercially available 0.05-mm-thick coated conductor with a thinner copper plating layer. The conductor Ic of the 0.05-mm-thick and 2-mm-wide coated conductor was set to 50 A or 100 A at 77 K. The cable Ic and Je of the sample cables constructed using the 0.12-mm-thick coated conductor are less than 4 kA and 200 A/mm2 at 20 T and 4.2 K for cable diameters less than 5 mm (plots and solid line in Fig. 7). The cable Ic and Je close to 8 kA and 400 A/mm2 at 20 T and 4.2 K are expected to be achieved using a 0.05-mm-thick coated conductor with the conductor Ic of 50 A at 77 K (dotted line in Fig. 7), and further improvement is expected by increasing the conductor Ic of the 0.05-mm-thick coated conductor (dash-dot line in Fig. 7). Reducing the core size is also essential to improve cable current density. However, the bending strain of the superconducting layer increases as the core size decreases, resulting in Ic degradation in the current conductor configuration. Therefore, to reduce the core size, the superconducting layer should be placed close to the neutral axis of the coated conductor to minimize strain induced Ic degradation. Fig. 5. V-I plots of the sample cables #1 to #5 measured in self-field at 77 K.TABLE IIICABLE IC AND JE MEASURED AT 77 K AND ESTIMATED AT 4.2 KCableno.Cable Ic (A)77KCable Ic (A)16 T, 4.2 KCable Ic (A)20 T, 4.2 KCable Je (A/mm2)20 T, 4.2 K#151 (52) a887422#2106 (109) a18215547#3170 (178) a29224862#4238 (262) a41034871#5496 (514) a853724102a The Ic values in parentheses are calculated with the coated conductor length measured from the outermost layer of the cable between the voltage taps.C. Cable Bending resultsFig. 9 shows the electric field versus current plots of the sample cables #2 to #4 measured in the bending test at 77 K. Fig. 10 summaries the cable Ic normalized to the initial value as a function of the bending radius. The Ic degradation was not observed for these cables when bending radii were 40 mm and 30 mm. Interestingly, the cable Ic of the sample cable #4 recovered by 4% under the 40-mm-radius bend. The measured and expected Ic of the sample cable #4 were 262 A and 312 A before bending. The coated conductor was subjected to compressive strain by winding it around the core during cable manufacturing, and it inside of the cable bend was subjected to tensile strain when the cable was bent. Therefore, bending the cable after manufacturing could partially release the strain and slightly recover the cable Ic. This Ic recovery indicates that the Ic degradation after cable construction could be a reversible degradation. In the bending test at a radius of 20 mm, the sample cable #4 shows the largest Ic degradation of approximately 10%, and the sample cable #2 shows the least Ic degradation. This tendency of the Ic degradation is not only caused by the increase in compressive strain in the outermost conductor layer as the cable diameter increases, but also may be due to further interference at intersections between the conductor layers. Furthermore, insufficient clearance between coated conductors can also cause the Ic degradation, although the gap was carefully controlled during cable construction. Overall, the sample cables have approximately 90% of the cable Ic before bending even after the 20-mm-radius bending. The flexible multi-wire core might have contributed to mitigating this Ic degradation. Fig. 9. Electric field versus current plots of the sample cables (a) #2, (b) #3, and (c) #4 measured from the bending test at 77K.Fig. 10. Cable Ic normalized to the initial value as a function of the bending radius for the sample cables #2 to #4.IV. ConclusionThe transport Ic of a 2-mm-wide and 0.12-mm-thick commercial REBCO coated conductor was measured at 77 K and 4.2 K. The magnetic field dependence of the conductor Ic was also determined to estimate the Ic at 20 T and 4.2 K. As a result, a lift factor of 1.46 was obtained from the fitting curve for the 77 K self-field. Five sample cables were constructed using this coated conductor and a 1.8-mm-diameter multi-wire core to investigate the cable Ic and Je at 20 T and 4.2 K. The bending properties of these sample cables were also measured at radii of 40 mm, 30 mm, and 20 mm. In cable construction, the single-layer cables #1 and #2 showed the expected Ic, while the multi-layer cables #3 to #5 showed a 10% to 16% Ic degradation. Although the interlayer interference may be reduced by installing the insulation layer, the dimensional uniformity of the coated conductor thickness is also important for this cable construction. The cable Ic and Je were estimated at 20 T and 4.2 K for the 0.12-mm-thick and 0.05-mm-thick coated conductors. These values of the sample cables made with the 0.12-mm-thick coated conductor were estimated to be less than 4 kA and 200 A/mm2 for cable diameters less than 5 mm. These values are expected to be improved by using thinner coated conductors with higher Ic. 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Technol., vol. 33, 2020, Art. no. 044011, doi: 10.1088/1361-6668/ab73ee. image1.pngimage2.pngimage3.pngimage4.pngimage5.pngimage6.pngimage7.pngimage8.pngimage9.pngimage10.pngimage11.pngimage12.png