1. Introduction
High-temperature-superconducting (HTS) magnet technology is crucial for the development of high-resolution NMR, next-generation particle accelerators and laboratory user magnets for scientific explorations [1]. REBa2Cu3O7−x (REBCO) coated conductors, in particular, are a promising candidate for applications in high-field scenarios [2], [3], [4]. Recent years have seen the design, construction and commission of several user magnets capable of generating center fields over 30 T [5], [6], [4], [7], [8], [9], [10], [11], [12], [13], as well as efforts towards commercialization [14].
Alongside the development of large-scale magnets, small test coils, with a shorter turnaround time and lower cost, can be a useful tool for the validation of key design concepts and provide valuable data for scientific research [15], [16], [17]. A prominent example using REBCO coated conductors is the no-insulation (NI) coil ’Little Big Coil’ (LBC) in [18], which generated a center field of 14.4 T in a 31.1 T background field, achieving a record field of 45.5 T. This study highlighted the favorable properties of REBCO coated conductors, including current carrying ability in high fields, mechanical strength, and thermal stability, and demonstrated its potentials in ultra-high-field applications. Meanwhile, posthumous examinations following the LBC experiments also drew growing concerns regarding the mechanical issues caused by screening currents [19], [20], [21].
As shown in Fig. 1, when energizing the solenoid insert placed in a background field provided by the outsert, the REBCO conductors are exposed to the self-generated and external magnet fields, and screening currents are subsequently induced due to the magnetization of superconductors. As most commercially available REBCO coated conductors nowadays share the feature of a flat and wide layer of superconductors, the persistent screening currents are allowed to flow over the cross-section with a large width-to-thickness aspect ratio [22]. The resultant highly non-uniform current distribution leads to a distortion of the magnetic field, where the screening-current-induced magnetic field (SCIF) contributes to the field hysteresis and temporal drift [22], [23], [24]. From the mechanical perspective, the distribution of current density is related to that of the Lorentz force. Studies have shown that local magnetic forces, considering the screening currents, can be proven excessive when exacerbated by a high background field [25], [26], [27], [28], [29], [30]. The screening-current-induced stresses/strains (SCIS) are commonly recognized as one of the major challenges for the development of high-field user magnets [4], [31], [32].
Fig. 1. Illustration of screening currents in a solenoid wound with REBCO coated conductors, and the enlarged view showing the current distribution and conductor deformation. |
In this study, we report the development and testing of a compact REBCO insert coil, focusing on the comparison of the screening currents in self-generated magnetic field and background field. Coil design, construction, and experimental setup are introduced in Section 2. The electromagnetic-mechanical models are described in Section 3. Section 4 summarizes the experimental results, which feature the stepped current sweep in standalone condition and the charging test in a background field. And Section 5 presents the analyses and discussions of coil behaviors in the self-field and a background field, including the screening-current-induced magnetic fields and stresses/strains. Lastly, the conclusions are summarized in Section 6.
2. Design, construction, and experimental setup
A compact design is required in order to maximize the center field within limited space. The coil dimensions were determined according to the specifications of a resistive user magnet. The outer diameter was limited to 34 mm by the bore size of the LHe dewar, and the inner diameter was 14 mm considering the minimal bending strain of the superconducting layer. The REBCO coated conductors were provided by SuperPower, with a nominal width of 4 mm and thickness of 100 μm. The coils were wound with a constant tension of 49 MPa without turn-to-turn insulation to maximize the engineering current density. The key parameters are summarized in Table 1.
Table 1. Parameters of the insert coil. |
| Parameter | Unit | Value |
|---|---|---|
| conductor width; thickness | [mm] | 4; 0.1 |
| inner diameter; outer diameter | [mm] | 14; 34 |
| number of single pancakes | 12 | |
| average turns per pancake | 100 | |
| total height | [mm] | 52 |
| total conductor length | [m] | 90 |
| magnetic coefficient at coil center | [mT/A] | 26.2 |
After winding, each double pancake, labeled DP1 to DP6, was tested individually in liquid nitrogen. Summary of coil performance in Fig. 2 showed good consistency. The critical currents are determined using a voltage criterion of 0.1 μV cm−1. On average, the coil critical current, power-law index, and inner bridge-type joint resistance are 40 A, 22, and 117 nΩ, respectively. The coils DP1 to DP6 were then assembled with polymer spacers for insulation, adding five extra outer joints between double pancakes. A small axial pressure was applied by hand through the screw nut. Preliminary test was carried out on the assembled coil in liquid nitrogen with a peak current of 20 A, showing an average joint resistance of 107 nΩ. This corresponds to an estimated resistivity of 77-95nΩcm2 depending on the locations of the joints, which met our expectations.
Fig. 2. Coil tests in liquid nitrogen at 77 K: (a) critical current, power-law index and joint resistance of each double pancake; (b) charging of the coil assembly coil up to 20 A. |
2.1. Self-field experiment setup in LHe
The insert coil was first tested in LHe without a background field. As shown in Fig. 3(a), two cryogenic Hall sensors (H1 and H2) were placed near the coil towards the axial direction. A specific charging sequence was defined to obtain the full hysteresis in each cycle. In Fig. 3(b), the charging and discharge current with reversed polarity reached peak values of 105 A, 250 A, and 350 A, sequentially. And the current ramping rates were 5 A/min, 10 A/min, and 10 A/min, respectively. The applied current was held for at least 90 s at intervals of 15 A, 25 A, or 50 A, depending on the peak current. This was sufficient for the bypass current to subside comparing to an average self-field time constant of 3.8 s.
Fig. 3. Self-field experimental setup: (a) positions of the Hall sensors H1 and H2, relative to the superconductor winding (not to scale); (b) profile of the applied current, where the polarity is reversed in turn, reaching peak currents of 105 A, 250 A, and 350 A. |
2.2. Experiment setup in a background field
The in-field charging experiment was carried out in a resistive user magnet at the High Magnetic Field Laboratory, Hefei Institutes of Physical Science, Chinese Academy of Sciences. A Hall sensor was placed at the center of the insert coil, and a Cernox temperature sensor was attached to the top of the coil near the copper current lead. Voltage taps were set up for each double pancake, as well as the total coil voltage excluding the current leads.
3. Electromagnetic-mechanical model
Research has shown that in a REBCO pancake coil, both magnetic fields and stresses can be affected by the screening currents [22], [26]. Measurements of center field hysteresis [30], [33] and hoop strain distribution [28], [30], [34] suggested potential interactions between conductor deformation and magnetic field, particularly in background field with a high axial-to-radial field ratio. Here, the coupled electromagnetic-mechanical model in [34] is adapted for the analysis of multiple coils.
The electromagnetic field is modeled by using the T-A formulation [35], [36], [37]. The model geometry is shown in Fig. 4(a). By symmetry over the middle plane, only the upper half of the coil geometry is built, which is labeled as pancake PA to PF. The superconducting layers are governed by current vector potential $T$, where, by applying the thin-strip approximation[35],
$-\frac{\partial}{\partial z}\left(E_{\phi}\left(J_{\phi}\right)\right)=-\frac{\partial B_{r}}{\partial t}, J_{\phi}=\frac{\partial T}{\partial z}$
Here, the power-law with an index of 31 is used in the nonlinear $E-J$ relationship of the superconductor at 4.2 K [38], where $E_{\phi}$ and $J_{\phi}$ are the azimuthal electric field and current density, respectively. The magnetic field and angular dependency of critical currents is described by the fitted equation proposed by Hilton et al. [39]. The air domain is solved by the A formulation. The homogeneity of background field intensity within the space occupied by the insert is estimated to be about 1% and considered uniform in the simulations. In view of the low ramping rate (detailed in Section 2.1), the radial current is estimated to be below 1 A. The interval between current steps were more than 10 times the characteristic time constant. The effects of NI transient behaviors on screening currents are therefore considered negligible and not included in the model.
Fig. 4. (a) Geometry of the electromagnetic model, where the single pancakes are labeled PA to PF from top to middle. (b) Boundary conditions in the mechanical analysis, where v is the axial displacement. Omitting the pancake-to-spacer contacts, constraints on the axial displacement are defined in each pancake and imposed on the lower right corner of the conductor. |
Similarly, the upper half composed of 6 single pancakes is built in the mechanical analysis (Fig. 4(b)). Each turn in the pancake coil is modeled individually, where a penalty contact is defined between neighboring turns. The layered structure of the coated conductor is simplified as transversely isotropic materials [31], with a longitudinal modulus of 125 GPa, a transverse modulus of 72 GPa, and a Poisson's ratio of 0.3 [40].
Lorentz force extracted from the magnetic field is applied to the coil. Due to conductor deformation, the local surface tangent deviates from the axial direction by a small angle [28], [30], [34], which is approximated as $\beta \approx \frac{\partial u}{\partial z}$, where u is the radial displacement. The perpendicular and parallel field components with respect to the conductor surface also change accordingly, as
$\left[\begin{array}{l} B_{\perp} \\ B_{\|} \end{array}\right]=\left[\begin{array}{cc} \cos \beta & -\sin \beta \\ \sin \beta & \cos \beta \end{array}\right]\left[\begin{array}{l} B_{r} \\ B_{z} \end{array}\right],$
where $B_{r}$ and $B_z$ are the radial and axial fields, and $B_{\perp}$ and $B_{||}$ are the perpendicular and parallel fields with respect to the conductor surface, respectively. In the coupled model, this interaction between the magnetic field and conductor displacement is taken into account by replacing the radial field $B_{r}$ in Eq. (1) with the perpendicular field $B_{\perp}$. The field angle in critical current density is also revised accordingly. In contrast, it is assumed in the sequential model that the coil deformation does not affect the electromagnetic behaviors. It should be noted that the tensile strain/stress dependency of critical currents [30], [34], [21] is not considered in this study, as the magnetic stresses are not expected to exceed the limit and cause sustained conductor damages.
Additionally, the following assumptions are applied for the analysis of multiple coils. In practice, the neighboring pancakes were separated by a thin sheet of polymer spacer for insulation. Although the axial spacer-to-pancake contacts can be included in models [33], [21], in our simulations, this sheet is omitted considering the relatively low axial pre-load and computational cost. Instead, constraints on the axial displacement are defined for each individual pancake, which are imposed on the lower right corner of the conductor, as shown in Fig. 4(b). Similar boundary conditions restricting the axial displacements are also set at the uppermost and lowermost boundaries of the bobbin. Given the more significant role of magnetic stress in dry-wound coils [41], [42] and the scope of this study centered on screening current related issues, winding stress and thermal contraction are not considered in the discussions.
4. Results
4.1. Self-field Experiment
Fig. 5 shows the measured field in comparison to the nominal field assuming the current flows uniformly across the conductor. During the charging parts of the current sweep cycles, the measured field obtained by Hall sensor H1 is stronger than the nominal field, while the total measured field at H2 is weaker. Hysterical behaviors are found in both. Particularly, at peak currents, the average field deviation relative to the nominal field at H1 reached 26%, 18%, and 13%, respectively, with -72%, -51%, and -36% at H2. The remnant fields after discharging from a positive peak current were −10 mT, −76 mT, and -173 mT at H1, corresponding to +3 mT, +21 mT, and +45 mT at H2. At the peak current of 350 A, the coil is expected to generate a nominal center field of 9.17 A.
Fig. 5. Total magnetic fields measured with Hall sensors H1 (left) and H2 (right). The arrows show the direction of the initial charging sequence, and the solid lines are the nominal field. The total magnetic field deviates from the nominal field with typical hysteresis behaviors. |
4.2. Charging behaviors in a background field
The profiles of the applied current, center field, total coil voltage, and temperature are shown in Fig. 6. The experimental sequence is described as follows.
Fig. 6. Applied current, center field, coil voltage, and temperature during the experiment in the background field. The total center field reached 32.58 T prior to quench, with 4.17 T contributed by the REBCO insert. |
1. The background field was raised and held at 23.15 T. Experiments showed that further increase of the background field led to an increase in temperature, which is believed to be related to the entrapment of helium bubbles and the Joule heat generated by induced currents in the NI coil [43]. Analysis of the temperature instability during this experiment is detailed in a separate paper [44].
2. The insert coil was energized at a ramping rate of 6 A/min, with intervals at 50 A, 100 A, and 150 A. At the peak current of 170 A, the total center field reached 27.32 T, with 4.17 T contributed by the insert. The temperature remained stable during this process.
3. The background field was then ramped up rapidly at 2.7T/min, with the coil voltage reaching 26 mV. The temperature rise was slow at first, followed by a sharp increase starting from a total center field of 29.22 T. At around 32.58 T, a quench event occurred, accompanied by a sudden disconnect from the power supply and a drop of the center field. It was later confirmed that this event was initiated by a burnout near the copper lead without causing serious damages to the coil.
5. Discussions
5.1. Screening-current-induced magnetic field
5.1.1. Self-field hysteresis
The screening current induced magnetic field $B_{sc}$ is defined by subtracting the nominal field generated by a uniformly distributed current $B_0$ from the total magnetic fields $B_{total}$ [22], which is
$\boldsymbol{B}_{\mathrm{sc}}=\boldsymbol{B}_{\text {total }}-\boldsymbol{B}_{0}$
where the total magnetic field $B_{total}$ corresponds to the measured field $B_{meas}$ or the simulated $B_{sim}$. For the sake of simplicity, as both Hall sensors were placed axially, the subscript for field direction is left out in the following discussions.
Fig. 7 shows the hysteresis of the screening-current-induced magnetic field, corresponding to the measured field in Fig. 5. The discrepancies between simulations and measurements can be considered reasonable, which is partially attributed to the field dependency of critical currents and the positioning of the Hall sensors. Very little difference is found between the field profiles obtained from the sequential model and those from the coupled model. This suggests that both models can provide satisfactory predictions regarding the evaluation of the screening-current-induced magnetic field in the self-field condition.
Fig. 7. Self-field screening-current-induced magnetic fields obtained by Hall sensors H1 (left) and H2 (right). Results from the coupled model and the sequential model are represented by the solid lines and the dashed lines, respectively. |
The current distributions with an applied current of 350 A are compared in Fig. 8. The similarity between the results from the sequential model and the coupled model mirrors that found in the magnetic field profiles. Even in the line plot Fig. 8(c), extracted from the 10th turn in the top and middle pancake, the current profiles from the coupled model are only marginally smoother near the peaks. In this case, the conductor deformation plays an insignificant role in the electromagnetic behaviors.
Fig. 8. Current distributions with an applied current of 350 A, obtained from (a) the sequential model and (b) the coupled model. (c) A close-up comparison of the current density profiles of the 10th turns in the top pancake and the middle pancake. |
Fig. 9 is the predicted screening current field hysteresis at the magnet center following the full charging sequence. According to the coupled model, at the peak currents (105 A, 250 A, and 350 A), the center field intensity is estimated to be lowered by 0.30 T, 0.54 T, and 0.60 T, respectively. These account for 10.9%, 8.3%, and 6.6% of the nominal fields, respectively. The corresponding sequential model yields very similar results. Although the field reduction relative to the nominal field can be mitigated by further increase of the peak current, it can contribute to the demand for a higher operating current. For instance, taking the nominal field at 350 A as the target field, an additional 23 A would be required to compensate for the center field loss of 0.60 T due to the screening currents.
Fig. 9. Calculated screening-current-induced magnetic fields at the coil center. Using the sequential model and the coupled model, the total field intensity is estimated to decrease by 0.60 T and 0.62 T, respectively, at the peak current of 350 A. |
5.1.2. Field deviation in a background field
Following step 2 in Section 4.2, the applied current in the insert coil increased to 170 A in a background field of 23.15 T. Excluding the constant background field, the difference between the nominal field and the total field generated by the insert is shown in Fig. 10. In view of the limited number of current steps (intervals per 50 A), the measured field during the full charging sequence is displayed, where the screening current field is represented by the circles connected by the dashed line. During ramping, the difference between total magnetic field and nominal field encompasses both the charging delay of no-insulation coils and the field deviation due to screening currents. During the intervals, the bypass current subsided fully, showing only the effect of screening currents. The screening current field lowered the center field intensity by about 0.28 T at the peak current of 170 A, accounting for 6.3% of the nominal field of the insert coil.
Fig. 10. Measured and calculated screening-current-induced magnetic field at the coil center in a background field of 23.15 T. The enlarged view shows the transient behaviors of the magnetic field corresponding to the relaxation of the bypass current. |
Unlike the self-field scenario in the previous section, the magnitude of screening-current-induced magnetic field predicted by the coupled model is lower than that from the sequential model. Fig. 11 compares the current distributions at the peak current 170 A. Biased by the background field primarily aligned in the axial direction, the total axial field is considerably higher than the radial field, which is mostly contributed by the insert. When the field angle becomes sufficiently small and comparable to the surface tangent relative to z-axis due to conductor deformation, the field component perpendicular to the conductor surface differs from the radial field. This leads to the contrast in the current distributions, and resultantly the magnetic field profiles. Particularly, for the top pancake with a higher radial field, the current distribution is characterized by an effective delay of the field penetration from the edges and a smoother transition in the middle. This effect is also stronger near the outer part of the winding pack with weaker structural supports. Next to the middle plane, a lower radial field compensated by conductor deformation lowers the current density peaks at the edges, leading to a more uniform distribution overall.
Fig. 11. Current distributions with an applied current of 170 A in a background field, calculated by (a) the sequential model and (b) the coupled model. (c) A close-up comparison of the current density profiles of the 90th turns in the top pancake and the middle pancake. |
Compared to model estimations, the measured screening current field lies between the results from the coupled model and the sequential model, albeit closer to the former. However, determining the precise sources of this discrepancy can be tricky. From the experimental point of view, with a background field of 23.15 T, it is estimated that the screening current field at the peak current 170 A only makes up for about 1% of the total center field. Disturbances in the background field magnet and linearity of the Hall probe can both have a strong influence on the measurements. From the modeling perspective, one conceivable cause may be that the stiffness of the coil structure can be stronger than the current geometrical assumption where the winding turns are simplified as frictionless concentric hoops. This inhibits the conductor deformation, thus lessening its effect on modification of the perpendicular field component. Within a pancake, the initial stress formed by winding tension, thermal contraction [41], turn-to-turn friction and coil structures like the soldered joints [34] can strengthen the coil structurally. Between double pancakes, the pancake-to-spacer friction with axial forces can also suppress conductor deformation near the edges [33], [21].
5.2. Screening-current-induced strains
5.2.1. Self-field at peak current 350 A
The distributions of hoop strains with a peak applied current of 350 A are demonstrated in Fig. 12. Not unlike the field and current distributions, the hoop strains from the coupled model bear a resemblance to those from the sequential model. Even though the top pancake PA is subjected to a high radial field and strong screening currents, the axial field component of the self-generated field, which contributes to the Lorentz force, is lower. The middle pancake PF, in contrast, experiences a higher axial field but a weaker radial field. Resultantly, the maximum hoop strain of 0.15% is located in pancake PD, the fourth pancake from the top, whereas the minimum −0.04% is found in the top two pancakes. Fig. 12(c) compares the maximum and minimum estimated hoop strains in each turn in pancake PA and PD. No significant difference is found between the coupled model and sequential model. Commonly, the maximum hoop stain decreases from the inner part of the coil to the outer.
Fig. 12. Hoop strain distributions with the peak current of 350 A, calculated by (a) the sequential model and (b) the coupled model. (c) Comparison of the ranges of hoop strains in pancake PA and PD. |
5.2.2. In-field condition at 170 A
Fig. 13 shows the hoop strains with an applied current of 170 A in a background field of 23.15 T. As the total axial field is dominated by the background field, the distribution of strains is largely determined by the screening currents. The maximum hoop strain estimated using the sequential model is up to 0.77%, located at the outermost turn of the third pancake from the top. Even when considering a bending strain of −0.15%, it is approaching the tensile limit of most commercially available coated conductors. However, no visible damages to the pancakes were found after the experiment. The coupled model yields a maximum hoop strain of 0.47% at the middle of the top pancake.
Fig. 13. Hoop strain distributions with the peak current of 170 A in a 23.15-T background field, calculated by (a) the sequential model and (b) the coupled model. (c) Comparison of the ranges of hoop strains in pancake PA and PF. |
The maximum and minimum calculated hoop strains in each turn are extracted and shown in Fig. 13(c). Specifically, with a stronger radial field at the top pancake, the hoop strain spans from compression to expansion. The ranges of hoop strains from both models are similar in the inner part of the winding, which start to diverge from approximately turn 60 outwards. Due to a lack of structural support for the outer part of the winding pack, the effect of conductor deformation to the perpendicular field component in the coupled model is more prominent. Consequently, the estimated maximum strains gradually deviate from those in the sequential model. The minimum hoop strains across a substantial part of the winding are predicted to lie between −0.1% to −0.2% in compression. This may suggest an elevated risk of structural instability such as buckling damages [29]. In contrast, the conductors in the middle pancake are subjected to azimuthal tension universally. It is also worth noticing that the small ranges from the coupled model indicate a rather uniform distribution of strains in the middle pancakes.
5.3. Field contribution by insert and outsert
By applying the coupled model, we can further discuss the role of the background field on the deformation of the insert. Within the background field range of 12 T to 30 T, the coil critical current is estimated to be around 417 A to 470 A, which corresponds to nominal center fields of 10.9 T to 12.3 T and varies by the background field. Fig. 14 summarizes the maximum hoop strains found in the coils, which are plotted against the center field contributed by the insert. Also shown is the percentage of conductors in the each pancake winding pack subjected to hoop strains over 0.5%. The simulation was terminated as the applied current reaches the estimated coil critical current. Take the background field 18 T as an example. Following the charging sequence, the maximum hoop strain firstly increases almost linearly, peaks at around 230 A (field contribution of 6 T), and then shifts from top pancake towards the middle. This corresponds to the pattern of current distribution. Initially, screening current is concentrated near conductor edges. This process is prolonged since the perpendicular field is partially compensated by deformation. As the radial field further increases with applied current in the insert, it eventually penetrates towards the conductor center. Although the location of the maximum hoop strain changes, the peaks only increase marginally. Meanwhile, due to the nonuniformity in current and stress distributions, the coil deformation may not be fully represented by the maximum strain. The percentage of conductor with $\varepsilon_{\text {hoop }}>0.5 \%$ shows that for the top three pancakes, even though the maximum hoop strain hits 0.6%, it only affects less than 2% of the respective winding pack.
Fig. 14. Maximum hoop strains when inserted in background fields from 12 T to 30 T and percentage of conductor in the each pancake with hoop strains over 0.5%. The plots are aligned by the center field contribution from the insert. |
Under different background fields, the linear sections almost overlap when aligned by the center field contribution from the insert (shown in the enlarged view in Fig. 14). The conductor deformation corresponding to the maximum hoop strain remains dominated by the tilting pattern, which is only slightly higher in a higher background field. In contrast, as the applied current increases, the plateau of strain is closely related to the background field. In this regime, the current distribution is to a large degree established by the further increase of radial field and the penetration of screening currents, which bears resemblance across different background fields. The maximum current density is determined by the local critical current density [27], [45]. Consequentially, the background field contributes considerably to the axial field, as well as the Lorentz force.
Fig. 15 shows the contour plot of maximum hoop strains overlaid with total center fields denoted by the dashed lines, with background field as the x-axis and applied current in the insert as the y-axis. The lower half of the plot corresponds to the linear section in Fig. 14. Regardless of the background field, the strain response of the insert when energized is expected to follow a similar trajectory. This indicates that, for the purpose of maximizing the total center field, one potential proposal could be to use a higher background field and limit the applied current in the insert within the linear regime. Considering the upper half of Fig. 15, the strain plateau is dominated by the axial field from the outsert. This suggests another design direction by taking advantage of the plateau, where the mechanical overstress may be controlled by limiting the background field and pushing the transport current in the insert towards the field dependent coil critical current instead.
Fig. 15. Contour plot of the maximum hoop strain by background field provided by the outsert and applied current in the insert, with dashed lines denoting the total center field. |
6. Conclusions
This paper presented a study on the behaviors of the screening-current-induced magnetic fields and strains of a compact REBCO coil. Experiments were carried out in the self-generated magnetic field and a background field, respectively. The coupled electromagnetic-mechanical model, which takes into account the perpendicular field modifications due to conductor deformation, is adapted for multiple coils and compared against the sequential model.
In the self-field condition, the coil was subjected to current sweeps with repeatedly reversed polarity and increasing peak currents. A strong hysteresis can be observed in the magnetic fields. With a maximum applied current of 350 A, the nominal center field of 9.17 T is estimated to decrease by 0.60 T due to screening currents. The coupled model and the sequential model yield similar results, both in good agreement with the experiments. The strain distribution is largely affected by the non-uniform current distribution due to screening currents. A maximum hoop strain of 0.15% is found in the fourth pancake from the top.
With a background field of 23.15 T, the applied current in the insert coil was ramped up to 170 A. The measured center field contributed by the insert was 0.28 T lower than the nominal field. As the axial field is dominated by a high background field, the electromagnetic-mechanical coupling has a stronger influence on the current and strain distributions. The screening-current-induced magnetic field at the coil center lies between the predictions from the sequential model and the coupled model, albeit closer to the latter. According to the coupled model, the maximum hoop strain is estimated to be 0.47%, located in the top pancake. Simulations also suggested potential design strategies to maximize the total center field by balancing the field contribution from the insert and outsert. While further increase of the background field led to a rapid temperature rise, a total center field of 32.58 T was achieved prior to quench.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
This work was supported by the National MCF Energy R&D Program under Grant No. 2022YFE03150103, the National Natural Science Foundation of China (NSFC) under Grant No. 52277026, and the BK21 FOUR program of the Education and Research Program for Future ICT Pioneers, Seoul National University in 2023.
