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[Y Takeda](https://orcid.org/0000-0001-7217-9853), [G Nishijima](https://orcid.org/0000-0001-7493-0559), U Nakai, T Motoki, J Shimoyama, [H Kitaguchi](https://orcid.org/0000-0002-5998-2649)

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[Angular dependence of resistance and critical current of a Bi-2223 superconducting joint](https://mdr.nims.go.jp/datasets/311b6c0f-ff9d-4460-b62e-5f8c6871dcab)

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Angular dependence of resistance and critical current of a Bi-2223 superconducting jointSuperconductor Science and TechnologyPAPER • OPEN ACCESSAngular dependence of resistance and criticalcurrent of a Bi-2223 superconducting jointTo cite this article: Y Takeda et al 2023 Supercond. Sci. Technol. 36 125010 View the article online for updates and enhancements.You may also likeDefining Millisecond PulsarsPriyam Halder, Satyaki Goswami,Protyusha Halder et al.-Development of a persistentsuperconducting joint between Bi-2212/Ag-alloy multifilamentary round wiresPeng Chen, Ulf P Trociewitz, Daniel SDavis et al.-Performance characteristics of REBCOcoated conductor joints fabricated by flux-free hybrid weldingArman Nisay and Hyung seop Shin-This content was downloaded from IP address 144.213.253.16 on 01/11/2023 at 01:31https://doi.org/10.1088/1361-6668/ad0565/article/10.3847/2515-5172/ad00ac/article/10.1088/1361-6668/30/2/025020/article/10.1088/1361-6668/30/2/025020/article/10.1088/1361-6668/30/2/025020/article/10.1088/1361-6668/ad0793/article/10.1088/1361-6668/ad0793/article/10.1088/1361-6668/ad0793Superconductor Science and TechnologySupercond. Sci. Technol. 36 (2023) 125010 (9pp) https://doi.org/10.1088/1361-6668/ad0565Angular dependence of resistanceand critical current of a Bi-2223superconducting jointY Takeda1,∗, G Nishijima1, U Nakai2, T Motoki2, J Shimoyama2 and H Kitaguchi11 National Institute for Materials Science, 3-13 Sakura, Tsukuba, Ibaraki 305-0003, Japan2 Department of Physical Sciences, Aoyama Gakuin University, 5-10-1 Fuchinobe, Chuo-ku, Sagamihara,Kanagawa 252-5258, JapanE-mail: TAKEDA.Yasuaki@nims.go.jpReceived 30 July 2023, revised 3 October 2023Accepted for publication 20 October 2023Published 31 October 2023AbstractLow resistance and high critical current are prerequisites for superconducting joints used inpersistent-mode magnets. Herein, we use a joint resistance evaluation system, previouslydeveloped by us, to systematically evaluate the angular dependence of resistance and criticalcurrent of a Bi-2223 superconducting joint in a closed-loop sample. The current decay ismeasured by rotating the sample incrementally. The time dependence of the loop current isevaluated at 4 K, 0.15–0.28 T, and magnetic field angles ranging from 90◦ to 0, wherein 90◦corresponds to the direction parallel to the tape surface. The results suggest that the resistanceand critical current of the joint depend on the angle of the magnetic field. The evaluated criticalcurrent increases as the angle increases. The angular dependence of resistance can be dividedinto three regions: low-resistance, transition, and high-resistance regions. The low-resistanceregion exists at high angles close to 90◦. In this region, the decay of the loop current is small,and the persistent current continues to flow. Furthermore, the joint resistance is less than1.4 × 10−13 Ω. In the transition region, the joint resistance significantly increases by threeorders of magnitude with sample rotation. This significant increase is attributed to an increase inthe perpendicular component of the magnetic field, which decreases the critical current of thejoint. At lower angles, the joint resistance remains high, ranging from 10−11 to 10−10 Ω. Asignificant decay in the loop current is observed in the high-resistance region. Based on thesefindings, we conclude that the design of a persistent-mode magnet must consider not only themagnitude but also the direction of the magnetic field applied to superconducting joints.Keywords: superconducting joint, HTS, angular dependence, critical current, joint resistance(Some figures may appear in colour only in the online journal)∗Author to whom any correspondence should be addressed.Original content from this workmay be used under the termsof the Creative Commons Attribution 4.0 licence. Any fur-ther distribution of this work must maintain attribution to the author(s) and thetitle of the work, journal citation and DOI.1361-6668/23/125010+9$33.00 Printed in the UK 1 © 2023 The Author(s). Published by IOP Publishing Ltdhttps://doi.org/10.1088/1361-6668/ad0565https://orcid.org/0000-0001-7217-9853https://orcid.org/0000-0001-7493-0559https://orcid.org/0000-0003-3218-0977https://orcid.org/0009-0007-1783-676Xmailto:TAKEDA.Yasuaki@nims.go.jphttp://crossmark.crossref.org/dialog/?doi=10.1088/1361-6668/ad0565&domain=pdf&date_stamp=2023-10-31https://creativecommons.org/licenses/by/4.0/Supercond. Sci. Technol. 36 (2023) 125010 Y Takeda et al1. IntroductionThe crystal structure of a cuprate high-temperature super-conductor (HTS) is layered with CuO2 planes sandwichedbetween charge reservoir layers. Owing to this structure, HTSmaterials often exhibit anisotropic electromagnetic proper-ties. This anisotropic property is observed in the critical cur-rent (Ic) of an HTS tape when a magnetic field is appliedin various directions, that is, the angular dependence of Ic.Commercially available REBa2Cu3Oy (REBCO, RE = rareearth) and (Bi,Pb)2Sr2Ca2Cu3Oy (Bi-2223) HTS tapes exhibita strong angular dependence of Ic [1–5]. In a superconduct-ing magnet, the magnetic field is applied in various direc-tions to superconducting wires/tapes. Superconducting mag-nets using HTS tapes have been designed to account for theangular dependence [6–9].Superconducting joints are used in persistent-modemagnets [10, 11]. Both high joint Ic (Icj) and low joint resist-ance (Rj) are required for a superconducting joint. Over thepast decade, significant progress has been made in supercon-ducting joint technology for HTS tapes/wires [11–21].The value of Icj is typically evaluated using a transportmeasurement, similar to the Ic measurement of a supercon-ducting tape/wire. In-field Icj values of REBCO and Bi-2223samples have been reported with the magnetic field perpen-dicular or parallel to the surface of the joined tape [18, 20,22–24]. However, in practice, the direction of the magneticfield applied to the superconducting joints in a persistent-modemagnet is not necessarily perpendicular or parallel. Therefore,the angular dependence of Icj for REBCO and Bi-2223 super-conducting joints must be investigated in detail not only forthe precise design of a persistent-mode magnet but also fora deeper understanding of materials science involved in HTSjoints.Low Rj is another important property of a superconduct-ing joint. Rj of 10−13–10−14 Ω is achieved in a routinely man-ufactured Nb-Ti superconducting joint for commercial mag-netic resonance imaging persistent-mode magnets [10]. For apersistent-mode 30.5 T (1.3 GHz) nuclear magnetic resonance(NMR) magnet that we are developing, Rj of less than 10−12 Ωat the operating current of 231 A is required for a supercon-ducting joint between HTS tapes [11, 25, 26]. Several studieshave evaluated the Rj of HTS joints [12, 14–16, 18, 20, 21,24–30]. However, to the best of our knowledge, no studies onthe angular dependence of Rj have been reported so far.Transport measurements, which are used to evaluate in-field Icj, are usually used to evaluate resistance. However,the lower limit of Rj that can be evaluated by the transportmeasurement is approximately 10−11 Ω [31, 32]. Therefore,these measurements cannot be used to evaluate the low resist-ance of a superconducting joint. Generally, the current decaymethod is typically used to evaluate Rj of less than 10−11 Ω[10, 33–41]. This method requires a closed loop comprising asuperconducting tape/wire with a superconducting joint con-necting both ends of the tape/wire. The decay of the currentintroduced in the superconducting loop (Iloop) is measured.An initial fast decay of Iloop is typically observed owing tothe current-sharing effect [33, 35, 36, 40, 41]. After the fastdecay is settled, a subsequent slow decay of Iloop is observed.Assuming that Rj is constant and corresponds to the circuit res-istance, the time (t) dependence of Iloop in the slow decay canbe described as follows:Iloop (t) = Iloop (0)exp(−RjLt), (1)where L is the self-inductance of the loop [10, 33].The magnetic field is typically measured to evaluate Iloop.Mostly, the center field trapped in the loop is measured usinga Hall sensor. A superconducting quantum interference devicevoltmeter or magnetometer is occasionally used to improve themeasurement sensitivity [35, 40].We have previously developed a joint resistance evaluationsystem that enables efficient current decay measurements[42]. In that system, a closed-loop sample is cooled using apulse-tube cryocooler. The loop diameter in each sample is100 mm. The number of turns in the loop is typically one,but more than one turn is acceptable. The value of L of theone-turn loop is 0.47 µH. The Iloop is introduced via mag-netic induction using a copper coil located at the center of theloop.In our measurements, the magnetic field near the super-conducting tape/wire, the so-called ‘self-field,’ was measuredusing the Hall sensor to evaluate Iloop. This is because theself-field is larger than the center field of the loop. The meas-urement sensitivity of this method is sufficient to evaluatethe decay of Iloop. However, uncertainty exists in the absolutevalue of Iloop obtained from the measured magnetic field, par-ticularly when the loop consists of a tape. To reduce uncer-tainty and improve precision, we have previously developeda current sensor consisting of a split core made of laminatedelectromagnetic steel and a Hall sensor [30].Using this system, if the introduced Iloop is sufficientlylower than Icj, Rj value less than 10−13 Ω can be evaluatedby measuring the current decay for several tens of minutes.If the introduced Iloop is close to or exceeds Icj, Icj value canbe evaluated using the time dependence of the Iloop or resid-ual Iloop observed after stabilizing the current decay. We haveevaluated not only Rj but also Icj for various superconductingloops using this system [20, 30, 42–45].Previously, we combined this system with a superconduct-ing solenoid magnet to evaluate Rj in a vertical magneticfield [30]. Recently, we introduced a split-pair superconduct-ing magnet instead of the solenoid. This split-pair magnetapplies a horizontal magnetic field (B) to the joint, as shownin figure 1(a). A system consisting of a motor and gears wasimplemented to rotate the closed-loop sample around the ver-tical axis. These enable us to evaluate the angular dependenceof Rj and Icj.To ensure the design of a Bi-2223 persistent-mode mag-net, it is crucial to evaluate the angular dependence of Rjand Icj, because Icj may lack sufficient margin. In this study,we evaluated the angular dependence of Rj and Icj in a Bi-2223 closed-loop sample with a superconducting joint. We2Supercond. Sci. Technol. 36 (2023) 125010 Y Takeda et alFigure 1. (a) Schematic of experimental setup. Horizontal magneticfield (B) is applied to the joint using a split-pair superconductingmagnet. The direction of magnetic field is controlled by rotating thesample. (b) Schematic showing the angle of magnetic field (θ). Theperpendicular component of the magnetic field applied to the tapesurface is Bx (=B cosθ).combined current decay measurements and sample rotation.To the best of our knowledge, this is the first systematic evalu-ation of the angular dependence of Rj and Icj of an HTS joint.2. Method2.1. Sample fabricationWe fabricated a Bi-2223 closed-loop sample with a super-conducting joint shown in figure 1(a). A 1.6 m long Ni-alloy-reinforced Bi-2223/Ag tape (DI-BSCCO® Type HT-NX [2, 4, 46, 47]) was used. The width and thickness ofthe tape were 4.5 and 0.25 mm, respectively. The rein-forcement at both ends, approximately 0.2 m long, wasremoved [26]. A praying-hands-type superconducting jointwas formed to connect both ends using a previously reportedprocess [17, 20, 45].To form the superconducting joint, a polycrystalline Bi-2223 intermediate layer was synthesized via heat treatment.As described in our previous study [45], during heat treat-ment, the sample was a one-turn loop with an approximately0.6 m long temperature transition zone. The joint was inser-ted into a tube furnace and heat-treated, whereas the looppart with the reinforcement was placed outside the furnaceand held at room temperature. After the heat treatment, theone-turn loop was wound into a three-turn loop with a dia-meter of 100 mm. The L of the sample was 1.4 µH, whichwas measured at room temperature before the ends wereconnected [42].2.2. Current decay measurements with sample rotationCurrent decay was measured by rotating the sample incre-mentally. The angle of the magnetic field (θ) was determinedas shown in figure 1(b). The direction of the magnetic fieldat θ = 90◦ was parallel to the tape surface. The time depend-ence of the voltage of the Hall sensor (VHall) in the currentFigure 2. Schematic of the sequence for measuring the currentdecay by incrementally rotating the sample. In sequence (5), thesample is rotated by 5◦ within 1 s. At each angle, t is the elapsedtime from when we started sample rotation. In sequences (6) and(7), we measured the current decay for approximately 10 min ateach angle from 0 to 85◦.sensor was measured at each angle. Iloop was calculated fromVHall using a linear relationship between a current and VHallobtained experimentally beforehand [20, 30].In a preliminary experiment, Icj reached the maximum at90◦. We started to rotate the sample (decrease θ) from 90◦at the experimental time (texp) of 0. At each angle, t wasthe elapsed time from when we started sample rotation. Themeasurement sequence, schematically shown in figure 2, isdescribed as follows:(1) The temperature of the sample was controlled to be 4 K.(2) A magnetic field (B) of 0.15–0.28 T was applied to thejoint at 90◦.(3) An Iloop of 220–221 A was introduced to the sample.(4) We waited until the initial current-sharing effect in thesample became negligible and the time variation VHallbecame flat, which required several tens of minutes.(5) The sample was rotated (θ was decreased) by 5◦ within 1 swhile the Iloop flowed. At texp = 0, the sample was rotatedfrom 90◦ to 85◦. This point corresponded to t = 0 at 85◦.(6) The time dependence of VHall was measured for approx-imately 10 min.(7) The 5◦ rotation and the 10minmeasurement were repeateduntil θ = 0.Using the measured VHall, we obtained the time depend-ence of Iloop (Iloop–t) for approximately 10 min at each angle.Because we measured VHall at a sampling rate of 1 Hz, therewere typically more than 600 data points in each Iloop–t curve.2.3. Evaluation of Rj and IcjTo evaluate Rj and Icj at each 5◦-incremental angle between0 and 85◦, we used 300 data points of the Iloop–t curve at300 s ⩽ t ⩽ 600 s. At 90◦, Rj was evaluated using 300 datapoints at −300 s ⩽ texp ⩽ 0.The value of Rj was obtained by fitting the data points ofthe Iloop–t curve to equation (1) using the least squares method.The value of Icj was estimated using the Iloop dependence ofthe voltage (V) obtained from the Iloop–t curve. When current3Supercond. Sci. Technol. 36 (2023) 125010 Y Takeda et aldecay was observed, we could calculate V using equation (2)as follows:V=−L∆Iloop∆t. (2)The Iloop dependence of the calculated voltage (V–Iloop)was smoothed using a 15-pointmoving average. The smoothedV–Iloop curve at a voltage ranging from 10−7 to 10−9 Vwas fit-ted to an empirical power law model (V = α Iloopn, where αand n are constants) using the least squares method. We estim-ated Icj at a voltage criterion (Vc) of 10−8 V, which correspon-ded to the Iloop value at V = 10−8 V. Some of the Iloop valuesat 10−8 Vwere estimated by the extrapolation from the fitting.3. Results and discussion3.1. Time dependence of Iloop obtained from VHallFigure 3 shows VHall as a function of texp at 4 K and 0.25 T.The inset shows the magnified view at approximately 70◦.From 90◦ to 75◦, a decrease in VHall with time was not clearlyobserved; that is, VHall–texp at each angle was almost flat.This implies that the decay of Iloop was negligible at 75–90◦,and the Iloop was considerably lower than Icj. By contrast,at angles less than 75◦, a decrease in VHall over time wasevident.The value of VHall increased by less than 1 mV for each 5◦rotation, as shown in the inset of figure 3. There are two pos-sible reasons for this increase in VHall: the first is the staticcomponent of the change in the offset of VHall. The offsetis primarily attributed to the leakage field of the split-pairmagnet, calculated to be approximately 1 mT in the direc-tion opposite to the magnetic field applied to the joint. Thethin-film Hall sensor used in the current sensor was paral-lel to the plane of the Bi-2223 tape in the loop. The off-set was approximately 0.6 mV at 90◦ and increased withsample rotation. At θ = 0, this static component showed thelargest value of 3.7 mV. The second reason is the dynamiccomponent showing an increase in Iloop owing to magneticinduction. The magnetic flux across the loop of the sampleowing to the leakage field is reduced by sample rotation.This reduction in magnetic flux induces a current in the loop.This induced current increases Iloop, resulting in an increasein VHall.The time variation of Iloop, Iloop–t, at 4 K, 0.25 T, and eachangle of 0–85◦ is shown in figure 4(a). The Iloop values wereobtained from the VHall values shown in figure 3. The offsetwas subtracted from VHall at each angle.Figure 4(a) shows that, at angles less than 70◦, the residualIloop, that is, the Iloop at 600 s decreased as the angle decreased.This corresponds to a decrease in Icj. Sample rotation fromhigh to low angle between 90◦ and 0 increased the perpendicu-lar component of the magnetic field applied to the tape surface,that is, Bx (=B cosθ) shown in figure 1(b). Because the inter-mediate layer was formed almost parallel to the tape surface[20], Bx was almost perpendicular to the intermediate layerof the superconducting joint. Furthermore, because Bi-2223Figure 3. Voltage of Hall sensor (VHall) in the current sensor as afunction of experimental time (texp) at 4 K and 0.25 T. We started torotate the sample from 90◦ at texp = 0 by 5◦ within 1 s. Inset showsa magnified view at approximately 70◦.Figure 4. Time dependence of (a) Iloop and (b) normalized Iloop at4 K, 0.25 T, and 0–85◦. Iloop values are calculated using VHall valuesshown in figure 3. At angles less than 70◦, Iloop at 600 s decreases asthe angle decreases owing to a decrease in Icj. A persistent currentcontinues to flow in the sample at high angles of 75–90◦.grains in the intermediate layer were weakly c-axis-aligned[45, 48], Bx was almost parallel to the c-axis of these grains.As Bx increased, Ic of the intermediate layer decreased signi-ficantly. Because Icj was primarily dominated by the Ic of theintermediate layer [48], Icj decreased as the angle decreasedand Bx (=B cosθ) increased.4Supercond. Sci. Technol. 36 (2023) 125010 Y Takeda et alFigure 4(b) shows the normalized Iloop using the max-imum value (Iloopmax) at each angle. The decay ratio(1 − Iloop/Iloopmax) at 75◦ for 600 s was 1.4 × 10−4. Thefield drift rate is less than 10−2 ppm h−1 in a typical400 MHz (9.4 T) Nb-Ti NMR magnet with 10 joints andL of 40 H at an operating current of approximately 100 A[10]. If the performance of the 10 joints is equivalent tothat of the Bi-2223 superconducting joint sample at 75◦, afield drift rate of 2.9 × 10−4 ppm h−1 can be extrapol-ated. This rate is considerably lower than that of the typ-ical NMR magnet. Consequently, a persistent current contin-ued to flow in the sample at 4 K, 0.25 T, and high anglesof 75–90◦.The decay ratio at 70◦ for 600 s was 1.3 × 10−3. This cor-responds to a field drift rate of 2.7 × 10−3 ppm h−1 using thesame extrapolation. Although this value is close to that of thetypical NMR magnet, the decay of Iloop at 70◦ is clearer thanat 75◦, as shown in figure 4(b). Therefore, we conclude that apersistent current did not flow at 0–70◦.3.2. Angular dependence of Icj and RjFigures 5(a)–(d) shows the angular dependence of Icj and Rj at4 K for 0.15, 0.20, 0.25, and 0.28 T, respectively. The ver-tical error bars for Rj, which are visible at 85◦ and 90◦ infigure 5(c), correspond to the standard uncertainty obtainedfrom fitting. At 0.15 and 0.20 T, the measurements at highangles close to 90◦ were performed at intervals of 15◦ and10◦, respectively. This is because Iloop was expected to beconsiderably lower than Icj, which caused negligible currentdecay.At a certain angle, Icj decreased as the magnetic fieldincreased. This was consistent with the field dependence of Icjevaluated by transport measurements using a Bi-2223 super-conducting joint sample [20]. The evaluated Icj increased asthe angle increased. The Icj probably showed a broad peak at90◦, similar to the angular dependence of Ic for Bi-2223 tapes[1, 5].Figure 6 shows the smoothed V–Iloop curve at 0.15 T and0–50◦. We calculated the voltage from the Iloop–t curve at300 s ⩽ t ⩽ 600 s using equation (2). When the decay of Iloopis significant,∆Iloop becomes large and the calculated voltageis also large. The range of the calculated voltage varies withthe angle. From the obtainedV–Iloop curve, Icj was evaluated atVc of 10−8 V for each angle. At 25–40◦, Icj was obtained fromthe intersection of V–Iloop and Vc, because Vc was within thevoltage range of V–Iloop. At 0–20◦, the V–Iloop curves wereextrapolated using the power law (V = α Iloopn) as shown bydashed lines in figure 6 because the voltage range was lowerthan Vc. Icj was estimated from the intersection of the extra-polated V–Iloop and Vc.At 45◦ and 50◦, the Icj values estimated from the intersec-tions were higher than the initially introduced Iloop of 220 A.Given that Icj was estimated from the current decay, Icj valueshigher than the initial Iloop value were not realistic. Thus, for0.15 T, we employed Icj only at 0–40◦.Figure 5. Angular dependence of Rj and Icj at 4 K for (a) 0.15 T, (b)0.20 T, (c) 0.25 T, and (d) 0.28 T. Vertical error bars for Rjcorrespond to the standard uncertainty obtained from fitting. Icjincreases as the angle increases. The angular dependence of Rj withsample rotation can be divided into three regions: (i) low-resistanceregion (Rj of less than 1.4 × 10−13 Ω), (ii) transition region (threeorders of magnitude change in Rj to its maximum, Rjmax), and (iii)high-resistance region (Rj of 10−11–10−10 Ω).The Icj values were evaluated in a similar way for 0.20,0.25, and 0.28 T. Icj values lower than the initial Iloop value(220 A) are shown in figure 5. This is the reason why Icj athigher angles are not plotted.The angular dependence of Rj with sample rotation canbe divided into three regions: (i) low-resistance region (Rj ofless than 1.4 × 10−13 Ω), (ii) transition region (three ordersof magnitude changes in Rj to its maximum, Rjmax), and5Supercond. Sci. Technol. 36 (2023) 125010 Y Takeda et alFigure 6. Smoothed V–Iloop curve at 0.15 T and 0–50◦. V–Iloop at0–50◦ is fitted to the power law model, as shown by dashed lines.(iii) high-resistance region (Rj of 10−11–10−10 Ω). The angu-lar dependence of Rj in each region is discussed below.(i) Low-resistance regionThis region is observed at high angles for each magnetic field.Figure 4(b) shows that the decay of Iloop at 75–90◦ and 0.25 T,corresponding to this region, was small. Because Iloop is con-siderably lower than Icj, low Rj is realized and the persistentcurrent continues to flow, as described in the previous section.At 0.25 T and 75◦, Rj was evaluated to be 1.4 × 10−13 Ω.The coefficient of determination (r2) in the fitting using theleast squares method was 0.99. This implies that Rj can beobtained quantitatively. However, r2 decreased at higherangles of 80–90◦ for 0.25 T, at which the lower Rj values wereobserved. As shown in figure 4(b), the Iloop–t curves werenearly flat at these angles. Although not visible in figure 3, thenoise of VHall of ±5 × 10−7 V influenced the Iloop–t curves,corresponding to ±2 ppm deviation in Iloop. Consequently,the uncertainty in the fitting for Rj derivation waslarge.In region (i), for Rj of less than 4 × 10−14 Ω, r2 was lessthan 0.8. This indicates that such low Rj values could not bequantitatively evaluated. Nevertheless, it is certain that the Rjvalues were less than the quantitative value of 1.4 × 10−13 Ωat 0.25 T and 75◦. This indicates that the persistent currentcontinued to flow in the sample owing to sufficiently low Rj.(ii) Transition regionThe value ofRj changed by approximately three orders ofmag-nitude to its maximum (Rjmax) in region (ii). Its values wereevaluated quantitatively because r2 was larger than 0.98 foreach fitting.As shown in figure 5, region (ii) shifted toward higherangles as the magnetic field increased. To clarify this shift,sections of Rj in region (ii) of figures 5(a)–(d) are shown infigure 7(a). Figure 7(b) shows this plot with the horizontal axischanged to B cosθ. The significant change in Rj at each mag-netic field was nearly identical at B cosθ of 6–11 × 10−2 T.The changes in Rj were independent of the magnitude of mag-netic field.As described in the previous section, Icj decreased owingto sample rotation with an increase in Bx = B cosθ. Rj isknown to increase as the ratio of Iloop to Icj increases, that is,as the load factor increases [30, 36, 38, 42]. In region (ii), thechanges in Rj were due to the following reason. Icj decreasedas Bx = B cosθ increased owing to sample rotation. Becausethe change in Iloop by sample rotation is small, this decreasein Icj caused an increase in the load factor. This resulted in asignificant increase in Rj. The load factor values were not cal-culated, because Icj could not be evaluated at most angles foreach magnetic field in region (ii).(iii) High-resistance regionThis region eventually appeared when θ approached zero withsample rotation. High Rj values of 10−11–10−10 Ω corres-ponded to the decay of Iloop by several amperes, as shown infigure 4(a).In region (iii), r2 in the fitting ranged from 0.99 to1.00, indicating that the Rj values were valid with suf-ficient precision. As shown in figure 5, Rj was higherat higher angles in each magnetic field. Using the eval-uated Icj values in region (iii), we quantitatively dis-cussed the relationship between the load factor (F) andRj. The value of F was calculated using equation (3)as follows:F=Iloop (t= 450s)Icj(Vc = 10−8V) , (3)where t = 450 s corresponds to the median of the range oft used to obtain Rj (300 s ⩽ t ⩽ 600 s). The value of Fcan be larger than 1.00 when Iloop (t = 450 s) exceeds Icj,because Icj is determined by a considerably low voltage cri-terion, Vc = 10−8 V.Figure 8 shows the relationship between F and Rj inregion (iii), where the gray dashed line is derived using theleast squares method. The value of F increased as the angleincreased. The F values of 0.974–1.02 suggest that Iloop wascomparable to Icj. For F values of 0.974–1.02, Rj appeared toincrease linearly. This suggests that, in region (iii), the changein Rj owing to sample rotation is primarily attributed to thechange in F.3.3. DiscussionWhen the sample is rotated, Iloop is probably influenced bythe screening current and current sharing in the sample. Thescreening current is induced by sample rotation owing to anincrease in Bx. Current sharing occurs when Iloop is close toor exceeds Icj, typically in regions (ii) and (iii). However, asdescribed in the previous section, the behavior of Rj couldbe explained using B cosθ and F in regions (ii) and (iii),6Supercond. Sci. Technol. 36 (2023) 125010 Y Takeda et alFigure 7. (a) Sections of Rj in region (ii) of figures 5(a)–(d). Region(ii) shifts toward higher angles as the magnetic field increases. (b)Relationship between B cosθ and Rj in region (ii). The significantchanges in Rj at each magnetic field are nearly identical at B cosθ of6–11 × 10−2 T, which are independent of the magnitude of themagnetic field.Figure 8. Relationship between load factor (F) and Rj in region(iii). Change in Rj owing to sample rotation is primarily attributed tochange in F.respectively. This implies that the influences of the screeningcurrent and current sharing were sufficiently small in ourmeasurements.As explained in 3.2, we employed the Icj values lower thanthe initially introduced Iloop of 220 A. Therefore, the highestangle at which Icj was obtained was 65◦ at 0.25 and 0.28 T. Ifa larger Iloop is introduced, larger Icj values can be evaluatedat high angles near 90◦.In a preliminary measurement at 0.3 T, an introduced Iloopof 220A decayed even at 90◦. A persistent current of 220A didnot flow at 0.3 T. This means that region (i) was not observed at0.3 T. To investigate the resistance transition from regions (i)–(iii) in this study, we chose 0.28 T as the maximum magneticfield.At present, Icj (Ic of the Bi-2223 superconducting joint) islower than Ic of a tape [2, 4]. To ensure sufficient current mar-gin, superconducting joints must be placed in a space at a lowmagnetic field in amagnet. In the 1.3 GHz (30.5 T) NMRmag-net being developed, the magnetic field applied to the Bi-2223superconducting joints is designed to be lower than 1 T [11,25]. We believe that the magnetic fields of 0.15–0.28 T usedin this study are in a realistic range for practical applications.The angular dependence of Rj suggests that, in the designof a persistent-mode magnet, we must consider not only themagnitude but also the direction of a magnetic field appliedto superconducting joints. The magnet must be designed suchthat superconducting joints are used in region (i). This allowsfor persistent-mode operation with a low Rj. If superconduct-ing joints must be used in regions (ii) or (iii), additional effortsmust be made to achieve a lower Rj. A recent study has shownthat when Iloop is close to Icj, Rj is almost inversely propor-tional to the elapsed time and decreases with an increase in thepinning potential of a superconducting joint [49]. This may beeffective for achieving a lower Rj.In region (iii),Rj decreased asF decreased. The relationshipbetween F and Rj shown in figure 8 implies that a low Rj, asobserved in region (i), may be achieved at F of less than 0.964.Evaluating the trend of Rj in detail at F equal to approxim-ately 0.964 will help clarify the conditions under which a suffi-ciently low Rj for a persistent-mode operation can be achieved.4. ConclusionIn this study, the angular dependence of Rj and Icj of a Bi-2223 closed-loop sample with a superconducting joint wassystematically evaluated at 4 K and 0.15–0.28 T. An eval-uation method combining current decay measurements andsample rotation was used. The sample was rotated from 90◦to 0, wherein the angle of 90◦ corresponded to the direction ofthe magnetic field parallel to the tape surface. The followingconclusions were drawn:(1) Rj and Icj are dependent on the angle of the magneticfield. The evaluated Icj increased as the angle increased.The angular dependence of Rj with sample rotation can bedivided into three regions:(i) In the low-resistance region, corresponding to highangles close to 90◦, the loop current was consider-ably lower than Icj. Rj of less than 1.4 × 10−13 Ω wasobserved and a persistent current continued to flow inthe sample.(ii) In the transition region, Rj significantly increased bythree orders of magnitude owing to an increase in theperpendicular component of the magnetic field, whichdecreased Icj. This caused an increase in the ratio ofthe loop current to Icj, that is, the load factor, resultingin an increase in Rj.7Supercond. Sci. Technol. 36 (2023) 125010 Y Takeda et al(iii) In the high-resistance region, corresponding to lowangles, Rj remained high, ranging from 10−11 to10−10 Ω. When the load factor was 0.974–1.02, Rjappeared to increase linearly.(2) In the design of a persistent-mode magnet, we mustconsider not only the magnitude but also the directionof a magnetic field applied to superconducting joints.Evaluating the trend of Rj in detail at the load factor ofapproximately 0.964 will help clarify the conditions underwhich a sufficiently low Rj for a persistent-mode operationcan be achieved.Data availability statementAll data that support the findings of this study are includedwithin the article (and any supplementary files).AcknowledgmentsThis work was supported by JST Mirai-Program Grant No.JPMJMI17A2 and JSPS KAKENHI Grant No. JP22K14482,Japan.ORCID iDsY Takeda https://orcid.org/0000-0001-7217-9853G Nishijima https://orcid.org/0000-0001-7493-0559T Motoki https://orcid.org/0000-0003-3218-0977J Shimoyama https://orcid.org/0009-0007-1783-676XReferences[1] Sunwong P, Higgins J S and Hampshire D P 2011 Angular,temperature, and strain dependence of the critical current ofDI-BSCCO tapes in high magnetic fields IEEE Trans. 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Introduction 2. Method 2.1. Sample fabrication 2.2. Current decay measurements with sample rotation 2.3. Evaluation of Rj and Icj 3. Results and discussion 3.1. Time dependence of Iloop obtained from VHall 3.2. Angular dependence of Icj and Rj 3.3. Discussion 4. Conclusion References