Quench and self-protecting behaviour of an intra-layer no-insulation (LNI) REBCO coil at 31.4 T

We fabricated an LNI-REBCO coil as shown in figure 2(a). The coil was wound using a single piece REBCO conductor (SuperPower, SCS4050-AP) under a winding tension of 4.9 N (0.5 kgf). Since a high winding tension might degrade the REBCO conductor during the layer-winding process, we chose such a low tension value. Specifications of the coil are listed in table 1.

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Figure 2(b) shows a schematic of the coil cross-section. We wound the REBCO conductor with the superconducting layer facing the inner side. For applying the LNI method, we inserted 26 µm thick sheets laminated with PET (18 µm) and copper (8 µm) between all layers with the copper surface facing the inner side, i.e. the copper surface of an inter-layer sheet faced the Hastelloy substrate layer side of the REBCO conductor. After winding, we impregnated the coil with paraffin wax and added over-banding made of 12-layer Ni-alloy tapes (width: 4.0 mm, thickness: 25 µm) with a winding tension of 0.5 kgf. The open circles in figure 3 shows a measured voltage–current characteristic of the coil in self-field at 77 K. These plots were obtained by a step-by-step charging with a current overshooting-and-holding operation at every step to remove residual voltages induced by relaxation of the screening current [4]. The plots are averaged coil voltages during current-holding after over-shooting. The coil I_c for 0.01 µV cm⁻¹ was 31.3 A which agrees with a calculated coil I_c considering field- and field angle-dependencies on I_c of the REBCO conductor [23], i.e. the coil was undamaged. Prior to the present high-field generation test, the coil had experienced several tests including a quench at 23 T [24], and the voltage–current characteristic of the coil had not changed. For applying more reinforcement to the coil for the present charging experiments, we additionally made over-banding with 60 layers of Ni-alloy tape (width: 4.5 mm, thickness: 30 µm) with a winding tension of 0.5 kgf. As a result, however, the coil I_c dropped to 30.2 A as shown by the open triangles in figure 3, i.e. the coil was degraded due to the additional over-banding process. Figure 4 shows an I_c distribution in the longitudinal direction measured by the non-contact measurement method [25] after the high-field tests as described in the following section. This data clearly indicates that the conductor I_c drops at almost every layer-change area at the top and bottom ends of the winding. In these areas, the conductor packing factor was low and there was room for the conductor to move due to external forces. Under such a condition, when a compressive hoop stress was applied to the conductor by over-banding, an excessive bending strain might occur and damage the conductor, which problem we will need to address in future work. Although the coil contained such I_c degradation, we conducted the high-field generation test described later.

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In general, an NI pancake coil has contact resistance R_c between turns, which is obtained from contact resistivity ρ_ct divided by contact area. Such a parameter strongly affects quench behaviour [26]. For an LNI coil, R_c or ρ_ct exists at the contact between each turn and the facing copper sheet. Figure 5 shows the variation of ρ_ct of the present LNI-REBCO coil obtained at 77 K (open triangles) and at 4.2 K (open squares). Each ρ_ct was determined by fitting a simulated magnetic field decay curve of an equivalent electrical circuit model [15] to the field decay curve measured in a power supply (PS) shutdown test. As shown in this figure, ρ_ct increased with number of PS shutdown test. The increase of ρ_ct was significant after thermal cycles and charging experiments, particularly after high field generation/quench experiments, as shown by the solid arrows in the graph. Although the mechanism is not clear, electromagnetic forces might have changed the contact condition inside the winding. Evaluated ρ_ct were in the range of 600–10 000 µΩ cm². The latest (and the largest) value of 10 000 µΩ cm² is comparable to ρ_ct of 25 000 µΩ cm² for the eight-layer LNI REBCO coil in our previous work [15] and is three orders of magnitude higher than the typical value of 70 µΩ cm² for an NI-REBCO pancake coil [27]. The effect of ρ_ct on quench behaviour will be discussed with numerical simulation results in a following section.

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We installed the LNI-REBCO coil inside the bore of an insulated Bi-2223 coil. These two coils were electrically connected in series. Specifications of the Bi-2223 coil are listed in table 1. As shown in figure 6, the series connected HTS insert was installed in the 130 mm cold bore of the 17 T low-temperature superconductor (LTS) magnet [28] of the Cryogenic Station, National Institute for Materials Science (NIMS). Table 2 shows the inductance matrix of the HTS insert and the LTS magnet. Figure 7 shows a schematic circuit for the high-field generation test. The HTS insert and the LTS magnet were individually charged using two DC power supplies. To precisely observe the LNI-REBCO coil voltage at current holds, we used a highly stabilized DC PS with current stability of 5 ppm h⁻¹ for the HTS insert. Both the LNI-REBCO coil and the Bi-2223 coil was connected to a 1 Ω dump resistor at room temperature. Currents (I_re, I_bi and I_lts) and voltages (V_re-p, V_re, V_re-n and V_bi) were measured as described in figure 7. Three Hall sensors were installed at the top end (B_top), at the centre (B_cen), and at the bottom end (B_bot) of the LNI-REBCO coil along the coil axis as shown in figure 2(b). For a quench detection in the HTS insert, the PS was set to shut down when V_re-p + V_re + V_re-n + V_bi exceeds 0.2 V.

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Operating parameters at a 30 T central field are listed in table 3. At I_re (≈I_bi) = 265 A, the central field reached 30 T in a background field of 17.2 T generated by the LTS coil. During this operation, I_c of the LNI-REBCO coil was estimated to be 733 A considering field- and field angle-dependencies of the I_c of the REBCO conductor [23]. Note that this estimation did not consider the conductor I_c drop due to the additional over-banding described in figure 4 and therefore the actual coil I_c should be lower than this value. The calculated maximum hoop stress B_zJR and the maximum compressive stress are 461 MPa and −16.7 MPa, respectively. Note that these stresses did not consider the effects of winding tension, over-banding, thermal contractions and Lorentz's forces generated by the screening current [8, 29–31].

Figure 8 shows results of the first charging test. The black solid line, the red dashed line, and the blue dashed-dotted line show the central field B_cen, the supply current to the HTS insert I_re (≈I_bi), and the LTS magnet PS current I_lts, respectively. Firstly, we charged the LTS magnet to 241.0 A to generate 17.2 T. We then step-by-step charged the HTS insert with 2–5 A overshooting operations to remove residual voltages generated by relaxation of the screening current. At I_re = 265.6 A, B_cen showed 30.0 T. This value is 2% lower than the calculated field of 30.6 T at 265.6 A, a difference which is mainly due to the effect of screening currents in the LNI-REBCO coil. After holding the coil currents for 15 min, all the coils were discharged without any quench.

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Figure 9 shows the voltage–current characteristics of V_re (open circle: coil winding), V_re-p (open triangle: soldered part between winding and outer electrode) and V_re-n (open square: soldered part between the winding and inner electrode) in the first charging test to 30 T. V_re does not show normal voltages in the charging and discharging processes. V_re-p shows normal voltage corresponding to 0.5 µΩ in the charging and discharging process. V_re-n shows those to ∼2.3 µΩ during charging and 3.3 µΩ during discharging, which implies that an electromagnetic force progressively delaminated the soldering between the REBCO conductor and the negative (inner) electrode under a high field. Although these results show that the coil winding itself did not degrade during charging/discharging, we need to design a countermeasure to avoid damage to soldered connections. We believe that locating a soldered joint in a low-field region, such as the space above the coil winding, is an effective approach and will employ such an option for future coils.

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3.2.1. Overview of the test result.

We charged the HTS insert again in the background field of the LTS magnet until a quench occurred in the LNI-REBCO coil. Figure 10 shows B_cen, I_re (≈I_bi) and I_lts traces of the second charging test. The central field reached 31.4 T at I_re = 289.6 A, which corresponds to a conductor current density of 723 A mm⁻² and a winding current density of 431 A mm⁻². Subsequent events are as follows. (a) Just after reaching 31.4 T, a quench occurred in the LNI-REBCO coil. (b) The DC power supplies for the HTS insert and the LTS magnet detected over-voltages and shut down. (c) The magnetic field generated by the HTS insert decayed in a few seconds. On the other hand, the LTS magnet did not quench and the magnet current was shorted through the cold diode of the protection circuit (see figure 7) and there remained a field of 17.7 T, which is slightly higher than the rated field of 17.2 T, due to an energy transfer from the HTS insert. (d) After the quench event, the LTS magnet was slowly discharged; to extract the energy from the LTS magnet before quenching, we operated the DC PS so as to dump most of the stored energy at room temperature, as seen in figure 10.

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Figure 11 shows the voltage–current characteristics of V_re (open circle), V_re-p (open triangle) and V_re-n (open square) in the second charging test. V_re showed a normal voltage for I_re > 280 A. V_re-n showed the same linear trace with 0.5 µΩ as the first charging test. V_re-p showed a jump at 264.5 A and this produced a Joule heat of 0.55 W just before the quench. We believe that the voltage jump was caused by progressive damage in the soldering; actually, the soldered part was found to be partly delaminated after unwinding the coil.

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After the test, we warmed up and disassembled the HTS insert to charge the LNI-REBCO coil at 77 K in self-field. The open squares in figure 3 shows the voltage–current characteristic. The plots with I_c = 29.7 A and n = 15 are in good agreement with the plots measured before the quench (the open triangles), which indicates that the coil was protected from the 31.4 T quench.

3.2.2. Transient behaviour during quenching.

Figures 12(a) and (b) respectively show I_re and V_re (solid line), V_re-p (dashed line) and V_re-n (dash-dotted line) just before the 31.4 T quench. The horizontal axes are calibrated such that t = 0 s corresponds to the shutdown of the DC PS for the HTS insert. At t = −23.5 s, we started increasing I_re from 289.4 A with a sweep rate of 0.1 A s⁻¹. V_re showed an inductive voltage of 8.5 mV. At t = −17.5 s, an unexpected rise of V_re was observed. Although we immediately started decreasing I_re, V_re gently increased for 17 s and eventually showed a steep irreversible take-off, i.e. quench. The stable V_re-p and V_re-n values indicates that the quench was initiated from the coil winding. The PS was shut down as V_re-p + V_re + V_re-n + V_bi exceeded the quench detection voltage of 0.2 V.

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Transient signals during the quench event are plotted in figure 13. Figure 13(a) shows I_re (solid line) and I_bi (dashed line). Figure 13(b) shows V_re (solid line) and V_bi (dashed line). Figure 13(c) shows axial magnetic fields; in order to observe the axial distribution of the magnetic field generated by the LNI-REBCO coil, the normalized axial magnetic fields generated by the LNI-REBCO coil ${\widehat B_{{\text{top-re}}}}$, ${\widehat B_{{\text{cen-re}}}}$ and ${\widehat B_{{\text{bot-re}}}}$ were calculated from measured B_top, B_cen and B_bot values by the following equations

$$\begin{align}\begin{array}{*{20}{c}} {{{\hat B}_{{\text{*}} - {\text{re}}}}\left( t \right) = \,\frac{{{B_{{\text{*}} - {\text{re}}}}\left( t \right)}}{{{B_{{\text{*}} - {\text{re}}}}\left( 0 \right)}}} \end{array}\end{align} \tag{ 1 }$$

$$\begin{align}\begin{array}{*{20}{c}} {{B_{{\text{*}} - {\text{re}}}}\left( t \right) = {B_{\text{*}}}\left( t \right) - {B_{{\text{*}} - {\text{bi}}}}\left( t \right) - {B_{{\text{*}} - {\text{lts}}}}\left( t \right)} \end{array}.\end{align} \tag{ 2 }$$

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Here, subscript '*' represents 'top', 'cen' or 'bot'; B_* are measured magnetic fields; B_*-bi are calculated magnetic fields generated by the Bi-2223 coil; B_*-lts are calculated magnetic fields generated by the LTS coil.

After the shutdown of the PS for the HTS insert, I_re and I_bi decreased with different time constants (see figure 13(a)). As shown by figure 13(b), V_re sharply increased and peaked at 58 V at t = 0.8 s. On the other hand, the Bi-2223 coil did not quench because transferred energy from the quenching LNI-REBCO coil to the Bi-2223 coil was so small that it did not exceed the stability margin. V_bi showed a negative inductive voltage induced by the reduction of the LNI-REBCO coil magnetic field and peaked at −62 V. The energy dissipated in the LNI-REBCO coil can be roughly estimated as 8.19 kJ by integrating the products of I_re and V_re during the quench. As a note, the actual dissipated energy should be larger than this value, because V_re included negative inductive voltage. Table 4 shows an energy matrix of the HTS insert just before the quench (I_re = 289.6 A). The table indicates the LNI-REBCO coil dissipated more energy than the self-stored energy, 3.6 kJ; i.e. the LNI-REBCO coil as well dissipated part of the Bi-2223 coil's stored energy.

Table 4. Stored energy matrix of the HTS insert (I_re = I_bi = 289.6 A).

	REBCO	Bi-2223
REBCO	2.0 kJ	1.6 kJ
Bi-2223	1.6 kJ	20.7 kJ
Total	3.6 kJ	22.3 kJ

As shown in figure 13(c), ${\widehat B_{{\text{top-re}}}}$, ${\widehat B_{{\text{cen-re}}}}$ and ${\widehat B_{{\text{bot-re}}}}$ were in good agreement, which indicates that the magnetic field homogeneously decayed along the axial direction during the quench. This is one of the specific behaviours of the LNI coil [15].

Figure 14(a) shows a comparison between the supply current to the LNI-REBCO coil normalized by the initial value ${\widehat I_{{\text{re}}}}$ (=I_re(t)/I_re(0)) and ${\widehat B_{{\text{cen-re}}}}$. ${\widehat B_{{\text{cen-re}}}}$ decayed more quickly than ${\widehat I_{{\text{re}}}}$ and this behaviour is caused by a reduction in the circumferential current due to current bypassing through copper sheets. Here, we introduce the current bypass ratio η, defined by the following equation

$$\begin{align} {\eta = \frac{{\left( {{{\hat I}_{{\text{re}}}} - {{\hat B}_{{\text{cen}} {\text{-}} {\text{re}}}}} \right)}}{{{{\hat I}_{{\text{re}}}}}}} .\end{align} \tag{ 3 }$$

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The parameter η gives a rough approximation of the 'current bypassing zone' propagation ratio inside the winding and η = 1 corresponds to full propagation. Figure 14(b) shows the time evolution of η during quenching. Immediately after the quench initiation, η increased and saturated at 0.45, i.e. the current bypassing zone did not fully propagate before the HTS insert was discharged.

We constructed a numerical simulation model of the LNI-REBCO coil based on an electrical circuit model in combination with a thermal conduction model. The electrical circuit model considers the magnetic field generated by the Bi-2223 coil and the LTS coil.

Figure 15 shows a schematic of the electrical circuit model, which is based on an equivalent circuit model for the LNI coil [15, 20] and on models for the NI pancake coil [32–34]. Each turn is composed of an inductor (L), the effective resistance of the superconductor (R_sc) and the resistance of the copper stabilizer (R_st). A turn is parallel connected to the resistance of the copper sheet (R_sht) through a contact resistance (R_c). We note that we neglected the contact resistances between axially adjacent turns since the axial contact areas were about 40 times smaller than the radial contact areas. R_sc is described by the following equation

$$\begin{align} {{R_{{\text{sc}},i,\,j}} = {E_{\text{c}}}{l_{i,\,j}}\frac{{{ }{I_{{\text{sc}},i,\,j}}^{n - 1}}}{{{ }{I_{{\text{c}},i,\,j}}^n}}} .\end{align} \tag{ 4 }$$

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Here, subscript i is layer number and subscript j is turn number in the ith layer. E_c, l, I_sc, I_c and n are the electric field criterion (1 µV cm⁻¹), the circumferential length of the turn, the current flowing in the superconducting layer, the critical current and n-index, respectively. The field (B) and field angle (θ) dependency of I_c are represented by a function described in [23]. The temperature (T) dependency of I_c was calculated by the following equation [35, 36]

$$\begin{align}{I_{\text{c}}}\left( {T,B,\theta } \right) = \frac{{{I_{\text{c}}}\left( {4.2,B,\theta } \right)}}{{\exp \left( { - 4.2/{T^*}} \right)}} \cdot \exp \left( { - \frac{T}{{{T^*}}}} \right).\end{align} \tag{ 5 }$$

Here T^* is a scaling parameter for the temperature dependence of I_c. We used T^* = 19.5 in the present simulation. In addition, the I_c drop distribution, presented in figure 4, was also considered. We obtained a local I_c in the winding by multiplying the I_c drop ratio (see the right vertical axis of figure 4) to the value obtained by equation (5). In addition, based on the voltage–current characteristic measurements of short conductor samples from the LNI-REBCO coil, the n-index for equation (4) was set as 50 for the no I_c drop turns, 16 for most I_c drop turns, and 10 only at the uppermost turn of the 89th layer, which is the lowest I_c turn.

R_c and R_sht shown in figure 15 are expressed by the following equations

$$\begin{align} {{R_{{\text{c}},i,j}} = \frac{{{\rho _{{\text{ct}}}}}}{{{l_{i,j}}w}}} \end{align} \tag{ 6 }$$

$$\begin{align} {{R_{{\text{sht}},i,j}} = {\rho _{{\text{cu}}}}\left( {T,B} \right)\frac{w}{{{l_{i,j}}{d_{{\text{cu}}}}}}} .\end{align} \tag{ 7 }$$

In this expression, ρ_ct, w, ρ_cu and d_cu are the contact resistivity between conductor and copper sheet, the width of the conductor, the resistivity of copper and the thickness of the copper sheet, respectively. Here, ρ_ct was set to 10 000 µΩ cm² which was obtained from the current dump measurements at 77 K in self-field after the 31.4 T quench (see figure 5).

Using Kirchhoff's law, circuit equations of the LNI-REBCO coil are simply expressed as the following equation

$$\begin{equation}\begin{array}{*{20}{c}} {\left[ {{C_1}} \right]\left\{ {{I_\theta }\left( t \right)} \right\} = \left\{ {{C_2}} \right\}} \end{array}.\end{equation} \tag{ 8 }$$

The vector {${I_\theta }$(t)} contains unknown circumferential current for each turn at a time step (t). Matrix [C₁] consists of R_sc, R_mt, R_c, R_sht and self and mutual inductance for each turn. Vector {C₂} consists of R_c, R_sht, self and mutual inductance for each turn, I_re, circumferential currents at the previous time step ${I_\theta }\left( {t - \Delta t} \right)$ and inducted voltages by the decay of Bi-2223 coil current.

Figure 16 shows a schematic of the thermal conduction model which assumes a single turn as a thermal element. For simplicity, the heat capacity of the copper/insulation sheets between the layers were combined into each element. Assuming that there is no cooling effect from outside of the coil, the heat balance equation for the element of the jth turn in the ith layer is expressed by the following equation

$$\begin{align} C\left( T \right)A{l_{i,j}}\frac{{{\text{d}}T}}{{{\text{d}}t}} &= {g_{{\text{J}}i,j}} - {h_{{\text{ct}}}}\left( {{T_{i,j}}} \right)w{l_{i,j}}\left( {{T_{i,j}} - {T_{i - 1,j}}} \right)\nonumber\\ &\quad - {h_{{\text{ct}}}}\left( {{T_{i,j}}} \right)w{l_{i,j}}\left( {{T_{i,j}} - {T_{i + 1,j}}} \right)\nonumber\\ &\quad - {h_{{\text{ct}}}}\left( {{T_{i,j}}} \right)d{l_{i,j}}\left( {{T_{i,j}} - {T_{i,j - 1}}} \right)\nonumber\\ &\quad { - {h_{{\text{ct}}}}\left( {{T_{i,j}}} \right)d{l_{i,j}}\left( {{T_{i,j}} - {T_{i,j + 1}}} \right).} \end{align} \tag{ 9 }$$

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In this equation, t, C, A, g_J, h_ct and d are respectively time, the combined heat capacity per unit volume, which comprises the heat capacities per unit volume of copper and Hastelloy, the cross-sectional area of the turn (or element), the Joule heat generation in the winding, the heat transfer coefficient between adjacent turns, and the overall thickness of the layer (or element). Here h_ct was determined based on [37]. While g_J consists of the Joule heating in each turn and those in the facing contact resistance and copper sheet, which were calculated from the current distribution obtained from the electrical circuit model. Considering 0.55 W Joule heating at the soldered part between the winding and the inner electrode, half of this value (0.275 W) was added to the inner-uppermost element.

Solving equations (8) and (9) simultaneously, we analysed the time-varying current distribution and temperature distribution inside the winding. As initial conditions, we set a uniform circumferential current distribution of 289.6 A and a temperature distribution of 4.2 K. Figure 17 shows I_c distribution at the initial state considering magnetic field- and magnetic field angle-dependencies [23] and I_c drop distribution (see figure 4). We assumed that I_re and I_bi start decaying with the waveforms obtained in the experiment, seen in figure 13(a), when the LNI-REBCO coil voltage reaches 0.2 V.

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Figures 18(a)–(c) show ${\widehat I_{{\text{re}}}}$ ${\widehat B_{{\text{top-re}}}},\;{\widehat B_{{\text{cen-re}}}},\;{\widehat B_{{\text{bot-re}}}}$ V_re and η obtained by the simulation. For comparison, the corresponding experimental results in figures 13 and 14 are presented again in figures 18(a')–(c'). The simulated transients are in good agreement with the experimental results. That is, the simulation model well reproduces the quench event. To obtain more accurate results, it may be necessary to take into account the effect of eddy currents induced in the copper sheets, the temperature dependency of ρ_ct, the effect of radial compression on ρ_ct, and the dependency of T^* on magnetic field and its angle.

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Figures 19(a)–(d) show simulated results of maximum circumferential currents, voltages, maximum temperatures and maximum hoop stresses (B_zJR), respectively; each result is plotted per ten layers.

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Figures 20(a) and 21(a) respectively show the corresponding distributions of circumferential current and temperature over the winding cross-section at t = 0.0 s, 0.1 s, 0.2 s, 0.3 s and 0.4 s. These figures give more details of the quench propagation. Supplementary videos (available online at stacks.iop.org/SUST/34/064003/mmedia) show the sequential transition from t = −0.1 s to 0.4 s of circumferential current (10000_IθDist_-0.1–0.4s_SuST.avi) and temperature (10000_TempDist_-0.1–0.4s_SuST.avi).

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As seen in figure 20(a), the current distribution was nonuniform and rapidly changed with time. This nonuniformity is a particular feature for NI and LNI coils having bypass circuits inside the winding.

As seen in figure 20(a)- 1, the quench started from the uppermost turn of the 89th layer, which was the lowest I_c region seen in figure 17 considering the I_c drop due to the over-banding and the magnetic field dependencies. The temperature of this region had been increasing from 4.2 K by Joule heating at the solder joint between the winding and the inner electrode, which led the coil to quench. The circumferential current distribution shown in figure 20(a) indicates that the circumferential currents of turns in this layer decreased by current bypassing to other turns through the contact resistances and copper sheet. Correspondingly, the voltage over the 81st–90th layers, including the quench initiation turn, started to rise as seen in figure 19(b). This 'current bypassing zone' propagated toward both inner and outer parts of the coil. Normal voltages appeared sequentially in an inner part (21st–80th layers) and the outer part (91st–180th layers). In contrast, the normal voltages did not appear in the innermost part (1st–20th layers), seen in figures 19(b) and 20(a)–5. As a result, the quench progressed with the propagation of the current bypassing zone. Howeve r, it should be noted that not all such zones necessarily transited to the normal state.

As shown in figures 20(a) and 21(a), the current bypassing zone and the temperature rise initially propagated in the axial direction, and then propagated in the radial direction along the top and bottom ends, where the temperature margin of the REBCO conductor is the smallest. The temperature propagation velocity in the axial direction (v_z ) was almost constant at 0.0 s < t < 0.4 s and was estimated to be 85 mm s⁻¹. On the other hand, the temperature propagation velocity along the radial direction (v_r ) noticeably depends on time domain; it was 10 mm s⁻¹ at 0.0 s < t < 0.12 s and 145 mm s⁻¹ at 0.12 s < t < 0.40 s.

There are two major driving forces for propagation of quenching (i.e. current bypassing): (a) Joule heating due to bypass current through the contact resistances and copper sheets, and (b) electromotive forces induced by the reduction in magnetic flux of quenching turns and by those of the Bi-2223 coil. The former, (a), is the main driving force for the axial quench propagation seen in figures 20(a)–1 and (a)-2. Figure 22(a) shows the distribution of the bypass current through the contact resistances and the copper sheet in the 89th layer at t = 0.0 s. Since the resistance of the copper sheet (R_sht) was two orders of magnitude lower than the contact resistance (R_c), Joule heating generated by current bypassing distributes over the entire layer and it accelerates the axial propagation. The latter, (b), dominates the propagation in the radial direction which is attributed to strong magnetic coupling between turns in the radial direction. Electromotive forces increase the currents of unquenched adjacent turns and make them quenched. In the present experiment, the electromotive force induced by the reduction in the magnetic field generated by the Bi-2223 coil also accelerates this type of propagation for t > 0.12 s since I_bi started to decrease at this time (see figure 13(a)). These driving forces provide a fast quench propagation of an LNI-REBCO coil compared to an ordinary insulated REBCO coil [38].

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As shown in figure 19(c), the peak of the maximum temperature inside the winding was 330 K, which is lower than a reported temperature causing degradation (>500 K) for a paraffin impregnated REBCO coil [39]. As shown in figure 21(a)- 5, the peak temperature located at the uppermost turn of the 89th layer, which was the quench origin turn. The temperature of the unquenched region was as low as 40 K; i.e. there was a large temperature gradient inside the winding. The peak temperature of 330 K is much lower than the peak temperature, ≫1000 K, estimated by the adiabatic heating model under current discharging mode [14]. This is owing to the fast propagation of quench, or current bypassing zone.

While the current bypassing zone rapidly propagates, additional currents were induced in unquenched turns. Thus the circumferential current peak at 420 A was formed in the unquenched zone of the outermost layer (see figures 19(a) and 20(a)–3), generating a peak hoop stress (B_zJR) of 718 MPa (see figure 19(d)). Although this stress is high, it does not exceed the irreversible stresses limit of the REBCO conductor (760 MPa [40] and 800–830 MPa [41]).

As seen in figure 20(a), the circumferential currents are distributed asymmetrically with respect to the central plane of the coil (z = 0 mm). Therefore, an axial net force (F_z ) was generated, due to decentring between the LNI-REBCO coil and the other outer coils [33]. Values of F_z can be obtained by integrating the product of the circumferential current and the radial magnetic field over the entire winding. Figure 19(e) shows the transient behaviour of F_z . The F_z peak was 74 N (7.6 kgf), which was not harmful for the coil.

Consequently, it is demonstrated that the LNI-REBCO coil was protected from damage during quenching at 31.4 T, which is consistent with the experimental results.

To investigate the effect of the contact resistivity on the quench propagation, we conducted a 31.4 T quench simulation with the ρ_ct value of 70 µΩ cm², which was typically reported for NI coils [27]. The other parameters were the same as the previous simulation.

Figures 19(a')–(e') respectively show simulated results of maximum circumferential currents, voltages, maximum temperatures, maximum (B_zJR) and F_z with ρ_ct = 70 µΩ cm²; note that each result is plotted per ten layers. Figures 20(b) and 21(b) respectively show circumferential current and temperature distributions over the winding at t = 0.000 s, 0.300 s, 0.325 s, 0.350 s, 0.375 s and 0.400 s. Supplementary videos show the sequential transition from t= −0.1 s to 0.4 s of circumferential current (70_IθDist_-0.1–0.4s_SuST.avi) and temperature (70_TempDist_-0.1–0.4s_SuST.avi).

At t = 0.000 s, current bypassing zone and temperature rise were slowly propagating from the uppermost turn of the 89th layer to neighbouring turns (see figure 20(b)-1) in the radial direction. The driving force of this propagation is (a) Joule heating generated by bypass current mentioned earlier. During 0.000 s < t < 0.300 s, v_r and v_z are estimated to be as low as 5 mm s⁻¹ and 8 mm s⁻¹, respectively, which were close to the velocity reported for the insulated REBCO coil [38]. Figure 22(b) shows the bypass current distribution in the 89th layer at t = 0.000 s. In this case, bypass current was localized since R_ct was comparable to R_sht. Therefore, the propagation velocity in the axial direction was low, unlike the case of ρ_ct = 10 000 µΩ cm². Incidentally, a similar discussion has been published for a NI REBCO pancake using conductive epoxy resin in [42]. The behaviour of a bypass current along the axial direction, which is related to the ratio between R_ct and R_sht, as described in figure 22, is similar to the acceleration mechanism of the normal zone propagation velocity of an REBCO conductor with an increased interfacial resistance between the superconducting layer and the stabilizer [43, 44].

At t = 0.300 s, an extremely rapid propagation of current bypassing zone appeared from an upper region in the outermost layer (see figure 20(b)-2); the current bypassing zone spread over the entire coil winding in just 0.1 s as shown in figures 19(a') and 20(b)-2–(b)-6. The driving force of this propagation is (b) electromotive forces induced by reduction in magnetic flux described earlier. While the current bypassing zone rapidly propagated, additional currents were induced in unquenched turns; such current increase is clearly shown in the yellow and red colours part in the gradation images in figures 20(b)-2–(b)-5. This results in the formation of a very high circumferential current peak of 826 A in the 174th layer at t= 0.350 s as seen in figure 19(a') and figure 20(b)-4. The current peak was quickly moving with time from the outer upper region to the inner lower region (see red arrows in figure 20(b)). The phenomenon enormously accelerated propagation of the current bypassing zone, i.e. quench, over the coil winding; this is a notable characteristic nature of the LNI coil having a low contact resistivity. Actually, during 0.300 s < t < 0.400 s, v_r and v_z are estimated to be 874 mm s⁻¹ and 555 mm s⁻¹, respectively; they are an order of magnitude faster than those for ρ_ct = 10 000 µΩ cm² and comparable to the quench propagation velocity for LTS coils.

Due to the high propagation velocities, the peak temperature was as low as 75 K (see figure 19(c')), which is four-fold lower than that for ρ_ct = 10 000 µΩ cm². To the contrary, the current peaks in this case becomes extremely high, resulting in a local hoop stress (B_zJR) near the current peak turn that reached 1398 MPa, as seen in figure 19(d'), which is nearly the double of the irreversible stresses of the REBCO conductor, hence causing mechanical damage. Due to the rapid movement of the extremely high hoop stress position across the winding, the coil winding might be mechanically loosened after quench. In addition, the peak F_z was increased to 371 N (37.9 kgf), five times larger than that with ρ_ct = 10 000 µΩ cm², although it does not seem to be a serious problem.

The simulation results indicate that ρ_ct strongly affects the peak values of electromagnetic stresses and temperature during quenching. Figure 23 shows the peak hoop stress σ_{θ, peak} and peak temperature T_peak during a 31.4 T quench as a function of ρ_ct. We added plots with ρ_ct = 600 µΩ cm² that was the lowest value obtained for the present LNI-REBCO coil (see figure 5) and ρ_ct = 25 000 µΩ cm² that was obtained for an LNI-REBCO coil in the previous report [15]. In the case of ρ_ct = 600 µΩ cm², σ_{θ, peak} is higher than the irreversible stress of the REBCO conductor, i.e. the coil will be mechanically damaged. In the case of ρ_ct = 25 000 µΩ cm², T_peak is higher than the temperature causing the degradation [39], i.e. the coil will be thermally degraded.

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Figure 23 indicates that there is a specific range of 7000 µΩ cm²< ρ_ct < 20 000 µΩ cm² in which the coil is not damaged either mechanically or thermally. Note that this range is not general and a particular ρ_ct range will depend on the coil parameters and the si tuation of a quench. In addition, the threshold values here, σ_peak < 760 MPa and T_peak < 500 K, are too high and they have to be set to reasonably low values when designing a protection scheme, e.g. σ_peak < 600 MPa and T_peak < 300 K. In this light, σ_peak and T_peak obtained for the present coil are quite high. In addition, a winding technology to achieve a target ρ_ct is indispensable.

The simulation results are summarized as follows:

• (a)  
  The quench propagation mechanism strongly depends on the value of ρ_ct.
• (b)  
  Figure 23 demonstrates the trade-off between σ_{θ, peak} and T_peak, i.e. a higher ρ_ct provides a higher T_peak and a lower σ_{θ, peak}; lower ρ_ct provides a lower T_peak and a higher σ_{θ, peak}. There is a range of ρ_ct that avoids both mechanical and thermal degradation.
• (c)  
  For the present LNI-REBCO coil at 31.4 T, the high ρ_ct of 10 000 µΩ cm² coincidentally provided protection from a high hoop stress, although it caused a moderately high local temperature. If the coil had a much lower ρ_ct value, such as 600 µΩ cm², it would be degraded due to a high hoop stress.

As a side note, we can consider coil behaviours out of the range of figure 23 as follows. When ρ_ct is orders of magnitude higher than the value of 10 000 µΩ cm², the coil should behave as an insulated coil, resulting in a very high T_peak and a moderate σ_{θ, peak}. When ρ_ct takes a much lower value, which might occur in an solder-impregnated NI/LNI coil, T_peak should be very low and σ_{θ, peak} extremely high. Under such a very fast current transient, there might appear a suppression effect on σ_{θ, peak} by an inductive reactance. In addition, a quench detection condition might affect T_peak and σ_{θ, peak} and such investigations will be made in the future.