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[FINAL VERSION.pdf](https://mdr.nims.go.jp/filesets/c2a875b8-8b77-4a0d-88cc-93cd5893c3bd/download)

## Creator

[Shin Hasegawa](https://orcid.org/0000-0001-8309-5022), [Satoshi Ito](https://orcid.org/0000-0001-9780-6649), [Gen Nishijima](https://orcid.org/0000-0001-7493-0559), [Satoshi Awaji](https://orcid.org/0000-0003-2043-1628), [Kohki Takahashi](https://orcid.org/0000-0002-8444-5538), Hidetoshi Hashizume

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[Quench Detection in Insulated, NI, and MI (RE)Ba2Cu3O7—x Coils With Superconducting Quench Detectors](https://mdr.nims.go.jp/datasets/54d4b143-576b-4abb-a6b9-bd14316b22f0)

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Quench Detection in Insulated, NI, and MI (RE)Ba2Cu3O7−x Coils with Superconducting Quench Detectors  Shin Hasegawa, Member, IEEE, Satoshi Ito, Gen Nishijima, Satoshi Awaji, Kohki Takahashi and Hidetoshi Hashizume     Abstract— We have proposed a quench detection method that uses a low-temperature superconducting quench detector (LTS QD) for rare-earth barium copper oxide (REBCO) coils at 4.2 K. Previous studies demonstrated the quench detection with a LTS QD in a layer-wound REBCO coil. In this study, the quench detection performance of LTS QDs for insulated, no-insulation (NI), and metal-as-insulation (MI) REBCO pancake coils was experimentally compared. An experiment that used a Nb–Ti/Cu–Ni QD installed in insulated, NI, and MI REBCO coils demonstrated a quench detection before a thermal runaway in the coil at 4.2 K and 0–9 T. Nb–Ti/Cu–Ni QD showed slower quench detection in the coils without turn-to-turn insulation. It would be due to the small heat density around the hot spot and large heat exchange between the Nb–Ti/Cu–Ni QD and REBCO coils. In conclusion, this study indicated that the turn-to-turn resistance  in the REBCO coil and thermal gap conductance between the coil and LTS QD are key parameters for the design of LTS QDs. Moreover,  feasibility of the quench detection with appropriate LTS QDs for the insulated, NI, and MI REBCO pancake coils was demonstrated at 4.2 K.  Index Terms— quench detection, quench protection, REBCO coil, no-insulation coil, metal-as-insulation coil, superconducting quench detector, Nb–Ti1 I. INTRODUCTION uench detection is important for a high-temperature superconducting (HTS) coil—for example, a rare-earth barium copper oxide (REBCO) coil—cooled with 4.2 K liquid helium (LHe) for high magnetic field application. A conventional quench detection method for superconducting coils is a direct voltage measurement. However, the normal zone propagation velocity in the HTS coil is 100–1000 times slower than that of low-temperature superconducting (LTS) coil [1]–[4]. Thus, detectable voltage in the HTS coil would be smaller than the quench detection criterion (> 0.1 V [5], [6]), which may lead to burning out of the coil. To address this issue, various new quench detection methods [7]–[27] have been proposed, as presented in Table I. Here, “insulated pancake coil”  This work was supported by the Grant-in-Aid for Japan Society for the Promotion of Science (JSPS) Fellows under Grant 19J10989 and JSPS Grant-in-Aid for Scientific Research (B) under Grant JP17H03507 and 20H01884 (Corresponding author: Shin Hasegawa). S. Hasegawa is with National Institutes for Quantum Science and Technology, Naka 311-0193, Japan, and ITER Organization, St. Paul Lez Durance 13067, France (e-mail: hasegawa.shin2@qst.go.jp) S. Ito and H. Hashizume are with Department of Quantum Science and Energy Engineering, Graduate School of Engineering, Tohoku University, Sendai 980-means the pancake coil with turn-to-turn insulation. However, only few cases were reported on the experimental demonstration at 4.2 K. Moreover, quench detection for the HTS coil without turn-to-turn electrical insulation—that is, no-insulation (NI) [28]–[33] and metal-as-insulation (MI) [34]–[36] coils—was reported in a small number of literature. These coils are considered more thermally stable than insulated coils. However, the actual protection performance of the NI and MI techniques is under investigation, and quench detection and active protection for these coils remains important in terms of failing safety [37]. Our previous works [38]–[40] proposed using superconducting quench detectors (QDs) [41], [42], which were LTS composite wires (LTS QDs), for REBCO coils operated at 4.2 K. Bias currents (monitoring current, Im) flow in the electrically insulated LTS QDs. Heat from a hot spot in the REBCO coil would lead the current sharing and voltage rises in the LTS QDs. If the voltage becomes sufficiently larger than the threshold voltage, detecting the quench before the thermal runaway in the REBCO coil is possible. Quench detection before thermal runaway in a REBCO tape and an insulated REBCO coil (“quick quench detection”) has been demonstrated by using Nb–Ti QDs at 4.2 K and 0–9 T [38]–[40]. Recently, it has also been suggested to apply the superconducting quench detector with similar concept for the HTS applications [43]–[46]. 8577, Japan (e-mail: satoshi.ito.e3@tohoku.ac.jp; hidetoshi.hashizume.a5@tohoku.ac.jp). G. Nishijima is with National Institute for Materials Science, Tsukuba 305-0003, Japan (e-mail: NISHIJIMA.Gen@nims.go.jp) S. Awaji and K. Takahashi are with High Field Laboratory for Superconducting Materials, Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan (e-mail: awaji@tohoku.ac.jp; kohki.takahashi.e5@tohoku.ac.jp). Q Table I Proposed quench detection method for HTS coil Method Operation temperature for experimental demonstration Tape / cable / solenoid Insulated pancake coil NI/MI pancake coils Secondary magnetic coupled coils - 77 K  [7]–[9] 20 K  [10] Poynting vectors - 77 K [11], [12] - Acoustic signals (active and passive) 77 K  [13]–[15] 77 K  [16], [17] - Optical fiber sensors 14–77 K  [18]–[23]  - 77 K [24] –[26] Turn-to-turn capacitance - 4.2 K [27] -   2 However, the quench detectability of the LTS QDs for the REBCO pancake coil under magnetic field has not been experimentally investigated. A past experiment [39] demonstrated a quench detection with the Nb–Ti QD with ~2 seconds margin before the thermal runaway in the insulated REBCO coil. Considering the risk of delay in the protection system, more time margin would be desired for safer quench protection by damping the coil current with a few seconds to minutes. In a practical operation environment, a magnetic field will increase the load factor of the LTS QD resulting in its quicker response with more margin as anticipated in [40]. A further interest is the performance of LTS QD in the NI and MI REBCO coils. Compared with the insulated coil, heat density around the hot spot becomes less in the NI and MI coils, which may lead to a delay in the response of the LTS QD. Although this study focuses on only the Nb-Ti QD, key parameters of the behavior of LTS QDs made of other superconductors, such as Nb3Al, MgB2, and iron-based superconductors, would be similar. Comprehension of the behavior of the LTS QD in the REBCO coils with different physical characteristics is crucial to formulate an universal design strategy for the LTS QD. We experimentally compared the quench detection performance of Nb–Ti/Cu–Ni QD for insulated, NI, and MI REBCO pancake coils cooled in 4.2 K LHe bath at 0–9 T. Section II describes the experimental method. Section III presents the results and discussion, followed by a conclusion in Section IV. II. EXPERIMENT A. Sample fabrications Three types of 20-turn REBCO single pancake coils (i.e., insulated, NI, and MI) were fabricated to demonstrate quick quench detection with LTS QDs. Previous studies indicated that LTS QDs with a high normal resistance are suitable for this method [38], [40]. Thus, a formal-insulated Nb–Ti wire with a Cu–Ni matrix (Supercon, SW-18) was chosen as the LTS QD (Nb–Ti/Cu–Ni QD). Fig. 1 shows a schematic view of the REBCO coil samples, in which a 4-mm-wide REBCO tape (SuperPower, SC4050) was wound on a glass fiber reinforced plastic (GFRP) bobbin. Fig. 2 shows the fabricated insulated, NI, and MI coils. For the insulated REBCO coil, a polyimide tape and the Nb–Ti/Cu–Ni QD were co-wound with the   Fig. 1 Schematic views of the REBCO coil samples; (a) insulated REBCO coil and (b) NI/MI REBCO coils  Fig. 2 Fabricated REBCO coil samples; (a) insulated, (b) NI, and (c) MI REBCO coils  3 REBCO tape. In the past experiment [39], the Nb–Ti/Cu–Ni QD was attached only on the outmost surface of the pancake coil. This arrangement could possibly lead to the delay in quench detection due to the long distance from the hot spot to the Nb–Ti/Cu–Ni QD. The co-winding method enables the LTS QD to be positioned in proximity to any hot spot location, allowing quicker quench detection. For the NI and MI coils, a 100-m-thick indium foil, the Nb–Ti/Cu–Ni QD, and a metal insert (Cu or 301 stainless steel (SS)) were co-wound with the REBCO tape. The Nb–Ti/Cu–Ni QD embedded in the indium foil is similar to an optical fiber installed in a REBCO tape [19]. The configuration of the NI coil in this experiment corresponds to the one with co-wound materials as shown in [47], [48]. A 4-mm-wide and 30-m-thick Cu sheet, and 6-mm-wide and 50-m-thick SS sheet were used for the NI and MI coils, respectively, as metal inserts between coil turns. Side of the MI coil was not smooth since the width of SS sheet was 2 mm larger than that of REBCO tape as shown in Fig. 2 (c). In real case, the MI coil can be stacked by using the REBCO tapes and SS tapes with the same width. Note that, a sufficiently thin LTS QD shall be installed in the turn-to-turn materials to prevent a decrease in engineering current density of the REBCO coil also in the practical applications. Alternatively, placing the LTS QD on the side surface of the REBCO coil is also a viable option [44]. Table II and Table III list the specifications of the REBCO coils and Nb–Ti/Cu–Ni QDs, respectively. Local defects due to the insufficient homogeneity in the tape can lead to the unexpected quench of the REBCO coil [37]. In this study, therefore, we made a local degradation in the REBCO coil assuming the unexpected quench during the magnet excitation. The critical current (Ic) of a 4-mm-wide × 3-mm-long region in the 10th turn was degraded to 0 A with a compressive force of 2000 N. The distance between the voltage taps was 1470 mm for both the REBCO coil (VRE) and Nb–Ti QD (VQD).  B. Experimental setup Fig. 3 shows the experimental setup. The REBCO coil sample was set on the sample holder, which was immersed in an LHe bath in an inner dewar of the 15-T superconducting Table III Specification of the Nb–Ti/Cu–Ni QD Items Values Diameter (bare / insulated) 75 m / 100 m Stabilizer Cu0.9–Ni0.1 Stabilizer ratio 1.5 Filament diameter 11 m Filament number 18 Ic at 4.2 K, 9 T ~0.81 A   Fig. 3 Experimental setup where the sample was immersed in LHe and magnetic field was applied to the sample by an external superconducting magnet Table IV Operation conditions of the Nb–Ti/Cu–Ni QD where the load factor of Im depends on Bex Im Bex Load factor of Im Tcs 0.31 A 0 T 0.01 9.4 K 5 T 0.062 9.2 K 9 T 0.38 7.5 K    Fig. 4 Measurement of turn-to-turn resistance in the NI/MI REBCO coils where the turn-to-turn voltages (Vtt and Vtb) were measured by applying the current (It)  Table II Specifications of the three types of REBCO coils samples: insulated, NI, and MI coils. Items Values Insulated NI MI Conductor width / thickness 4.0 mm  / 95 m 4.0 mm  / 95 m  4.0 mm  / 95 m Ic at 77 K, s.f. ~126 A ~126 A ~126 A Thickness of indium sheet - 100 m 100 m Thickness of turn-to-turn insert 135 m (Polyimide) 30 m (Cu) 50 m (Stainless steel) Width of turn-to-turn insert 4 mm 4 mm 6 mm Inner diameter 20 mm 20 mm 20 mm Outer diameter 24.7 mm 28.5 mm 29.1 mm Total turns 20 20 20 Coil inductance ~13 H ~13 H ~13 H   4 magnet. Nb–Ti/Cu–Ni QD would be used at less than 10 T considering its critical current. Thus, the magnetic field around the REBCO coil (Bex) was set to 0, 5, and 9 T in this experiment. Im for the Nb–Ti/Cu–Ni QD was determined by using the procedure described in [40]. Table IV shows Im, Bex dependence of its load factor (= Im/Ic), and current sharing temperature (Tcs). Operation current in the REBCO coil (Iop) was ramped up from 0 A with a certain sweep rate (op). The current sources for REBCO coil and LTS QD were manually shut down after the quench detection. Exceptionally, an interlock system of the current source interrupted the current at the detection of open circuit. Im of the LTS QD should be dumped after the quench detection to avoid its burning out also in the practical application. Iop at quench detection (IopQD) would depend on op with the following reason. We now consider a lumped-capacitance model of the hot spot in the REBCO coil where influence of three-dimensional thermal diffusion is not taken into account. Then, the following heat-balance equation holds, CtapedThsdt = tape(IopAtape)2 = tapeAtape2op2 t2, (1) where Ths, Ctape, tape, t, and Atape are hot-spot temperature, heat capacity and resistivity of the REBCO tape at normal state, time, and the cross-sectional area of the REBCO tape, respectively.  Integrating the equation (1) from t = 0 (Ths = Top) to t = tQD (Ths = ThsQD), it yields ThsQD = tapeop2 tQD33Atape2Ctape + Top = tape3Atape2CtapeIopQD3op + Top, (2) where tQD, Top and TopQD are t at quench detection, operation temperature, and Ths at t = tQD. When tape, Ctape, Atape, and ThsQD are the constants, IopQD should be proportional to 1/3 power of op. For this reason, op would be the influential parameter on the quench detection performance of LTS QD. Thus, op was set to 1, 5, and 10 A/s for the insulated REBCO coil to determine its influence on the LTS-QD performance; it was fixed at 10 A/s for NI/MI coils. The current distribution in the NI and MI REBCO coils evaluated with turn-to-turn resistance is important to know which heat leads to the quench in the LTS QD. Fig. 4 shows that, in the NI and MI REBCO coils, additional taps (Vtt and Vtb) were installed at two locations around the degraded region to measure the turn-to-turn resistance before the quench detection experiment. 30-m-thick copper sheets used for Vtt and Vtb were soldered to the REBCO tape or indium foil. The bonding surface of the voltage taps was 1 mm × 3 mm. PSW-720H800 (TEXIO TECHNOLOGY CORP., Yokohama, Japan) and PAS16-500LS (KIKUSUI ELEC TRONICS CORP., Yokohama, Japan) constant current sources supplied the current to the Nb–Ti/Cu–Ni QD and the REBCO coil, respectively. The sample voltages were recorded by using an MR8741 data logger (HIOKI E.E. CORP., Ueda, Japan) with a sampling rate of 200 Hz. The background noise was in the order of 10-5–10-3 V in our experimental environment. 0.1 V was used as a quench detection criterion [5], [6]. III. RESULTS AND DISCUSSION A. Quench detection performance of Nb-Ti/Cu-Ni QD for insulated REBCO coil Time margin from the conventional quench detection to the thermal runaway in the insulated REBCO coil was first confirmed prior to the experiment with the LTS QD. Fig. 5 shows the voltage VRE and operation current Iop in the REBCO coil when thermal runaway occurred in the REBCO coil with op = 10 A/s at Bex = 9 T. VRE started to rapidly increase at Iop ~172 A (19.4 s), and the coil was finally burned out in the degraded region. This localized thermal runaway is reasonable because Ic of the REBCO tape except in the degraded area is ~400 A at 4.2 K and 9 T considering its temperature and field dependence [49][50]. The coil current was automatically damped since the open circuit of the burned coil was detected by the current source. VRE exceeds 0.1 V also at Iop ~172 A (20 s). The time margin for the quench protection is less than 1 second due to the rapid thermal runaway in the coil, and the conventional method may lead to the failure of coil protection considering the delay of protection system. A quench detection experiment was performed with a new insulated coil where the Nb–Ti/Cu–Ni QD was co-wound. Table V lists the tQD and IopQD at 0.1 V detection by the LTS QDs for different Bex and op in all the REBCO coils. The  Fig. 5 Quench detection with the conventional method and thermal runaway in the insulated REBCO coil at op = 10 A/s and Bex = 9 T Table V tQD and IopQD at 0.1 V detection by LTS QD for different external magnetic fields (Bex) and current ramping rates (op) in the insulated, NI, and MI REBCO coils Coils Bex op tQD IopQD Insulated 0 T 10 A/s 9.6 s 92.3 A 5 A/s 18.6 s 91.9 A 1 A/s 102 s 91.7 A 5 T 10 A/s 6.5 s 61.9 A 5 A/s 12.8 s 62.6 A 1 A/s 69.5 s 61.4 A 9 T 10 A/s 4.8 s 47.0 A 5 A/s 9.2 s 44.2 A 1 A/s 51.8 s 43.9 A NI 0 T 10 A/s 45.8 s 472 A 5 T 10 A/s 30.8 s 313 A 9 T 10 A/s 16.9 s 133 A MI 0 T 10 A/s 14.4 s 147 A 5 T 10 A/s 12.4 s 109 A 9 T 10 A/s 8.4 s 79.7 A   5 results for the NI and MI REBCO coils are discussed in the next sub-section. IopQD decreased with the increasing field due to the load factor of Im and Tcs as shown in Table IV. Fig. 6 shows VRE, VQD, and Iop at 0 T, 5 T, and 9 T when op = 10 A/s. VQD exceeds 0.1 V when Iop (time) was 92.3 A (9.6 s), 61.9 A (6.5 s), and 47.0 A (4.8 s) at 0 T, 5 T, and 9 T, respectively. Nb–Ti/Cu–Ni QD quickly detected quench in the insulated REBCO coil at Bex = 0–9 T, as well as in the case of the REBCO tape [41]. Assuming the result of thermal runaway in the REBCO coil shown in Fig. 5, the Nb–Ti/Cu–Ni QD (Fig. 6 (c)) was able to detect the quench with a 13.5-seconds margin before the thermal runaway at Bex = 9 T and op = 10 A/s. We also compared the quench detection sensitivity of the Nb–Ti/Cu–Ni QD with respect to the op. Fig. 7 and Fig. 8  show VRE, VQD, and Iop at 0–9 T when op = 5 A/s and 1 A/s, respectively. In the case op = 5 A/s, 0.1 V was detected when Iop (time) was 91.9 A (18.6 s), 62.6 A (12.8 s), and 44.2 A (9.2 s) at 0 T, 5 T, and 9 T, respectively. In the case op = 1 A/s, 0.1 V was detected when Iop (time) was 91.7 A (102 s), 61.4 A (69.5 s), and 43.9 A (51.8 s) at 0 T, 5 T, and 9 T, respectively. IopQD varied only by 1.2%–6.2% difference in the range of op = 1 A/s–10 A/s. Thus, the quench detection performance of the LTS QD does not depend on the operating conditions of the REBCO coil. This would be because three-dimensional heat diffusion from the hot spot led to the gradual increase of the hot-spot temperature in the REBCO coil, which is not considered in the equations (1) and (2) of the lumped-capacitance model. It then resulted in weak op dependence of IopQD. Moreover, the result at op = 1 A/s suggests the Nb–Ti/Cu–Ni QD detects the quench more than one minute before the   Fig. 6 Results of quench detection experiment with insulated REBCO coil at op = 10 A/s: (a) Bex = 0 T, (b) Bex = 5 T, and (c) Bex = 9 T   Fig. 7 Results of quench detection experiment with insulated REBCO coil at op = 5 A/s: (a) Bex = 0 T, (b) Bex = 5 T, and (c) Bex = 9 T    Fig. 8 Results of quench detection experiment with insulated REBCO coil at op = 1 A/s: (a) Bex = 0 T, (b) Bex = 5 T, and (c) Bex = 9 T  6 thermal runaway in the REBCO coil where Iop is ~172 A, which is improved more than 10 times by the co-winding method compared to [39]. Since the current ramp rate is slow in the 30-T-class coil (< 1 A/s [51]–[53]), more time margin would be expected and it will be sufficient for the quench protection with a-few-seconds current damp. Thus, it was experimentally demonstrated that the implementation of the  LTS QD would be effective for the quench protection system of the application under magnetic field. B. Quench detection performance of Nb-Ti/Cu-Ni QD for NI/MI REBCO coils The turn-to-turn resistivity was estimated for the NI and MI REBCO coils (t). Table VI lists t of the NI and MI coils which is multiples of the turn-to-turn resistance (Rt) and bonding area of the voltage taps (1 mm × 3 mm). By applying the current (It) and measuring the voltage in Vtt and Vtb as shown in Fig. 4, Rt was estimated by mean value of the proportional coefficient of It and Vtt, It and Vtb. Fig. 9 illustrates a simplified circuit of the NI/MI REBCO coils based on the partial element equivalent circuit (PEEC) model [54] where Rcoil, r, Rcoil, , and Lcoil are resistance in the radial direction, resistance in the circumferential  direction, and inductance, respectively. Table VI also lists their calculated values. Mean value of inner and outer diameters was considered as coil diameter for the calculation. Ir and I are the currents in the radial and circumferential directions, respectively. If I is 0 A at initial condition, I becomes Iθ = C1 {exp (−t) − 1}  + C2opt, (3) where   Fig. 10 Results of the quench detection experiment with MI REBCO coil at op = 10 A/s: (a) Bex = 0 T, (b) Bex = 5 T, and (c) Bex = 9 T   Fig. 11 Results of the quench detection experiment with NI REBCO coil at op = 10 A/s: (a) Bex = 0 T, (b) Bex = 5 T, and (c) Bex = 9 T Table VI Local turn-to-turn resistivity (t), anisotropic resistances (Rcoil, r and Rcoil, ), and inductance (Lcoil) of the NI and MI REBCO coils Coils t Rcoil, r Rcoil,  Lcoil NI 0.95 cm 59    at superconducting state except for the degraded region 13 H MI 2.1 cm 129    at superconducting state except for the degraded region 13 H    Fig. 9 Simplified circuit model of the NI and MI REBCO coils based on the PEEC model [54]  7 C1 = Rcoil, rLcoilop(Rcoil, r + Rcoil, )2, (4) C2 = Rcoil, rRcoil, r + Rcoil, , (5)   = 𝐿coilRcoil, r + Rcoil, . (6) Table VII lists the calculated C1, C2, and . Since Lcoil is small in this experiment, first term on the right-hand side in the equation (3) become small (< 1.3 A) and I becomes nearly Iop = aopt. This indicates that the coil current mostly flows in the circumferential direction except in the degraded region. Thus, the quench of LTS QD would be induced only by the local heating around the hot-spot in the REBCO coil. In the case of the NI/MI REBCO coils with large inductance, the heating due to Ir would increase the temperature of the LTS QD. This shall be considered in the design of the LTS QD. Table V lists the tQD and IopQD in the NI and MI REBCO coils for different Bex. Fig. 10 shows the voltage in the Nb–Ti/Cu–Ni QD (VQD) and MI REBCO coil (VRE), and coil operation current (Iop) at Bex = 0, 5, and 9 T. IopQD (tQD) was 147 A (14.4 s), 109 A (12.4 s), and 79.7 A (8.4 s) at Bex = 0 T, 5 T, and 9 T, respectively. IopQD is 2.8–5.1 times larger than that of the insulated coil shown in Fig. 6 and Table V. The heat density around the hot spot may influence the behavior of VQD in terms of the initiation of the normal zone in the LTS QD. Heat can easily diffuse around the hot spot in the MI coil compared to the case of an insulated coil with an insulating material having low thermal conductivity. Further, turn-to-turn current sharing reduces the heat density around the hot spot. These led to a slow temperature rise in the Nb–Ti/Cu–Ni QD and larger IopQD than in the case of the insulated REBCO coil. The change in VQD with respect to time was more gradual than that shown in Fig. 6. Fig. 11 shows VRE, VQD, and Iop for the NI coil at Bex = 0 T, 5 T, and 9 T. IopQD (tQD) was 472 A (45.8 s), 313 A (30.8 s), and 133 A (16.9 s) at Bex = 0 T, 5 T, and 9 T, respectively. This result shows slower quench detection than in the case of the MI coil. This also might be caused by the difference in the heat density around hot spot of the REBCO coil. The turn-to-turn resistance of the coil would be one of the key parameters. The t of the MI coil was higher than that of the NI coil as shown in Table VI. Thus, it is considered the larger heat density around the hot spot contributed the quicker initiation of the normal zone in the LTS QD in the case of the MI coil. C. Normal zone propagation in LTS QD co-wound in insulated, NI, and MI REBCO coils After the initiation of the normal zone in the LTS QD, normal zone propagation velocity (NZPV) determines VQD. Thermal diffusion from the LTS QD to the REBCO coil may highly influence the NZPV in the LTS QD. VQD quickly reaches 0.1 V in the cases of the insulated (Fig. 6) and MI coils (Fig. 10), while VQD reaches 0.1 V with gradual increase in the case of the NI coil at Bex = 0 T and 5 T (Fig. 11). This different behavior indicates the difference in NZPV. A simplified NZPV for the LTS QD (NZPVeq) can be expressed by the following equation [55], NZPVeq =  − 2CQD( − 1)√PQDheffA, (7)  =  Im2 QDAPheffcs,  (8) where A, P, QD, CQD, and QD are cross-sectional area, perimeter, equivalent resistivity, equivalent heat capacity, and equivalent thermal conductivity of the LTS QD at its Tcs. The heat transfer coefficient of the coolant is normally used as heff, while heff corresponds to the thermal conductance between the REBCO coil and the LTS QD in this study. Although too small heff may delay the initiation of normal zone in the LTS QD, smaller heff would lead to larger NZPV resulting in the quicker voltage increase in the LTS QD. cs is defined as the difference Table VIII NZPVexp estimated from the equation (9) and heff giving agreement between NZPVeq and NZPVexp Coils Bex NZPVexp heff Insulated 0 T 5.12 × 10-1 m/s 2.39 × 103 W/m2K 5 T 6.30× 10-1 m/s 2.27 × 103 W/m2K 9 T 1.79 m/s 2.15 × 103 W/m2K MI 0 T 2.35 × 10-1 m/s 2.84 × 103 W/m2K 5 T 4.77 × 10-1 m/s 2.55 × 103 W/m2K 9 T 1.52 m/s 2.67 × 103 W/m2K NI 0 T 2.32 × 10-4 m/s 3.18 × 103 W/m2K 5 T 2.96 × 10-4 m/s 3.31 × 103 W/m2K 9 T 1.10 m/s 3.40 × 103 W/m2K  Table VII Parameters on the equation (3) calculated by the equations (4)–(6) for the NI and MI REBCO coils Coils C1 C2  NI 1.29 A 0.76 0.17 s MI 0.78 A 0.87 0.089 s  Table IX The constants used for the calculation of NZPVeq and NZPVexp defined in the equations (7) and (8) Constants Values Im 0.31 A P 0.24 mm A 4.4 × 10-3 mm2 QD 0.36 m at 0 T 0.36 m at 5 T 0.36 m at 9 T CQD 20.1. kJ/m3K at 0 T 20.1. kJ/m3K at 5 T 12.1 kJ/m3K at 9 T QD 3.14 W/mK at 0 T 3.03 W/mK at 5 T 2.14 W/mK at 9 T Tcs 9.4 K at 0 T 9.2 K at 5 T 7.4 K at 9 T   8 between Tcs of the LTS QD and temperature of the REBCO coil.  According to the experimental results, VRE is almost proportional to the Iop indicating the normal zone propagation in the REBCO coil is negligible. Then, it can be assumed that the boundary of normal zone in the LTS QD always faces to the REBCO tape at superconductive state at ~ Top = 4.2 K. Thus, cs can be approximated as cs ~ Tcs − 4.2 K. Table VIII lists the NZPV calculated from the time derivative of VQD around VQD = 0.1 V by the following equation (NZPVexp).  NZPVexp=AQDdVQDdt|VQD(t)~0.1 V.  (9) Table IX lists the value of the constants used for the calculation of NZPVeq and NZPVexp. Electrical resistivity, heat capacity, and thermal conductivity of Nb-Ti and Cu-Ni were referred from [56]–[58]. NZPVexp became smaller than the general NZPV of the LTS wire, such as 1–100 m/s, because of the small load factor of the Im. When heff remains constant, the equations (7) and (8) indicate that NZPVexp does not change if the specification of the LTS QD and Bex are the same. However, the different coils show different NZPVexp even with the same LTS QD at the same Bex. Table VIII also lists the heff  which gives agreement between the NZPVexp and NZPVeq. heff shows different value in the different REBCO coil, while it does not show obvious dependence on Bex in the same REBCO coil. Thus, it can be regarded as a parameter featuring the thermal diffusion from the LTS QD to a certain REBCO coil. The largest and smallest thermal diffusion are indicated in the cases of the NI REBCO coil with largest heff and insulated REBCO coil with smallest heff, respectively. Although there might be contribution of thermal contact resistance between the LTS QD and REBCO coil, the result is quantitatively reasonable by considering the thermal diffusivity of materials around the LTS QD. For instance, thermal diffusivities of polyimide, austenitic stainless steel, and copper (RRR = 30) are, 9.8×10-6 m2/s, 1.2×10-5 m2/s, and 0.2 m2/s, respectively [57], [59], [60]. This result shows thermal conductance between the LTS QD and REBCO coil would be a key parameter to design the LTS QD in terms of both initiation of normal zone and normal zone propagation in the LTS QD. The results indicated the key parameters for the behavior of the LTS QDs in the REBCO coils, and the feasibility of the quench detection with the LTS QD for three types of REBCO pancake coils (insulated, NI, MI) was demonstrated at 4.2 K and 0–9 T. For future research, further experimental demonstrations with LTS QDs for higher magnetic field applications or higher operation temperatures (such as Nb3Al, iron-based super-conductors, and MgB2) are required. Recent studies [61]–[63] indicate that the flexible Nb3Al wires with a dimeter of 30–80 m show small difference between critical current density with the wind-and-react and react-and-wind processes. Thus, it would be a good option to use the thin Nb3Al wire as LTS QD without reducing the engineering current density of the REBCO coil. Similarly, LTS QDs with a higher critical temperature (Tc), such as, MgB2 and iron-based superconducting QDs are expected to be used even at > 4.2 K as suggested in [43],  [45], [46]. Falese quench detection by the low-Tc LTS QD due to its small temperature margin would be concerned in the real case. The higher-Tc LTS QDs would mitigate this risk although this should be discussed with their sensitivity in further studies. IV. CONCLUSION In this study, the quench detection performance of LTS QDs for insulated, NI, and MI REBCO coils cooled with LHe was investigated. This study indicated the key parameters related to the behavior of the LTS QDs in the REBCO coils, and demonstrated the feasibility of the quench detection with appropriate LTS QDs for three types of REBCO pancake coils (insulated, NI, MI) operated at 4.2 K and 0–9 T.  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