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

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[Superconducting Properties of a Nb3Sn Bundle Cable Made of Ultra-Fine Wires](https://mdr.nims.go.jp/datasets/2082dafc-937b-49eb-80f3-6375f45ccad9)

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3LPo2H-02   Template version 8.0d, 22 August 2017. IEEE will put copyright information in this area See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. 1 Superconducting Properties of a Nb3Sn Bundle Cable Made of Ultra-fine Wires  Xudong Wang, Kiyosumi Tsuchiya, Akio Terashima, Yasuo Iijima, and Akihiro Kikuchi    Abstract—We have been developing A15 cables made of ultra-fine wires for the high-field superconducting magnets using react-and-wind (R&W) technology. Recently, we succeeded to fabricate a bronze-processed Nb3Sn ultra-fine wire with a minimum diame-ter of 30 µm. This wire contains 19 filaments and has a Cu/Non-Cu ratio of 0.89. In this study, we measured the transport critical current (Ic) of a Nb3Sn bundle cable made by twisting 19 wires with a diameter of 50 µm at 4.2 K and under an external field up to 18 T. The Non-Cu critical current density (Jc) was also calculated from the Ic results. To replicate the R&W process, the cable was wound on glass fiber reinforced plastic cylinder (GFRP) bobbins after the heat treatment in straight geometry. To investigate the bending characteristics of the bundle cables, we prepared four GFRP bobbins with diameters of 50 mm, 30 mm, 25 mm, and 20 mm for Ic measurements. As a result, Ic degradation was ob-served only in the case of the 20 mm diameter bobbin. This indi-cates that the bending characteristics of the bundle cables are, as expected, greatly improved due to the smaller size of the wires. We also measured the critical temperature (Tc) and magnetization characteristics of the bundle cable by using a magnetic property measurement system of Quantum Design. The onset Tc was con-firmed to be 17.1 K from the normalized magnetic moment. The low field Non-Cu Jc was also estimated from the magnetization data at 4.2 K, 6 K, 8 K, and 10 K.    Index Terms—Nb3Sn, ultra-fine wire, bundle cable, react-and-wind, critical current, critical temperature, magnetization. I.  INTRODUCTION EVELOPMENT of high-field superconducting magnets for accelerator and nuclear fusion reactor applications using A15 superconductors is in progress [1–9]. The magnet fabrica-tion using Nb3Sn, a representative material for A15 supercon-ductors, is very complicated due to the dedicated heat treatment and stress/strain sensitivity [10–13]. This problem limits the use of reacted Nb3Sn wires and cables for coil winding. Instead of the R&W method, the wind-and-react (W&R) technology was usually adopted for the Nb3Sn magnet fabrication. However, the W&R technique causes other issues such as dimensional changes after reaction [14, 15] and unexpected training quench [2, 5, 16]. On the other hand, the flexibility of the A15 cables  Manuscript receipt and acceptance dates will be inserted here. This work was supported by the Japan Society for the Promotion of Science KAKENHI under Grant 21H04477. Xudong Wang, Kiyosumi Tsuchiya, and Akio Terashima are with the High En-ergy Accelerator Research Organization (KEK), Tsukuba 305-0801, Japan (e-mail: wanxdon@post.kek.jp).  Yasuo Iijima and Akihiro Kikuchi are with the National Institute for Materials Science (NIMS), Tsukuba, Ibaraki 305-0028, Japan.  Digital Object Identifier will be inserted here upon acceptance. could be enhanced by bundling fine wires. The flexible cable has a higher potential to overcome the limitation of the R&W technology for A15 magnets. From this point of view, we have been developing ultra-fine A15 wires to realize the magnet made by R&W technologies with the flexible cable [17–20].  Recently, we succeeded to fabricate a bronze-processed Nb3Sn wire with a minimum diameter of 30 µm [20]. We also made several prototype bundle cables using the ultra-fine wires. In this study, we measured the transport critical current, critical temperature, and magnetization of the bundle cables made by twisting 19 wires with a diameter of 50 µm. The Non-Cu critical current density of the bundle cables was estimated from the crit-ical current and magnetization measurements. The bending properties of the bundle cables were investigated by the R&W process.  II. EXPERIMENTAL SETUP The specifications of the wire and bundle cable are listed in Table 1. The bundle cable was made by twisting 19 bronze-pro-cessed Nb3Sn wires of 50 µm diameter without soldering as shown in Fig. 1. The wire containing 19 filaments was extruded and drawn from a 45.2 mm diameter billet. The billet consists of a bronze matrix, 19 pure Nb rods inside of the matrix, a Nb barrier wrapped around the matrix, and an oxygen-free copper tube outside the matrix. Details of the strand fabrication are de-scribed in our previous studies [20].  The Ic measurements were performed at the NIMS Tsukuba Magnet Laboratory, a high magnetic field facility in Japan. To replicate the R&W process, the Nb3Sn bundle cable was reacted in straight geometry at 650 °C for 48 hours before Ic measure-ments, and then wound on the GFRP bobbin and soldered to copper current leads. Four bobbins with diameters of 50 mm, 30 mm, 25 mm, and 20 mm were prepared to investigate the D TABLE I SPECIFICATIONS OF NB3SN WIRE AND BUNDLED CABLE  Parameters Value Nb3Sn wire  Outer diameter 50 μm No. of filaments 19 Filament diameter 3 μm Cu/Non-Cu ratio 0.89 Barrier Nb Bronze composition Cu-14mass%Sn-0.3mass%Ti [20] Nb3Sn bundled cable  Minimum outer diameter 250 μm  No. of strands 19 Twist pitch 4 mm    2 bending properties of the bundle cable as shown in Fig. 2. The bundle cable was placed in a V-shaped groove to hold it to the bobbin. Transport Ic of the bundle cable was measured by DC four probe method in liquid helium (4.2 K) and under an exter-nal magnetic field (Bext) up to 18 T. The Bext was applied per-pendicular to the bundle cable, and the electromagnetic force induced by the Bext and the transport current (It) on the bundle wire was directed towards the center of the bobbin. The length between Ic voltage taps of each measurement ranged from 70 mm to 140 mm, and the distance from the Ic voltage tap to the current lead was arranged longer than 30 mm to avoid heat transfer from the current lead to the Ic measurement region.  The critical temperature and magnetic moment of the Nb3Sn bundle cable were measured by the magnetic property measure-ment system (MPMS) of Quantum Design. A 5-mm-long bun-dle cable was set in the MPMS for these measurements. The Bext was applied perpendicular to the bundle cable as in the Ic measurement. For the critical temperature measurement, 1 mT was applied to the bundle cable after cooling to 4.2 K in zero field. The temperature was then swept from 4.2 K to 18 K in 0.1 K steps and from 18 K to 25 K in 0.5 K steps. The magnetic moment was measured between 5 T and –5 T after cooling to the test temperatures of 4.2 K, 6 K, 8 K, and 10 K in zero field. The Bext was changed by 0.05 T steps between 1 T and –1 T, and 0.1 T steps in the higher magnetic field region.  III. RESULTS AND DISCUSSION A. Transport Critical Current (Ic) and Non-Cu Critical Cur-rent Density (Jc) Fig. 3 shows the electric field versus current (E-I) curves measured by the four kinds of bobbins at 4.2 K and under the Bext from 1 T to 18 T. The electric field was calculated by di-viding the measured voltage by the distance between the Ic volt-age taps for each measurement. Fig. 4 shows external magnetic field dependence on Ic and Non-Cu Jc of the four bobbin meas-urements and that measured without bending as a reference. The Ic was determined by 1.0 µV/cm criterion, and the Non-Cu Jc was calculated by dividing the Ic by the Non-Cu cross-sec-tional area (0.01974 mm2) of the bundle cable. The reference data without bending was measured by a sample holder used in the previous study [20]. As shown in Fig. 3 and Fig. 4, Ic deg-radation was only observed in the bending result of the 20 mm diameter bobbin. The Ic variations between the reference data without bending and the other three bobbin measurements were within 5%. This error is mainly caused by sample-to-sample variation. The measurement error is assumed to be within 2%. In case of the no-degradation results (without bending, 50 mm,  Fig. 3. E-I curves measured on the four bobbins with diameters of (a) 50 mm, (b) 30 mm, (c) 25 mm, and (d) 20 mm at 4.2 K and under the Bext from 1 T to 18 T. Full Bext results from 1 T to 18 T are shown on the left and zoomed results from 8 T to 18 T are shown on the right.  Fig. 1. Cross-sectional view of the Nb3Sn bundled cable and wire (a) before and (b) after the heat treatment at 650 °C for 48 hours.   Fig. 2. Photographs of the four GFRP bobbins with diameters of 50 mm, 30 mm, 25 mm, and 20 mm. The bundled cable was wound on the bobbin and soldered to current leads after reacting.   3 30 mm, and 25 mm), the average Ic and average Non-Cu Jc were 40 A and 2026 A/mm2 at 4 T, 9.1 A and 461 A/mm2 at 12 T, and 1.8 A and 91 A/mm2 at 18 T. Comparing with the reference data [21], the Non-Cu Jc of the test sample is about 20% lower than that of the reference value. We will improve the Non-Cu Jc by increasing the Sn concentration and optimizing the bronze to Nb filament ratio in the next work. The bending strains of the cables on the 25 mm and 20 mm bobbins are estimated to be 0.2% and 0.25% when calculated with the wire diameter of 0.05 mm. They are 1% and 1.25% when calculated with the cable diameter of 0.25 mm. Consider-ing that the Ic degradation was not observed in the case of 25 mm bending, the 1% strain estimated from the cable diame-ter is too high to explain the no-degradation result compared to the previous study [10–13]. These bending properties were also observed in a thicker bundle cable made of 49 wires with the same size used in this study [20]. From these results, the bend-ing strain of the bundle cable could be estimated to depend on the wire diameter rather than the cable diameter, and the bend-ing limit of the cable bundling with the 50 µm wire is between 25 mm and 20 mm in diameter.  B. Critical Temperature (Tc) Fig. 5 shows temperature dependance on magnetic moment and normalized moment of the bundle cable under an external magnetic field of 1 mT. Two transitions around 9 K and 17 K, which were induced by the Nb barrier and the Nb3Sn superconductor, were observed in the measured magnetic mo-ments. The normalized moment was determined with the aver-age moment above 20 K as zero and the moment at 10 K as –1. The onset Tc of 17.1 K was defined by a threshold of –0.001 from the normalized moment. This Tc value agrees well with the previous study measured by DC four probe method [20]. C. Magnetization Fig. 6 shows magnetization results of the bundle cable meas-ured at 4.2 K, 6 K, 8 K, and 10 K. There is a sharp peak below 0.5 T due to the magnetization of the Nb barrier [22]. The flux jump was not observed from the sample. Fig. 7 shows the Non-Cu Jc calculated from the magnetizations at 4.2 K, 6 K, 8 K, and 10 K. These data were rescaled using the transport results for the 50 mm diameter bobbin measured at 4.2 K and 4 T as shown in Fig. 4(b). The Non-Cu Jc below 0.5 T was not shown in Fig. 7 to exclude the magnetization of the Nb barrier. The Non-Cu Jc can also be derived by (1) for the filament model using the av-erage magnetic moment (Δm). The Δm is obtained from the measured moment in Fig. 6. Non-Cu 𝐽c =3𝜋42𝑑eff ∆𝑚𝑉Non−Cu                                            (1) where deff and VNon-Cu are the effective filament diameter of the Non-Cu area and the total Non-Cu volume of the bundle cable, respectively. The VNon-Cu was the product of the deff and the ca-ble length of 5 mm. The deff of the normalized Non-Cu Jc is 15% larger than the nominal diameter in this case.  Comparing the results at 4.2 K, the error of Non-Cu Jc be-tween the magnetization and the Ic measurement increased with  Fig. 4. Magnetic field dependance on Ic and Non-Cu Jc determined by 1.0 µV/cm. A data without bending and the four bobbin measurements with diameters of 50 mm, 30 mm, 25 mm, and 20 mm are summarized in these results. A reference data of the bronze-processed Nb3Sn wire [21], which has 14.3%Sn almost the same as that of the test sample, is shown in Fig. 4(b).   Fig. 5. Temperature dependance on (a) magnetic moment and (b) normalized moment of the Nb3Sn bundle wire under an external magnetic field of 1.0 mT. The inset shows a magnified view around the onset Tc.    4 decreasing magnetic field. This error is mainly caused by the self-field effect in the Ic measurement. The maximum self-field of the bundle cable is estimated to be about 0.0015 T/A by a 3D finite element analysis. Fig. 8 shows the comparison of the Non-Cu Jc with and without the self-field correction. The cor-rected Non-Cu Jc of the Ic measurement agrees well with that of the magnetization as shown in Fig. 8. The differences between the data with and without correction are 16% at 1T and less than 1.5% above 4 T. This self-field effect indicates that the fitting error between the Ic and magnetization measurements above 4 T is negligible in this case.  IV. CONCLUSION We succeeded to fabricate a bronze-processed Nb3Sn bundle cable consisting of the ultra-fine wires with a diameter of 50 µm. The magnetic field dependance on the Ic and Non-Cu Jc of the bundle cable at 4.2 K were characterized. The bundle cable was wound on the GFRP bobbin after the heat treatment in straight geometry for the measurements to replicate the R&W process. The bending properties of the bundle cable were meas-ured by the four bobbins with diameters of 50 mm, 30 mm, 25 mm, and 20 mm. As a result, the Ic degradation was only ob-served from the 20 mm diameter bending. A similar result was also found in the previous study from a thicker bundle cable made of 49 wires with the same size used in this study. These experimental data indicate that the bending of the bundle cable depends on the wire size rather than the cable size, and the bending limit of the bundle cable made of the 50 µm wire is between 25 mm and 20 mm in diameter. The onset Tc of the bundle cable was 17.1 K after the reacting at 650 °C for 48 hours. The magnetizations of the bundle cable were measured at 4.2 K, 6 K, 8 K, and 10 K. 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