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. 2022 Nov 10;121(19):194101. doi: 10.1063/5.0122493

On fault-mode phenomenon in no-insulation superconducting magnets: A preventive approach

Fangliang Dong 1, Dongkeun Park 1,a), Wooseung Lee 2, Luning Hao 3, Zhen Huang 4, Juan Bascuñán 1, Zhijian Jin 4, Yukikazu Iwasa 1
PMCID: PMC9652021  PMID: 36388449

Abstract

Here, we present experimental and analytical results of a preventive approach applied to a fault-mode phenomenon caused by electrodes or power-source failure in a no-insulation (NI) high-temperature superconducting REBa2Cu3O7−x (REBCO, RE = rare earth) magnet. It is generally agreed that the NI magnets, at least those of laboratory scale, are self-protected from overheating and, therefore, from quenching, chiefly because of turn-to-turn current bypassing unique to NI. However, these NI magnets do experience unexpected quenches, e.g., when the current through the magnet suddenly drops due to the aforementioned fault-mode phenomenon. Here, we report this phenomenon of a sudden-discharging-triggered quench of an NI REBCO coil, conduction-cooled, and operated at 4.2 K. We also present our preventive approach for this phenomenon that relies on an appropriately designed resistor shunted across the coil terminals. With this shunt resistor, a quench was prevented by suppressing the quench initiating turn-to-turn heat and induced overcurrent within the NI winding, and the coil current decayed safely.

Protection is one of the most challenging issues in the operation of the high-temperature superconducting (HTS) magnet due to its slow normal-zone propagation velocity and consequent difficulty in early-stage quench detection. The no-insulation (NI) winding technique using HTS conductors was first introduced by Hahn et al.1 and has demonstrated its self-protecting characteristics against overcurrent and overheating.2–6 The key idea of the self-protection in the NI technique is to remove turn-to-turn insulation within the HTS winding and to allow, in the case of a hot spot occurs, the current to be bypassed and the energy to be released through the turn-to-turn contact, which can prevent overheating and consequential permanent burn-out on the hot spot.7,8 In addition to the self-protecting characteristic, removal of the insulation and reduction in the amount of copper matrix by the NI technique also enables highly compact HTS magnets with larger current densities. Thus, the NI technique has been considered a promising and enabling technology for various magnet applications, such as electrical devices,9–11 high-speed transportations,12,13 nuclear magnetic resonances (NMR),14–16 energy storages,17 magnetic resonance imaging (MRI),18–20 and fusion reactors.21,22

The NI HTS magnets are relatively safe and reliable against local hot spots or small defects in the superconducting conductors, possibly causing burn-out and quench in conventional insulated magnets. However, we have experienced quenches in NI magnets at some point when the supplying current through the magnets suddenly drops in specific operating conditions (i.e., sudden discharging). The quenches in NI magnets reported so far have occurred mostly during the magnet energizing process,23–26 which appeared to be caused by any types of defects, and these energizing quenches may be avoided by some appropriate designs and approaches,27–30 whereas the sudden-discharging quench reported here can occur at any time due to unexpected external faults, such as electrode damages or power-supply failures, even if the NI magnet itself is well-designed, non-defective, and well-operated. As the compact high-field NI HTS magnets are designed to operate with a high current density at low temperature to maximize their performance and cost effectiveness, the quench energy margin is relatively small and space for cooling may be limited within the magnet structure that increase the risk of quench by external faults like sudden discharging. Once the quench initiates, very high induced current fluctuations in the entire NI magnet that are magnetically coupled can cause a cascading entire magnet quench and mechanically damage the magnet by unbalanced force and excessive hoop stresses, as also seen in the quench case of our previous three-nested-coil 18.8-T NI HTS magnet.25,26

Therefore, we believe that proper protection is necessary for NI HTS magnets against the quench caused by unexpected and sometimes unavoidable external fault modes. Here, we focus on one of the very severe external fault modes—the external power supply failure that suddenly drops the current directly to zero. In this paper, we have first experimentally and analytically demonstrated this quench by the external power shut-down to understand its mechanism. Then, we introduced and validated the proposed approach to prevent this quench by using an external shunt resistor across the magnet terminals. The external shunting can provide an energy-releasing path in addition to the existing turn-to-turn current-bypassing path in the NI windings.

To demonstrate the proposed quench preventative approach, we used an NI HTS coil as shown in Fig. 1 and conducted the following steps: (1) sudden discharge the coil without a shunt resistor at different initial operating current levels to reproduce the quench; (2) simulate the transient quench dynamics by using the finite element method to understand the mechanism; (3) attach selected-value shunt resistors across the current terminals in parallel with the NI coil and sudden discharge the shunted coil as in step (1); and (4) compare the experimental and simulated results with a shunt resistor to explain the quench prevention mechanism and mechanical improvements.

FIG. 1.

FIG. 1.

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Photo of the NI HTS coil used for demonstration. This pancake coil has 655 turns wound with a 65-μm-thick, 6-mm-wide HTS REBa2Cu3O7−x (REBCO, RE = rare earth) conductor. All the tests were carried out at an initial temperature of ∼4.2 K in the conduction-cooling test rig. The inductance and turn-to-turn contact resistance are 20.9 mH and 4.78 mΩ, respectively. Two brass shunt resistors of ∼3.79 and ∼1.92 mΩ were selected to compare their effects during the quench.

For step (1) without a shunt resistor, we energized the coil to a predetermined initial current Iini and waited for the magnetic field and temperature settlement before cutting off the power supply current by a knife switch. The magnetic field at the coil center, which can represent the NI coil current, was recorded. We repeated tests with increasing Iini from 100 to 350 A, and the results are shown in Fig. 2. A quench, i.e., a rapid field drop to zero within only ∼450 ms, occurred at Iini = 350 A, whereas the fields decayed exponentially with a time constant τ ≈ 4.37 s in the cases of Iini = 100–300 A without quenches.

FIG. 2.

FIG. 2.

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The recorded coil center field decay in sudden discharging tests without a shunt resistor. Inset: detailed quench process, where the simulated result will be described in step (2).

For step (2), we established a model fully coupled with electromagnetic, thermal, and mechanical simulations to reveal the quench dynamics in the NI coil. The electromagnetic model is constructed in the frame of H-formulation,31 which originally simulates the conventional insulated HTS coils without radial turn-to-turn current flows. For the simulation in this paper, based on rotated anisotropic resistivity,32 we improved the model and enabled it to account for the radial turn-to-turn current flow in an NI coil—it is unachievable by a regular H-formulation model. As shown in Fig. 3(a), the 655-turn demonstrative NI coil, originally built turn by turn in the model with dense simulation intensity required, is simplified here to six homogenized 2D parts while keeping accurate results by the homogenization method.33 We have shown the simulated results in Fig. 2 and compared them with the experiments both in the quenched and unquenched cases, confirming that the simulation is trustable and in good agreement with the experimental results.

FIG. 3.

FIG. 3.

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The simulation for the quench dynamics. (a) The 2D homogenized model. It is divided into six winding parts, #I–VI, but all of the physical variables keep continuous between parts. (b) Changes in coil currents (Icoil) and corresponding critical currents (IC) during the quench process. The shadows are the overlaps of IC and Icoil curves, which indicate quenches. The plots in the figure are the winding current density (Jcoil) distributions (normalized by JC(T,B,θ), the local temperature T-, and anisotropic field θ-B-dependent critical current density). Quench happens when the legend >1. (c) Changes in temperatures in the quench process. The plots in the figure are temperature distributions.

Figures 3(b) and 3(c) show the simulated sudden-discharging quench dynamics within each winding part, including (1) coil currents in the φ direction (Icoil) and the corresponding critical currents (IC) and (2) the temperatures, respectively. After cutting off the power supply circuit at 5 ms, Icoil decay in the winding part I is observed to be the fastest. This is because the winding part I has the lowest inductance L and the highest turn-to-turn resistance RC compared to those of the other winding parts, resulting in the fastest exponential decay time constant τ = L/RC. Because of turn-to-turn joule heat, the temperature rising in the winding part I is also the fastest. However, Icoil decay in the winding part I does not mean that a quench happens in this time range (t = [5 ms, ∼90 ms]). Then, due to thermal diffusion, the winding part II is heated, leading to its IC degradation faster than its Icoil decay. At the moment of t1 ≈ 90 ms in Fig. 3(b), we believe that the partial quench initiates, as IC drops lower than Icoil in the winding part II, i.e., the Icoil and IC curves have overlapped area colored in orange shadow in the figure. Due to electromagnetic coupling and flux conservation, Icoil in parts III–VI rises in a sequence exceeding its corresponding IC and then quenches just as the overlapped areas with colored shadows indicated in the figure. The quench happens like an avalanche spreading toward the outermost winding part, with increasing overcurrent level and propagation speed. Finally, at t4 ≈ 345 ms, all of the shadows are overlapped, indicating the entire coil is quenched.

For a more detailed revelation of the quench propagation, we show the normalized coil current density (Jcoil) distributions in the winding at typical time points, as the plots shown in Fig. 3(b). We can see that the quenched area (i.e., red area) pushes and squeezes the superconducting area (i.e., yellow and green areas) toward the outermost winding part and finally fills out all of the winding. Also, as the plots shown in Fig. 3(c), the heat moves with the quench propagation and accumulates, forming a hottest spot in the outermost winding part at t = 345 ms.

We calculated the quench in radial propagation is 0.17 m/s and concluded that the sudden-discharging-triggered quench is initiated by turn-to-turn heat even when Icoil < IC, and then the quench is spread out by induced overcurrent, whereas the currently widely reported energizing quench23–26 happens when Icoil > IC due to local defects—a different mechanism to our reported quench in this paper.

According to the simulation in step (2), the key point of this quench prevention is to avoid initial heat generated by the turn-to-turn current—this is also the preferential consideration in the selection of an appropriate shunt resistor. That is, the portion of the in-winding current diverted by the external bypassing must be significant enough in order to suppress the turn-to-turn joule heat to be always lower than the cooling capacity during the sudden discharging. The macroscopic electrical behaviors of the shunted NI coil including the amount of diverted current are governed by a circuit model, which consists of a shunt resistor and lumped equivalent circuits of each NI winding part, as shown in Fig. 4(a). The effect of shunting mainly relates to cooling condition, turn-turn heating, and magnetic coupling in NI winding.

FIG. 4.

FIG. 4.

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For the shunted coil (a) its governing circuit model has inductors including both self- and mutual-inductances (L and M), with azimuthal REBCO conductor resistors (Rφ) connecting in series and turn-to-turn contact resistors (RC) connecting in parallel, where Rφ mainly has three components: RHas from the Hastelloy layer, RCu from the copper stabilizer, and Rsc from the superconductor. (b) The sudden discharging results with a 350 A initial current. With the 1.92 mΩ shunting (Rsh2), the quench is completely eliminated. Plots: the normalized winding current density distributions at typical time points show no quenches during the entire discharging.

For step (3), considering the rated cooling capacity of the cryocooler we used (Sumitomo RDK-408D2: 1 W at 4.2 K and 50 W at 43 K) and turn-to-turn contact resistance RC ≈ 4.78 mΩ, we first estimated the initial maximum turn-to-turn current in the winding has to be lower than 102 A base on the joule heat equation (i.e., 102 A × 102 A × 4.78 mΩ < 50 W)—this indicates the external shunting needs to divert at least 248 A (i.e., 350 – 102 = 248 A). Therefore, the corresponding shunt resistance is calculated to be 1.97 mΩ (i.e., 248 A/102 A ≈ RC/1.97 mΩ). To fast while safely release the energy by the shunt, inductive magnet terminal voltage also needs to be considered. With this shunting, ∼0.5 V is calculated—this is acceptable for the demonstrative coil because the inductance is not very large. In the test, we used two external shunt resistors measured Rsh1 = 3.79 mΩ and Rsh2 = 1.92 mΩ, the latter is set as close as the calculated value, and the former is set about twice larger for effect comparison.

The sudden discharging tests on the shunted coil with Iini = 350 A are shown in Fig. 4(b). With Rsh1, the quench still occurs but is delayed to ∼2 s, more than four times longer compared to that of the unshunted case. The longer the quench is delayed, the less the initial quench energy remains, and thus, the lower the damage risk would be. While with Rsh2, the quench is completely eliminated, and the coil center field decays exponentially with an average τ ≈ 15.28 s. Figure 4(b) also shows the simulated diverted current in Rsh2, it is ∼260 A at the beginning, meeting the required >248 A estimated above, and suppressing the initial turn-to-turn heat.

Under the given resistance of 1.92 mΩ, we adopt eight round brass rods connected in parallel as the shunt resistor. Each rod has 1-mm diameter and 23-cm length. Compared to copper and stainless steel, brass has better thermal and electrical stability while transporting the diverted current under adiabatic heating condition. After the test, the final temperature on the brass shunt is estimated to be <240 K.34

In step (4), with the shunt resistor Rsh2 in place, we again simulated the normalized current density distributions and the temperature changes within the winding [Fig. 4(b), the inserted plots and Fig. 5, respectively). From the results, the normalized current density distributions at typical time points 5 s (t1), 10 s (t2), and 15.28 s (t3, i.e., τ) indicate that the coil has no induced overcurrent exceeding the critical current, and consequentially, no quench during the entire sudden-discharging process. The maximum temperature reached is ∼39 K, which is much lower than that of the unshunted case in Fig. 3(c). Through steps (3) and (4), we proved that the proposed external shunt resistor suppresses the turn-to-turn heat and the induced overcurrent during the sudden discharging, maintaining the superconducting region in the winding without quench. Moreover, we compared the winding stress induced by electromagnetic forces (e.g., the radial stress in Fig. 6). Simulation results show that the maximum stress reduces from 428 MPa during quench down to 115 MPa without quench, which proves that the proposed external shunting can mechanically protect the coil as well. This mitigation of force fluctuation is essential to operation safety, especially for large-scale magnets.

FIG. 5.

FIG. 5.

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Winding temperature changes when applied with a shunt resistor Rsh2.

FIG. 6.

FIG. 6.

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The maximum radial winding stress simulated in the cases of shunted and unshunted. The stress during quench (i.e., the brown line) has a high peak at 328.5 ms due to rapid electromagnetic fluctuations in the winding without shunting. Plots: forces and stress distributions at the maximum values, for the shunted case, at 0.25 s (the lower plot) and for the unshunted case, at 328.5 ms (the upper plot).

Note that this shunting concept intrinsically results in a longer time constant, here, 15.28 s (shunted) and 4.37 s (unshunted), and thus, longer time to energize the magnet.

In conclusion, a preventive approach against sudden-current-discharging quench, a fault-mode phenomenon in NI HTS magnets, is proposed and demonstrated both experimentally and analytically. Based on the validated simulation model, the turn-to-turn joule heat in the inner winding parts initiates a partial quench, and then the induced overcurrent fast spreads out the partial quench toward the outer winding parts, resulting in an entire quench within the NI coil. The external shunt resistor, as the key idea in this proposed preventive approach, is made of thin brass rods for thermally and electrically stable operation during the quench. This external shunt resistor can effectively reduce the joule heat (i.e., the quench initiator) by bypassing the winding current and then suppresses the induced current (i.e., the quench spreader) not to exceed the critical current, remaining sufficient superconducting areas within the winding for a safe coil discharging without a quench. Meanwhile, the risk of mechanical damage in the quench is also significantly reduced. To extrapolate this shunt resistor to a more general magnet, first, the needed diverted current based on the specific cooling condition is estimated, then the shunt resistance based on the diverted current and the turn-to-turn contact resistance is determined, at last, if the discharging voltage of the magnet is still too high, then the shunt resistance is further reduced. In practical applications, this fault-mode phenomenon preventive approach has the advantage of being able to add, adjust, or replace the shunt resistor even after completing and pre-testing the main magnet, and this is impossible with a conventional NI HTS magnet. It is also very convenient just by adding this shunt resistor across the two electrodes (i.e., the current leads) and can have the magnet protected. We believe that the above-mentioned merits enable the proposed preventative approach highly compatible and practically applicable for quench prevention in most NI HTS magnets.

Acknowledgments

This work was supported by the National Institute of General Medical Sciences of the National Institutes of Health under Award No. R01GM137138. The authors thank Pu Duan and Jingdong Li, from the School of Electrical and Electronic Engineering, Huazhong University of Science and Technology, Wuhan, China, for important suggestions on modeling. The authors also thank the support from SJTU Scholarship.

AUTHOR DECLARATIONS

Conflict of Interest

The authors have no conflicts to disclose.

Author Contributions

Fangliang Dong: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Resources (equal); Software (equal); Supervision (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Dongkeun Park: Conceptualization (equal); Funding acquisition (equal); Methodology (equal); Project administration (equal); Supervision (equal); Writing – review & editing (equal). Wooseung Lee: Data curation (equal); Formal analysis (equal); Methodology (equal); Software (equal); Validation (equal). Luning Hao: Software (equal); Visualization (equal); Writing – review & editing (equal). Zhen Huang: Software (equal); Visualization (equal); Writing – review & editing (equal). Juan Bascunan: Funding acquisition (equal); Project administration (equal); Supervision (equal); Writing – review & editing (equal). Zhijian Jin: Writing – review & editing (equal). Yukikazu Iwasa: Conceptualization (equal); Funding acquisition (lead); Project administration (lead); Supervision (lead); Writing – review & editing (equal).

DATA AVAILABILITY

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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Associated Data

This section collects any data citations, data availability statements, or supplementary materials included in this article.

Data Availability Statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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