Angular dependence of resistance and critical current of a Bi-2223 superconducting joint

Low resistance and high critical current are prerequisites for superconducting joints used in persistent-mode magnets. Herein, we use a joint resistance evaluation system, previously developed by us, to systematically evaluate the angular dependence of resistance and critical current of a Bi-2223 superconducting joint in a closed-loop sample. The current decay is measured by rotating the sample incrementally. The time dependence of the loop current is evaluated 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 resistance and critical current of the joint depend on the angle of the magnetic field. The evaluated critical current increases as the angle increases. The angular dependence of resistance can be divided into three regions: low-resistance, transition, and high-resistance regions. The low-resistance region 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 than 1.4 × 10−13 Ω. In the transition region, the joint resistance significantly increases by three orders of magnitude with sample rotation. This significant increase is attributed to an increase in the perpendicular component of the magnetic field, which decreases the critical current of the joint. At lower angles, the joint resistance remains high, ranging from 10−11 to 10−10 Ω. A significant decay in the loop current is observed in the high-resistance region. Based on these findings, we conclude that the design of a persistent-mode magnet must consider not only the magnitude but also the direction of the magnetic field applied to superconducting joints.

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Introduction
The crystal structure of a cuprate high-temperature superconductor (HTS) is layered with CuO 2 planes sandwiched between charge reservoir layers.Owing to this structure, HTS materials often exhibit anisotropic electromagnetic properties.This anisotropic property is observed in the critical current (I c ) of an HTS tape when a magnetic field is applied in various directions, that is, the angular dependence of I c .Commercially available REBa 2 Cu 3 O y (REBCO, RE = rare earth) and (Bi,Pb) 2 Sr 2 Ca 2 Cu 3 O y (Bi-2223) HTS tapes exhibit a strong angular dependence of I c [1][2][3][4][5].In a superconducting magnet, the magnetic field is applied in various directions to superconducting wires/tapes.Superconducting magnets using HTS tapes have been designed to account for the angular dependence [6][7][8][9].
The value of I cj is typically evaluated using a transport measurement, similar to the I c measurement of a superconducting tape/wire.In-field I cj values of REBCO and Bi-2223 samples have been reported with the magnetic field perpendicular or parallel to the surface of the joined tape [18,20,[22][23][24].However, in practice, the direction of the magnetic field applied to the superconducting joints in a persistent-mode magnet is not necessarily perpendicular or parallel.Therefore, the angular dependence of I cj for REBCO and Bi-2223 superconducting joints must be investigated in detail not only for the precise design of a persistent-mode magnet but also for a deeper understanding of materials science involved in HTS joints.
Low R j is another important property of a superconducting joint.R j of 10 −13 -10 −14 Ω is achieved in a routinely manufactured Nb-Ti superconducting joint for commercial magnetic resonance imaging persistent-mode magnets [10].For a persistent-mode 30.5 T (1.3 GHz) nuclear magnetic resonance (NMR) magnet that we are developing, R j of less than 10 −12 Ω at the operating current of 231 A is required for a superconducting joint between HTS tapes [11,25,26].Several studies have evaluated the R j of HTS joints [12, 14-16, 18, 20, 21, 24-30].However, to the best of our knowledge, no studies on the angular dependence of R j have been reported so far.
Transport measurements, which are used to evaluate infield I cj , are usually used to evaluate resistance.However, the lower limit of R j that can be evaluated by the transport measurement is approximately 10 −11 Ω [31,32].Therefore, these measurements cannot be used to evaluate the low resistance of a superconducting joint.Generally, the current decay method is typically used to evaluate R j of less than 10 −11 Ω [10,[33][34][35][36][37][38][39][40][41].This method requires a closed loop comprising a superconducting tape/wire with a superconducting joint connecting both ends of the tape/wire.The decay of the current introduced in the superconducting loop (I loop ) is measured.An initial fast decay of I loop is typically observed owing to the current-sharing effect [33,35,36,40,41].After the fast decay is settled, a subsequent slow decay of I loop is observed.Assuming that R j is constant and corresponds to the circuit resistance, the time (t) dependence of I loop in the slow decay can be described as follows: where L is the self-inductance of the loop [10,33].The magnetic field is typically measured to evaluate I loop .Mostly, the center field trapped in the loop is measured using a Hall sensor.A superconducting quantum interference device voltmeter or magnetometer is occasionally used to improve the measurement sensitivity [35,40].
We have previously developed a joint resistance evaluation system that enables efficient current decay measurements [42].In that system, a closed-loop sample is cooled using a pulse-tube cryocooler.The loop diameter in each sample is 100 mm.The number of turns in the loop is typically one, but more than one turn is acceptable.The value of L of the one-turn loop is 0.47 µH.The I loop is introduced via magnetic induction using a copper coil located at the center of the loop.
In our measurements, the magnetic field near the superconducting tape/wire, the so-called 'self-field,' was measured using the Hall sensor to evaluate I loop .This is because the self-field is larger than the center field of the loop.The measurement sensitivity of this method is sufficient to evaluate the decay of I loop .However, uncertainty exists in the absolute value of I loop obtained from the measured magnetic field, particularly when the loop consists of a tape.To reduce uncertainty and improve precision, we have previously developed a current sensor consisting of a split core made of laminated electromagnetic steel and a Hall sensor [30].
Using this system, if the introduced I loop is sufficiently lower than I cj , R j value less than 10 −13 Ω can be evaluated by measuring the current decay for several tens of minutes.If the introduced I loop is close to or exceeds I cj , I cj value can be evaluated using the time dependence of the I loop or residual I loop observed after stabilizing the current decay.We have evaluated not only R j but also I cj for various superconducting loops using this system [20,30,[42][43][44][45].
Previously, we combined this system with a superconducting solenoid magnet to evaluate R j in a vertical magnetic field [30].Recently, we introduced a split-pair superconducting magnet instead of the solenoid.This split-pair magnet applies a horizontal magnetic field (B) to the joint, as shown in figure 1(a).A system consisting of a motor and gears was implemented to rotate the closed-loop sample around the vertical axis.These enable us to evaluate the angular dependence of R j and I cj .
To ensure the design of a Bi-2223 persistent-mode magnet, it is crucial to evaluate the angular dependence of R j and I cj , because I cj may lack sufficient margin.In this study, we evaluated the angular dependence of R j and I cj in a Bi-2223 closed-loop sample with a superconducting joint.We combined current decay measurements and sample rotation.To the best of our knowledge, this is the first systematic evaluation of the angular dependence of R j and I cj of an HTS joint.

Sample fabrication
We fabricated a Bi-2223 closed-loop sample with a superconducting joint shown in figure 1(a).A 1.6 m long Nialloy-reinforced Bi-2223/Ag tape (DI-BSCCO ® Type HT-NX [2,4,46,47]) was used.The width and thickness of the tape were 4.5 and 0.25 mm, respectively.The reinforcement at both ends, approximately 0.2 m long, was removed [26].A praying-hands-type superconducting joint was formed to connect both ends using a previously reported process [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 treatment, the sample was a one-turn loop with an approximately 0.6 m long temperature transition zone.The joint was inserted into a tube furnace and heat-treated, whereas the loop part with the reinforcement was placed outside the furnace and held at room temperature.After the heat treatment, the one-turn loop was wound into a three-turn loop with a diameter of 100 mm.The L of the sample was 1.4 µH, which was measured at room temperature before the ends were connected [42].

Current decay measurements with sample rotation
Current decay was measured by rotating the sample incrementally.The angle of the magnetic field (θ) was determined as shown in figure 1(b).The direction of the magnetic field at θ = 90 • was parallel to the tape surface.The time dependence of the voltage of the Hall sensor (V Hall ) in the current  5), the sample is rotated by 5 • within 1 s.At each angle, t is the elapsed time from when we started sample rotation.In sequences ( 6) and ( 7), we measured the current decay for approximately 10 min at each angle from 0 to 85 • .
sensor was measured at each angle.I loop was calculated from V Hall using a linear relationship between a current and V Hall obtained experimentally beforehand [20,30].
In a preliminary experiment, I cj reached the maximum at 90 • .We started to rotate the sample (decrease θ) from 90 • at the experimental time (t exp ) of 0. At each angle, t was the elapsed time from when we started sample rotation.The measurement sequence, schematically shown in figure 2, is described as follows: (1) The temperature of the sample was controlled to be 4 K.Using the measured V Hall , we obtained the time dependence of I loop (I loop -t) for approximately 10 min at each angle.Because we measured V Hall at a sampling rate of 1 Hz, there were typically more than 600 data points in each I loop -t curve.

Evaluation of R j and I cj
To evaluate R j and I cj at each 5 • -incremental angle between 0 and 85 • , we used 300 data points of the I loop -t curve at 300 s ⩽ t ⩽ 600 s.At 90 • , R j was evaluated using 300 data points at −300 s ⩽ t exp ⩽ 0.
The value of R j was obtained by fitting the data points of the I loop -t curve to equation (1) using the least squares method.The value of I cj was estimated using the I loop dependence of the voltage (V) obtained from the I loop -t curve.When current decay was observed, we could calculate V using equation ( 2) as follows: The I loop dependence of the calculated voltage (V-I loop ) was smoothed using a 15-point moving average.The smoothed V-I loop curve at a voltage ranging from 10 −7 to 10 −9 V was fitted to an empirical power law model (V = α I loop n , where α and n are constants) using the least squares method.We estimated I cj at a voltage criterion (V c ) of 10 −8 V, which corresponded to the I loop value at V = 10 −8 V. Some of the I loop values at 10 −8 V were estimated by the extrapolation from the fitting.Figure 4(a) shows that, at angles less than 70 • , the residual I loop , that is, the I loop at 600 s decreased as the angle decreased.This corresponds to a decrease in I cj .Sample rotation from high to low angle between 90 • and 0 increased the perpendicular component of the magnetic field applied to the tape surface, that is, B x (=B cosθ) shown in figure 1(b).Because the intermediate layer was formed almost parallel to the tape surface [20], B x was almost perpendicular to the intermediate layer of the superconducting joint.Furthermore, because Bi-2223   The field drift rate is less than 10 −2 ppm h −1 in a typical 400 MHz (9.4 T) Nb-Ti NMR magnet with 10 joints and L of 40 H at an operating current of approximately 100 A [10].If the performance of the 10 joints is equivalent to that of the Bi-2223 superconducting joint sample at 75 • , a field drift rate of 2.9 × 10 −4 ppm h −1 can be extrapolated.This rate is considerably lower than that of the typical NMR magnet.Consequently, a persistent current continued to flow in the sample at 4 K, 0.25 T, and high angles of 75-90 • .

Time dependence of I loop obtained from V Hall
The decay ratio at 70 • for 600 s was 1.3 × 10 −3 .This corresponds to a field drift rate of 2.7 × 10 −3 ppm h −1 using the same extrapolation.Although this value is close to that of the typical NMR magnet, the decay of I loop at 70 • is clearer than at 75 • , as shown in figure 4(b).Therefore, we conclude that a persistent current did not flow at 0-70 • .

Angular dependence of I cj and R j
Figures 5(a)-(d) shows the angular dependence of I cj and R j at 4 K for 0.15, 0.20, 0.25, and 0.28 T, respectively.The vertical error bars for R j , which are visible at 85 • and 90 • in figure 5(c), correspond to the standard uncertainty obtained from fitting.At 0.15 and 0.20 T, the measurements at high angles close to 90 • were performed at intervals of 15 • and 10 • , respectively.This is because I loop was expected to be considerably lower than I cj , which caused negligible current decay.
At a certain angle, I cj decreased as the magnetic field increased.This was consistent with the field dependence of I cj evaluated by transport measurements using a Bi-2223 superconducting joint sample [20].The evaluated I cj increased as the angle increased.The I cj probably showed a broad peak at 90 • , similar to the angular dependence of I c for Bi-2223 tapes [1,5].
Figure 6 shows the smoothed V-I loop curve at 0.15 T and 0-50 • .We calculated the voltage from the I loop -t curve at 300 s ⩽ t ⩽ 600 s using equation (2).When the decay of I loop is significant, ∆I loop becomes large and the calculated voltage is also large.The range of the calculated voltage varies with the angle.From the obtained V-I loop curve, I cj was evaluated at V c of 10 −8 V for each angle.At 25-40 • , I cj was obtained from the intersection of V-I loop and V c , because V c was within the voltage range of V-I loop .At 0-20 • , the V-I loop curves were extrapolated using the power law (V = α I loop n ) as shown by dashed lines in figure 6 because the voltage range was lower than V c .I cj was estimated from the intersection of the extrapolated V-I loop and V c .
At 45 • and 50 • , the I cj values estimated from the intersections were higher than the initially introduced I loop of 220 A. Given that I cj was estimated from the current decay, I cj values higher than the initial I loop value were not realistic.Thus, for 0.15 T, we employed I cj only at 0-40 • .The I cj values were evaluated in a similar way for 0.20, 0.25, and 0.28 T. I cj values lower than the initial I loop value (220 A) are shown in figure 5.This is the reason why I cj at higher angles are not plotted.
The angular dependence of R j with sample rotation can be divided into three regions: (i) low-resistance region (R j of less than 1.4 × 10 −13 Ω), (ii) transition region (three orders of magnitude changes in R j to its maximum, R j max ), and (iii) high-resistance region (R j of 10 −11 -10 −10 Ω).The angular dependence of R j in each region is discussed below.
(i) Low-resistance region This region is observed at high angles for each magnetic field.Figure 4(b) shows that the decay of I loop at 75-90 • and 0.25 T, corresponding to this region, was small.Because I loop is considerably lower than I cj , low R j is realized and the persistent current continues to flow, as described in the previous section.
At 0.25 T and 75 • , R j was evaluated to be 1.4 × 10 −13 Ω.The coefficient of determination (r 2 ) in the fitting using the least squares method was 0.99.This implies that R j can be obtained quantitatively.However, r 2 decreased at higher angles of 80-90 • for 0.25 T, at which the lower R j values were observed.As shown in figure 4(b), the I loop -t curves were nearly flat at these angles.Although not visible in figure 3, the noise of V Hall of ±5 × 10 −7 V influenced the I loop -t curves, corresponding to ±2 ppm deviation in I loop .Consequently, the uncertainty in the fitting for R j derivation was large.
In region (i), for R j of less than 4 10 −14 Ω, r 2 was less than 0.8.This indicates that such low R j values could not be quantitatively evaluated.Nevertheless, it is certain that the R j values were less than the quantitative value of 1.4 × 10 −13 Ω at 0.25 T and 75 • .This indicates that the persistent current continued to flow in the sample owing to sufficiently low R j .
(ii) Transition region The value of R j changed by approximately three orders of magnitude to its maximum (R j max ) in region (ii).Its values were evaluated quantitatively because r 2 was larger than 0.98 for each fitting.
As shown in figure 5, region (ii) shifted toward higher angles as the magnetic field increased.To clarify this shift, sections of R j in region (ii) of figures 5(a)-(d) are shown in figure 7(a).Figure 7(b) shows this plot with the horizontal axis changed to B cosθ.The significant change in R j at each magnetic field was nearly identical at B cosθ of 6-11 × 10 −2 T. The changes in R j were independent of the magnitude of magnetic field.
As described in the previous section, I cj decreased owing to sample rotation with an increase in B x = B cosθ.R j is known to increase as the ratio of I loop to I cj increases, that is, as the load factor increases [30,36,38,42].In region (ii), the changes in R j were due to the following reason.I cj decreased as B x = B cosθ increased owing to sample rotation.Because the change in I loop by sample rotation is small, this decrease in I cj caused an increase in the load factor.This resulted in a significant increase in R j .The load factor values were not calculated, because I cj could not be evaluated at most angles for each magnetic field in region (ii).
(iii) High-resistance region This region eventually appeared when θ approached zero with sample rotation.High R j values of 10 −11 -10 −10 Ω corresponded to the decay of I loop by several amperes, as shown in figure 4(a).
In region (iii), r 2 in the fitting ranged from 0.99 to 1.00, indicating that the R j values were valid with sufficient precision.As shown in figure 5, R j was higher at higher angles in each magnetic field.Using the evaluated I cj values in region (iii), we quantitatively discussed the relationship between the load factor (F) and R j .The value of F was calculated using equation ( 3) as follows: where t = 450 s corresponds to the median of the range of t used to obtain R j (300 s ⩽ t ⩽ 600 s).The value of F can be larger than 1.00 when I loop (t = 450 s) exceeds I cj , because I cj is determined by a considerably low voltage criterion, V c = 10 −8 V. Figure 8 shows the relationship between F and R j in region (iii), where the gray dashed line is derived using the least squares method.The value of F increased as the angle increased.The F values of 0.974-1.02suggest that I loop was comparable to I cj .For F values of 0.974-1.02,R j appeared to increase linearly.This suggests that, in region (iii), the change in R j owing to sample rotation is primarily attributed to the change in F.

Discussion
When the sample is rotated, I loop is probably influenced by the screening current and current sharing in the sample.The screening current is induced by sample rotation owing to an increase in B x .Current sharing occurs when I loop is close to or exceeds I cj , typically in regions (ii) and (iii).However, as described in the previous section, the behavior of R j could be explained using B cosθ and F in regions (ii) and (iii),  respectively.This implies that the influences of the screening current and current sharing were sufficiently small in our measurements.
As explained in 3.2, we employed the I cj values lower than the initially introduced I loop of 220 A. Therefore, the highest angle at which I cj was obtained was 65 • at 0.25 and 0.28 T. If a larger I loop is introduced, larger I cj values can be evaluated at high angles near 90 • .
In a preliminary measurement at 0.3 T, an introduced I loop of 220 A decayed even at 90 • .A persistent current of 220 A did not flow at 0.3 T. This means that region (i) was not observed at 0.3 T. To investigate the resistance transition from regions (i)-(iii) in this study, we chose 0.28 T as the maximum magnetic field.
At present, I cj (I c of the Bi-2223 superconducting joint) is lower than I c of a tape [2,4].To ensure sufficient current margin, superconducting joints must be placed in a space at a low magnetic field in a magnet.In the 1.3 GHz (30.5 T) NMR magnet being developed, the magnetic field applied to the Bi-2223 superconducting joints is designed to be lower than 1 T [11,25].We believe that the magnetic fields of 0.15-0.28T used in this study are in a realistic range for practical applications.
The angular dependence of R j suggests that, in the design of a persistent-mode magnet, we must consider not only the magnitude but also the direction of a magnetic field applied to superconducting joints.The magnet must be designed such that superconducting joints are used in region (i).This allows for persistent-mode operation with a low R j .If superconducting joints must be used in regions (ii) or (iii), additional efforts must be made to achieve a lower R j .A recent study has shown that when I loop is close to I cj , R j is almost inversely proportional to the elapsed time and decreases with an increase in the pinning potential of a superconducting joint [49].This may be effective for achieving a lower R j .
In region (iii), R j decreased as F decreased.The relationship between F and R j shown in figure 8 implies that a low R j , as observed in region (i), may be achieved at F of less than 0.964.Evaluating the trend of R j in detail at F equal to approximately 0.964 will help clarify the conditions under which a sufficiently low R j for a persistent-mode operation can be achieved.

Conclusion
In this study, the angular dependence of R j and I cj of a Bi-2223 closed-loop sample with a superconducting joint was systematically evaluated at 4 K and 0.15-0.28T.An evaluation method combining current decay measurements and sample rotation was used.The sample was rotated from 90 • to 0, wherein the angle of 90 • corresponded to the direction of the magnetic field parallel to the tape surface.The following conclusions were drawn: (1) R j and I cj are dependent on the angle of the magnetic field.The evaluated I cj increased as the angle increased.
The angular dependence of R j with sample rotation can be divided into three regions: (i) In the low-resistance region, corresponding to high angles close to 90 • , the loop current was considerably lower than I cj .R j of less than 1.4 × 10 −13 Ω was observed and a persistent current continued to flow in the sample.(ii) In the transition region, R j significantly increased by three orders of magnitude owing to an increase in the perpendicular component of the magnetic field, which decreased I cj .This caused an increase in the ratio of the loop current to I cj , that is, the load factor, resulting in an increase in R j .
(iii) In the high-resistance region, corresponding to low angles, R j remained high, ranging from 10 −11 to 10 −10 Ω.When the load factor was 0.974-1.02,R j appeared to increase linearly.(2) In the design of a persistent-mode magnet, we must consider not only the magnitude but also the direction of a magnetic field applied to superconducting joints.Evaluating the trend of R j in detail at the load factor of approximately 0.964 will help clarify the conditions under which a sufficiently low R j for a persistent-mode operation can be achieved.

Figure 1 .
Figure 1.(a) Schematic of experimental setup.Horizontal magnetic field (B) is applied to the joint using a split-pair superconducting magnet.The direction of magnetic field is controlled by rotating the sample.(b) Schematic showing the angle of magnetic field (θ).The perpendicular component of the magnetic field applied to the tape surface is Bx (=B cosθ).

Figure 2 .
Figure 2. Schematic of the sequence for measuring the current decay by incrementally rotating the sample.In sequence (5), the sample is rotated by 5 • within 1 s.At each angle, t is the elapsed time from when we started sample rotation.In sequences (6) and (7), we measured the current decay for approximately 10 min at each angle from 0 to 85 • .
(2) A magnetic field (B) of 0.15-0.28T was applied to the joint at 90 • .(3) An I loop of 220-221 A was introduced to the sample.(4) We waited until the initial current-sharing effect in the sample became negligible and the time variation V Hall became flat, which required several tens of minutes.(5) The sample was rotated (θ was decreased) by 5 • within 1 s while the I loop flowed.At t exp = 0, the sample was rotated from 90 • to 85 • .This point corresponded to t = 0 at 85 • .(6) The time dependence of V Hall was measured for approximately 10 min.(7) The 5 • rotation and the 10 min measurement were repeated until θ = 0.

Figure 3
Figure 3 shows V Hall as a function of t exp at 4 K and 0.25 T. The inset shows the magnified view at approximately 70 • .From 90 • to 75 • , a decrease in V Hall with time was not clearly observed; that is, V Hall -t exp at each angle was almost flat.This implies that the decay of I loop was negligible at 75-90 • , and the I loop was considerably lower than I cj .By contrast, at angles less than 75 • , a decrease in V Hall over time was evident.The value of V Hall increased by less than 1 mV for each 5 • rotation, as shown in the inset of figure 3.There are two possible reasons for this increase in V Hall : the first is the static component of the change in the offset of V Hall .The offset is primarily attributed to the leakage field of the split-pair magnet, calculated to be approximately 1 mT in the direction opposite to the magnetic field applied to the joint.The thin-film Hall sensor used in the current sensor was parallel to the plane of the Bi-2223 tape in the loop.The offset was approximately 0.6 mV at 90 • and increased with sample rotation.At θ = 0, this static component showed the largest value of 3.7 mV.The second reason is the dynamic component showing an increase in I loop owing to magnetic induction.The magnetic flux across the loop of the sample owing to the leakage field is reduced by sample rotation.This reduction in magnetic flux induces a current in the loop.This induced current increases I loop , resulting in an increase in V Hall .The time variation of I loop , I loop -t, at 4 K, 0.25 T, and each angle of 0-85 • is shown in figure 4(a).The I loop values were obtained from the V Hall values shown in figure 3. The offset was subtracted from V Hall at each angle.Figure4(a) shows that, at angles less than 70 • , the residual I loop , that is, the I loop at 600 s decreased as the angle decreased.This corresponds to a decrease in I cj .Sample rotation from high to low angle between 90 • and 0 increased the perpendicular component of the magnetic field applied to the tape surface, that is, B x (=B cosθ) shown in figure1(b).Because the intermediate layer was formed almost parallel to the tape surface[20], B x was almost perpendicular to the intermediate layer of the superconducting joint.Furthermore, because Bi-2223

Figure 3 .
Figure 3. Voltage of Hall sensor (V Hall ) in the current sensor as a function of experimental time (texp) at 4 K and 0.25 T. We started to rotate the sample from 90 • at texp = 0 by 5 • within 1 s.Inset shows a magnified view at approximately 70 • .

Figure 4 .
Figure 4. Time dependence of (a) I loop and (b) normalized I loop at 4 K, 0.25 T, and 0-85 • .I loop values are calculated using V Hall values shown in figure 3.At angles less than 70 • , I loop at 600 s decreases as the angle decreases owing to a decrease in I cj .A persistent current continues to flow in the sample at high angles of 75-90 • .

Figure 4 (
Figure 4(b)  shows the normalized I loop using the maximum value (I loop max ) at each angle.The decay ratio (1 − I loop /I loop max ) at 75 • for 600 s was 1.4 × 10 −4 .The field drift rate is less than 10 −2 ppm h −1 in a typical 400 MHz (9.4 T) Nb-Ti NMR magnet with 10 joints and L of 40 H at an operating current of approximately 100 A[10].If the performance of the 10 joints is equivalent to that of the Bi-2223 superconducting joint sample at 75 • , a field drift rate of 2.9 × 10 −4 ppm h −1 can be extrapolated.This rate is considerably lower than that of the typical NMR magnet.Consequently, a persistent current continued to flow in the sample at 4 K, 0.25 T, and high angles of 75-90 • .The decay ratio at 70 • for 600 s was 1.3 × 10 −3 .This corresponds to a field drift rate of 2.7 × 10 −3 ppm h −1 using the same extrapolation.Although this value is close to that of the typical NMR magnet, the decay of I loop at 70 • is clearer than at 75 • , as shown in figure4(b).Therefore, we conclude that a persistent current did not flow at 0-70 • .

Figure 5 .
Figure 5. Angular dependence of R j and I cj 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 R j correspond to the standard uncertainty obtained from fitting.I cj increases as the angle increases.The angular dependence of R j with sample rotation can be divided into three regions: (i) low-resistance region (R j of less than 1.4 × 10 −13 Ω), (ii) transition region (three orders of magnitude change in R j to its maximum, R j max ), and (iii) high-resistance region (R j of 10 −11 -10 −10 Ω).

Figure 6 .
Figure 6.Smoothed V-I loop curve at 0.15 T and 0-50 • .V-I loop at 0-50 • is fitted to the power law model, as shown by dashed lines.

Figure 7 .
Figure 7. (a) Sections of R j 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 R j in region (ii).The significant changes in R j at each magnetic field are nearly identical at B cosθ of 6-11 × 10 −2 T, which are independent of the magnitude of the magnetic field.

Figure 8 .
Figure 8. Relationship between load factor (F) and R j in region (iii).Change in R j owing to sample rotation is primarily attributed to change in F.