Experiment and numerical simulation of the combined effect of winding, cool-down, and screening current induced stresses in REBCO coils

The experimental apparatus seen in figure 4 demonstrates the stress modification effect due to the screening current [9]. Two five-turn REBCO dry pancake coils, 79.5 mm in inner diameter, were installed inside a 5 T NbTi coil; we used a 4 mm wide SuperPower REBCO tape for both coils. Coil A is fixed in the middle of the upper half of the 5 T NbTi coil, while Coil B is at the top end of the NbTi coil. We bonded three strain gauges on the outer surface of each test coil for measuring the circumferential stress distribution along the conductor width, as seen in figure 4. The operating current for Coil A is 693 A under the external magnetic field of B_z = 4.8 T and B_r = 0.4 T, while that for Coil B is 300 A under B_z = 2.8 T and B_r = 1.6 T. We tested them at 4.2 K. A graph at the center of figure 5 shows the measured circumferential stress (strain) distribution vs position along the conductor width; Z_RE = −2 mm is the lowest edge, while Z_RE = 2 mm is the highest edge of the conductor. The left axis shows the circumferential strain, while the right axis is the corresponding stress. The circumferential stress measured by the strain gauge increases with Z_RE due to the screening-current effect, as expected from the numerical simulation described in the previous section; note that each conductor separates from the other. The circumferential stress at Z_RE = 1 mm for Coil A is 615 MPa, about double that for Coil B, 225 MPa, due to a higher magnetic field, B_z , and higher coil current density. Another unique feature for Coil B is that the circumferential stress at the lower part of the conductor at Z_RE < −1 mm seems to be compressive. They will be compared with the numerical simulation later.

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Figure 5 also shows the coil performance at 77 K after the charging experiment. Coil A on the right does not show degradation, although the maximum circumferential stress is high. On the contrary, Coil B shows degradation. We can infer that the circumferential compressive stress results in buckling damage at the lower part of the conductor, degrading the coil performance. Figure 6 proves the buckling at the lower edge of the coil, showing cracks and delaminations on the right and critical current degradation on the left.

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The screening current effect results in the circumferential stress hysteresis for Coil B, as shown in figure 7. We observed a hysteresis effect while the NbTi coil current is swept up and down without the any current flow in the test coil; the interaction between induced screening current and axial magnetic field of the NbTi coil results in a circumferential stress distribution. The hysteresis is due to the difference in induced screening current during charging and discharging the coil. The circumferential strain for Z_RE = −1 mm seen by a solid green line is negative (i.e. compressive) while increasing the NbTi coil current, resulting in buckling damage of the coil. Thus, stress modification due to the screening current results in (a) excessive tensile damage at the upper edge of the conductor and (b) buckling damage at the lower edge of the conductor.

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The numerical simulations of the stress modification effect due to the screening current for the five-turn REBCO dry pancake coils, as seen in figure 4 [9], were performed. This coil is a dry wound with polyamide-insulated REBCO tape conductor. The thickness of the insulator is 35 µm; each turn in the dry coil deforms separately and move freely. The contact between turns is modeled using gap elements. In the simulation, winding, cool-down and screening current-induced stresses are considered. The simulation circumferential strains are shown in figure 8(a). The solid green line shows the numerical simulation results for Coil A, and the solid blue line is for Coil B. The strain shown in figure 8 includes both electromagnetic and bending contribution. Turns are separated from each other, as seen in figure 8(b). Therefore, the circumferential strain distributions along the REBCO tape width, considering a screening current, is different from that for uniform current case (green and blue dashed lines). The circumferential stress is concentrated at the top of the tape while it decreases at the bottom. As seen in figure 8(a), the simulation results (solid lines) agree very well with the experimental results (triangle); the maximum tensile strain 0.6%, corresponding to ∼800 MPa at Z_RE = 2 mm. In comparison, the maximum compressive strain for Coil B is −0.06%, corresponding to −100 MPa at Z_RE = −2 mm. The conductor is not degraded in the former case in the experiment, as seen in figure 5. On the contrary, it is the degraded in the latter case as seen in figures 5 and 6. Thus the numerical results are in reasonable agreement with experiments.

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Based on the numerical simulation, we observed the hysteresis of the circumferential strain for Coil B as seen in figures 9(a)–(c), agreeing very well with the experimental result seen in figure 7. Figure 9(d) shows the deformation and circumferential stress distributions in a cross-section of winding. Although the hysteresis of circumferential strain in figures 9(a)–(c) is very similar to the experiment, the values are different. The reason is errors in the mechanical properties of the REBCO conductors or the plastic deformation of composing materials.

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As described in the previous section, if the cumulative radial stress for a coil is not sufficiently negative, conductors are separated from each other, and therefore each conductor reacts individually to the electromagnetic force. In this case, the REBCO conductor is bent in wave pattern due to the circumferential stress distribution along the width, as the REBCO conductor's flexural rigidity is minimal. This bending sometimes results in degradation of the coil performance. On the contrary, as described in the last section, if the compressive radial stress is significant, the conductor is tightly pressed together, enhancing the flexural rigidity of the winding. Thus, we can suppress the wavy bending of the conductor, reducing the stress modification and degradation of the coil performance. Higher winding tension and thinner insulation, such as a no-insulation coil, are adequate for suppressing the coil degradation [16].

On the contrary, in the case of epoxy-impregnated coils, the coil winding acts as bulk; therefore, the flexural rigidity of the winding is significant regardless of the cumulative radial stress. Thus, we can control the stress modification effect and suppress degradation of the coil performance, as described in the previous section [16].

However, a drawback of REBCO conductors is the weakness against peeling [6, 24]. If we impregnate a REBCO coil with epoxy resin, tensile stress is created between a REBCO conductor and the epoxy resin during cool-down, resulting in peeling off a REBCO layer, thereby degrading the coil performance [6]. An electrodeposited polyimide layer spread over REBCO surface [25] decouples the REBCO-conductors from the epoxy resin, suppressing the peeling damage during cool down [6]. We will show charging test results of an epoxy impregnated REBCO coil wound with a polyimide electrodeposited REBCO conductor.

A 10 μm thick polyimide layer is electrodeposited on the REBCO conductor's surface. A four-turn solenoid, 80.0 mm in inner diameter, 81.0 mm in outer diameter, and 94.8 mm in height, was produced. A wet winding process with epoxy resin was employed as seen in figure 10, as vacuum impregnation was difficult due to the minimal space between turns and layers.

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Figure 11(a) shows the coil voltage vs current at 4.2 K in an external magnetic field of 11 T [26]. Resistive voltage and voltage spikes do not appear below 406 A, as shown by the red open circles. However, the coil voltage suddenly jumped to 0.9 mV at 408 A with a time duration of <40 ms, as shown in figure 11(b). The coil voltage becomes constant after the voltage jump, and therefore the voltage jump is due to the sudden failure of the REBCO conductor. The 408 A value is 65% of the short sample critical current, corresponding to the circumferential tensile stress, i.e. BjR, 469 MPa; B is the axial magnetic field, j is the coil current density, and R is the coil radius. This tensile stress is not amplified by the screening current as the coil is impregnated with epoxy resin; the circumferential tensile stress is insufficient for conductor failure. While discharging the REBCO coil, the resistive voltage remains in the range from 410 A to 250 A. The irreversible behavior results from conductor failure by the electromagnetic force; the coil critical current decreases from 621 A to 250 A, 40% of the initial value.

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After the coil charge test, we found a conductor fracture at a top turn of the 2nd layer, as seen in figure 12 [26]. Epoxy did not satisfactorily penetrate cavities at both ends of the solenoid coil. Therefore, the top turn of the second layer was not adequately supported by adjacent layers. Thus, it behaves like a self-supported single turn; the stress enhancement due to screening current becomes remarkable, resulting in conductor fracture.

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Figure 13 shows the numerical results for layer wound epoxy-impregnated coil as shown in figure 10. In epoxy impregnated coil, the coil winding acts as a bulk; therefore, stress modification is much reduced as seen in figure 3; i.e. epoxy impregnation has beneficial effects in reducing stress modification and coil degradation [16]. However, as seen in figure 13, the stress enhancement due to screening current becomes remarkable at both ends of the layer-winding coil, as they are not supported by the adjacent layer's tape conductor. Based on the numerical simulation, the enhanced tensile stress at the conductor's top edge becomes as high as 1.3 GPa, sufficient for conductor fracture., Thus, a conductor fractures at a top turn of the 2nd layer as shown in figure 12. The simulation result is reasonable for experiment. The top turns of layer winding were isolated from adjacent layers and are not adequately supported by adjacent layers, even if the coil is impregnated with epoxy resin. As seen in figure 13(b), the tensile stress dramatically decreases if we fill the space at both ends of the coil winding with stainless steel tape.

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As a step towards developing a 1.3 GHz NMR magnet (30.55 T) [27], we developed a 30 T class ultra-high field (UHF) magnet comprising a REBCO inner coil, a Bi₂Sr₂Ca₂Cu₃O_x (Bi-2223) middle coil, and an LTS outer coil [28]; at the operating field of 30.5 T, the REBCO coil generates 9.3 T, the Bi-2223 coil is 4.0 T, and the LTS outer coil is 17.2 T. The stress modification effect for the 30 T class UHF LTS/Bi-2223/REBCO magnet is described here.

The REBCO conductor used for the REBCO inner coil is 4.03 mm in width and 0.097 mm in thickness. It is 17.6 mm in inner diameter, 67 mm in outer diameter, 40.1 mm in length; the number of turns is 9 (turns) × 180 (layers). A coil was wound with a winding tension of 4.9 N (12.5 MPa). We inserted an interlayer laminate sheet between each winding layer; the sheet comprises an 8 μm thick copper and 18 μm thick polyethylene terephthalate layer. A copper sheet vertically shorts the turns, and therefore this coil is a kind of no-insulation coil; we call this coil an intra-layer no-insulation (LNI) coil [29]. A 25 μm thick nickel alloy sheet overbanded the REBCO coil with a winding tension of 5 N (50 MPa); the over banding thickness is 2.1 mm. While charging the magnet, we measured a circumferential strain of the outer surface at the top of the over-banding.

After charging the outer LTS coil to 17.2 T, the current of the series-connected REBCO and Bi-2223 coil was gradually increased. In the first test, the magnet was charged to 30 T without quenches and discharged. The second test reached 31.4 T and was quenched. After the coil quench, we tested the magnet in liquid nitrogen, and it was confirmed that the quench did not damage the magnet.

Figure 14 shows the binder's hoop strain vs HTS coil current measured in the first test (figure 14(a)) and the second test (figure 14(b)). The strain shows a hysteresis, which demonstrates that the strain is due to the screening current.

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The numerical simulations of the stress for the 30 T LNI coil were performed. The 2D numerical structure model for a cross-section of layer winding is adopted, as shown in figure 15. We considered the detailed structure, such as the inserted interlayer laminate sheet and over-banding. Figure 16 shows the numerical results of the circumferential stress and strain distributions in cross-section at 30 T, increasing at the top and bottom of the coil because of the screening current. The numerical circumferential strain at the top of the over-banding is ∼0.25%, as seen in figure 16(b), 25% larger than the experimental result, ∼0.2%, seen in figure 14(b) Then the REBCO winding experiences the maximum circumferential strain of ∼0.7%, corresponding to the stress of ∼1.0 GPa. Figure 17 shows the numerical results of circumferential and radial stresses vs radius at REBCO layer in the uppermost turns; the red solid line shows the stress in the upper side, while the blue solid line is that in the lower side. As seen in figure 17(a), the circumferential stress at upper side is higher than that of lower side, as they are not sufficiently supported by the adjacent layer's polyimide sheet. Furthermore, the circumferential stress decreases in the outer turns by the effect of over-binding, as seen in figure 17(b).

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The conductor damage was not observed in the experiment. Therefore, the simulation gives an overestimate of the circumferential stress and strain compared with the experiment. We can assume that the electromagnetic force tilts the conductor, and the induced screening current reduces, resulting in a decrease in circumferential stress. The friction between tapes can be dealt as parameter for matching between experimental and numerical result. In particular, it is possible that the friction effect shows a significant impact in high field layer-wound magnet because of large electromagnetic force. The mechanisms of sliding motion and its effects at 4.2 K were studied in detail for several metal/insulator pairs in superconducting magnet windings models [30]. It reported that the friction coefficient was 0.2–0.3. However, we have not verified the friction effect in REBCO winding coil yet. The friction between tapes will be an issue to be addressed in the future.