HTS conductor coil by in-situ winding technology for large-scale high-field magnet

High temperature superconducting (HTS) conductors have become important candidates to be used in large-scale high-field magnets, owing to its high critical current density as well as good mechanical properties. At present, there are various forms of HTS conductors proposed. In this work, we reported the fabrication of the REBCO HTS coil using in-situ winding technology. The six-layer coil with a diameter of 410 mm achieved a total current of 2562 A, and generated a central magnetic field of 7.8 mT at 77 K. The stress, deformation, and defect caused during conventional winding procedure could be significantly decreased using in-situ winding technology, indicating it has great potential for the large-scale high-field magnets in next-generation fusion reactors.


Introduction
High temperature superconducting (HTS) tapes have great potential to make high field magnets, power cables, and various superconducting power devices.In order to maximize current-carrying capacity, allow sufficient cooling, and Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
There have been many studies on CORC conductors, such as the current-carrying abilities [22,23], experiments on the mechanical properties of straight CORC conductors [24][25][26], and mechanical simulations [27,28].There are also studies on the AC loss of straight CORC conductors [29,30] and AC loss analysis of circular CORC coils [31].
In the design of HTS conductors for fusion reactors, however, the problem of stress concentration caused by the winding method and manufacturing process is always an urgent problem.When making HTS conductors, the winding stress will lead to a series of problems, such as the attenuation of critical current, the local quench of the coil, and the increase of loss, which will have a significant adverse effect on the device [32][33][34][35].
Conventional winding method for CORC coils is to wrap the tape around the straight skeleton first, and then bend the straight conductor into a coil.In this work, an HTS coil has been built by CORC type conductors using a novel in-situ winding technology.In-situ winding technique refers to the technique of winding at the original position, and the position of the skeleton and the tapes will not change after winding.The details of the cable design are provided.The stress, critical current, magnetic field distribution, and AC losses of the coil has been studied.The proposed HTS conductor coil using the in-situ winding technology has good current carrying capacity and great potentials for making the high-performance magnets in next-generation fusion reactors.

Materials
REBCO tapes with SS304 lamination were used in this work, which were produced by Shanghai Superconductor Technology Co., Ltd.The width was 6 mm, the thickness was 0.23 mm, and I c at 77 K in self-field was 165 A with inhomogeneity less than 5%.A copper tube with outer diameter d = 12 mm, and pipe thickness t = 1 mm was used as the skeleton after bending to the circular shape with a diameter D = 410 mm, as shown in figure 1.The size of the coil skeleton is determined based on the size of the magnet we designed, and the copper tube radius is a important parameter that considers both the critical current density and heat dissipation efficiency while ensuring no critical current attenuation.

In-situ winding technology
In-situ winding technology refers to the technique of winding at the initial position.The coils wound using this technique should follow the method of first bending the skeleton and then winding the tape/composite tape to ensure that the tape/composite tape will not have displacement, stretching and compression during the bending process.Taking the tripletapes densely wound coils made by in-situ winding method in this paper as an example, the winding process needs some attention: Before winding, three tapes were combined and insulated to a unit by Kapton tapes.Then, a combined tape (figure 2(a)) was densely wound on the skeleton as the first layer, which is   shown in figure 2(b).In this process, the inner side of the skeleton circle needs to be fully wrapped with tapes, with no gap.Then, another combined tape was wound onto the first layer with the winding direction cross to the first layer, as can be seen in figure 2(c).The CORC coil after completing winding is shown in figure 3(b).Angle θ is defined as the angle between the length direction of the tape and the direction normal to the circle.Pitch P is defined as the chord length of a turn of arc on the inside of the ring [31].The details of pitch and angle are shown in table 1.A recent report showed that for CORC conductors under a magnetic field (6 T to 16 T), the larger the gap in the cross-section of the conductor, the greater the maximum stress it experiences in the magnetic field, which poses a risk of critical current attenuation to the conductor [36].A densely wound coil can minimize the gap in the cross-section of the CORC and improve the stability of the conductor.For the coils wound by in-situ densely winding method, if the major radius of skeleton and tube radius are determined, the winding angle of the same width tape has already been determined.Previous researches [27,37,38] showed that, under the same copper tube bending radius, the smaller the winding angle is, the less damage the tape will suffer.Therefore, for the coil in this work, the winding angle of the in-situ densely wound coil and the radius of the skeleton correspond to the critical bending radius of conductor (without extrusion).

Multi-tapes densely winding structure.
Previous studies have proved that triple tapes densely wound are one of the most efficient ways in terms of the CML (central magnetic field/transport AC loss) parameter [31].Therefore, we chose the triple tapes densely wound structure and used the in-situ winding method.

Terminal and joint.
In this work, the layers of the coil are connected in series by crimping them in a terminal box.The terminal box refers to the container for crimping the layers of the coil.The terminal box needs good thermal conductivity, and we use copper as the material of the terminal box.The terminal box used the superconducting tape bridge method.Indium flake was between tapes and tapes.The effect of indium flakes was to protect the tape from the uneven stress during the bonding process.When the bridge joint was finished, we pressed the copper block on the joint to ensure the stability of the joint, shown in figure 4(b).The connections are shown in figure 4(a).The equivalent total current in the coil I coil is equal to the output current of the current source × the number of layers.

Experiment set-up
All the following experiments were using a liquid nitrogen environment.The terminal box was connected to a DC power supply (AMETEK SGX1200), and the voltage taps were connected to a KEITHLEY 2182 A nanovoltmeter.A CH1700 Hall probe was used to measure the magnetic field at each position inside the coil.The magnetic field scan plane is 4 mm away from the bottom of the coil, and the spatial magnetic field scan resolution is 2 mm.After the spatial magnetic field scan is completed, the Hall probe is fixed at the center of the coil to measure the central magnetic field size under different current.To measure the distribution and redistribution of currents, three pairs of voltage taps attached on three REBCO tapes of the outermost layer in the coil were contacted to a multichannel acquisition system consisting of the signals above (nanovoltmeter and a Keysight 34 972A).

AC losses of multi-layers CORC coil
The AC losses of the coil have been studied.We took the transport AC losses as examples.We have calculated the transport AC losses with different layer numbers and different winding structures, using the three-dimensional T-A formulation.The model sets the original critical current of each tape to 165 A, and the critical current was controlled by the J c (B) equation according to the attenuation relationship of the magnetic field.The geometric parameters of the coil were set according to the actual winding parameters of the coil.The J c (B) equation used in the coil model is: In the three-dimensional model, the parallel magnetic field and the perpendicular magnetic field in the J c (B) equation can be given by the following equations: where α corresponds to the rotation angle of the whole coil about the central axis, and a section through the calculation point was made at this angle.At this section, the rotation angle of the calculation point is β with the center of the circular tube as the origin.

Stress analysis
We performed a strain simulation on the commonly used prewound and post-bent winding method of CORC conductor coils, considering the winding parameters.The simulation consists of two stages.In the first stage, testing constraints were applied between the tape and the outer surface of the copper tube, with a friction coefficient of 0.2 between the tape and the copper tube.The load was applied to the tape based on the winding angle, and the copper tube was rotated to wind the tape onto it.In this paper, the force load applied to the tape material during winding was 50 N and the winding angle is 28 degrees.In the second stage, constraints were applied at both ends of the copper tube to bend it.In this model, the stress and strain distributions in the first phase would be taken as the initial conditions for the stress and strain in the second stage, and the settings of boundary conditions of the model can be referred to [27].It should be noted that the model we used was a simplified multi-layer structure of the tape, neglecting the buffer layer and silver layer, while the winding skeleton parameters are from the actual copper material.The reason why the silver layer and buffer layer were ignored was that they were both thin and have little effect on the overall mechanical performance of the tape.However, for the superconducting layer, although it was also very thin, it was the main layer for current.Therefore, this needed to be considered.

Mechanical simulation
In this work, we analyzed the strain of the straight CORC (figure 5(a)) and calculated the strain distribution after bending (figure 5(b)).The strain in the compressed region along the skeleton inner diameter was smaller than that in the stretched region along the skeleton outer diameter.The end part in figure 5(b) corresponds to the tape tying and copper tube loading part, which had end effects.Therefore, the strain distribution of the tape should be observed from the middle section.
It could be concluded that after bending, the strain in the compressed region of the tape was small, but in the stretched region, the strain of the tape has increased by 143 times compared to the central region during the winding process.In-situ winding technology could avoid the rapid increase of stress in CORC conductor during bending, thus avoiding the critical current decline of the tape.Further research is needed on the strain analysis in the in-situ winding process.

Critical current and magnetic field test
The critical current was determined by the electric field criterion of 1 µV cm −1 .As our coil was insulated between layers and the joint box is connected in series, the transport current was unevenly distributed inside the combined tape.We took the channel that reaches the critical voltage criterion last among the three channels as the result.We set up voltage leads on one side of the circle which were close to the terminal box.
There was no bridging joint between the voltage leads to avoid the resistance of the joint.The critical current is 427 A. As shown in figure 6, corresponding to equivalent total current We measured the critical current of single-layer circular CORC coils with the same parameters to eliminate the influence of critical current attenuation during winding process.The critical current measured at 77 K under self-field is 483 A, which was consistent with the initial value.Therefore, in-situ winding method would not cause the degradation of the critical current of the tape.
We measured the magnetic field at the center of the CORC coil under different currents, and the results are shown in figure 7. The magnetic field generated by the current element in space can be described by the Biot-Savart law: where Idl represents the current element, r represents the length from the current element to any point in space,⃗ r represents the vector from the current element to any point in space, and µ 0 is the vacuum permeability.The central magnetic field is within the following range: where R represents the large radius of the CORC coil, r 0 represents the radius of the copper tube, and I represents the total current of the coil.Since the radius R of the circle is much greater than the radius of the cross-section of the skeleton, the actual distance r between the current element and the center of the circle is equivalent to the radius R of the circle.In this case, the radius of the coil R is 205 mm and the radius of the copper tube r 0 is 6 mm.Taking the innermost magnet of the central solenoid (CS) coil of the China fusion engineering test reactor (CFETR) [39, 40] as an example, its R is 750 mm and r 0 is 32.6 mm.At this scale, we can assume that: Therefore, where B is the magnetic field generated by the circular current at the center, I coil is the equivalent total current in the coil, R is the radius of the circle, and µ 0 is the vacuum permeability.The magnitude of the central magnetic field is calculated using this equation as shown in figure 7. The measured results are almost consistent with the calculated magnetic field, indicating that the winding method and equivalent total current calculation method in this work are accurate and the interlayer insulation of the coil is not damaged.Moreover, the non-uniformity of the current distribution in the conductor can be ignored.Magnetic fields at different positions in the coil were measured, shown in figure 8.
In order to obtain the influence of magnetic field on the critical current of the coil, the critical current under the self-field of the tape was first measured, and then the vertical and parallel background magnetic fields were applied to the tape, and the corresponding critical current was measured.The experimental results are shown in figure 9.
The critical current under the self-field of a single tape was 165 A. After calculation, the magnetic field in the innermost layer was 75.5 mT, and the magnetic field direction was parallel to the tape.According to the data in figure 9, the innermost critical current decayed to 88.7% of the tape's self-field critical current, 439 A, which was close to the measurement.

AC losses calculation
Simulation of the AC losses of single-tape densely wound, double-tapes densely wound, and triple-tapes densely wound with two-layers, four-layers, and six-layers round coils using T-A equation is performed.The calculation results of transport losses are shown in figure 10.Compared to the coils with the same number of layers but different angles, the greater the angle, the greater the transport loss.This is due to the increase of the total current resulting in the increase of the magnetic field on the surface of the tape, and eventually leading to the increase of the transport loss.

Estimation of critical current and magnetic field at 4.2 K
The feasibility was verified at 77 K, and then an estimate was made to determine the feasibility of the CORC coil as a CS magnet for fusion magnet at 4.2 K.According to the data given in figure 11, the self-field critical current of the tape was approximately 1980 A under 4.2 K.The internal magnetic field of the copper tube was approximately 0.9 T obtained by finite element simulation of the simple coil current model.The magnetic field inside the copper tube is parallel to the surface direction of the tapes.The parallel magnetic field could not greatly decay the critical current at 4.2 K [41].The central magnetic field was calculated by equation ( 7), and the central magnetic field was approximately 0.11 T. Estimations showed that the total critical current of the six-layer CORC conductor at 4.2 K was 35.6 kA and the single coil at 4.2 K could generate a central magnetic field of approximately 0.11 T. It can be noted that, for fusion magnets, the maximum magnetic field design of different coils is completely different, and the influence of external magnetic field on the critical current of the coil should be considered.The design of the CS coil in CFETR has a maximum magnetic field of 12 T, and the critical current of the six-layer coil will be 7.13 kA at the maximum field position.This paper only studies the magnetic field generated by a single six-layers coil.If the winding method was extended to 20 layers, and with three sets of 460 turns of coils designed by CFETR [39,40], the strong magnetic field required for next generation of fusion reactor could potentially be obtained.

In-situ winding technology
Straight conductors would generate stress after bending, and the electromagnetic force caused by current passing through would amplify this stress, causing irreversible damage to the coil.In-situ winding technology could avoid the stress by bending [28].The critical current attenuation around the curved conductor was small.For large coils in magnets, the winding technology can improve the performance of coils and reduce the risk of tripping caused by local stresses.The closewound coil can improve the utilization of space and integrate greater current density in the limited space.By connecting multiple tapes in parallel, the winding angle can be adjusted to increase the component of current along the skeleton axis, thus increasing the central magnetic field.Moreover, the closewound tapes support each other, which can offset the stress along the radial direction of the skeleton.The combination of three tapes in parallel can increase the contact between the tapes, and every bad point generated by every tape can redistribute the current in the three tapes, thus improving the stability of the conductor.
The coils studied in this paper were wound manually, and the winding tension was uncontrollable.In the future, an industrial winding machine can be designed to wind larger coils with more controlled winding tension.

Gap
Due to the influence of the skeleton curvature, the diameter of the inner and outer walls was inconsistent, so that there were some gaps in the outer wall of the coil, shown in figure 12.The maximum gap distance d can be represented as, where the radius of the copper tube is r, the outer radius of the frame is R, and the width of the tape is w.Equation ( 8) indicates that the larger the frame of the coil is, the smaller the gap will be.Therefore, the impact of gap will be smaller for large magnets.Based on the equation above, the larger that R is, the smaller d is.Therefore, for large magnets, the effect of the gap of the magnet with a larger radius will be negligible.From this perspective, the in-situ winding technology is suitable for large magnets.
The outermost gap distance obtained by the parameters in this article entering the formula was 0.75 mm, and the measurement result was 0.76 mm.This gap was inevitable in the bending and dense winding.In a strong electromagnetic field, these gaps could cause the movement of tapes, thus reducing the stability of the magnet.In the future, we will consider to use a filling and curing method to reinforce the mechanical structure of the coil.
Recently, some scholars have proposed a non-dense way to wind CORC conductors, so the CORC conductors wound in this way can make the tapes between different turns without contacting each other when bent into the coil, to avoid damage caused by partial bending stress [27].However, for the multi-layer coils wound in the non-dense way, due to the gaps in the middle, the overall strength of the coils will be weaker than that of the dense coils.When in the presence of strong magnetic fields, the electromagnetic force generated by the coils will cause irreversible damage to the nondense conductors.The use of dense coils can improve the utilization of space so that more current can be integrated into a smaller space to further obtain a higher central magnetic field.

Series connection joint
This kind of joint allowed us to obtain a large total current using a laboratory-scale current source, which could be used as the principal verification method for large-scale conductors.

Critical current attenuation
All CORC winding modes will generate a larger magnetic field inside the copper tube, and the direction of the magnetic field is parallel to the tapes.It can be seen from the 'magnetic field vs critical current density' curve that the magnetic field would cause a significant attenuation of the critical current, making the critical current smaller than the critical current of the three tapes in parallel.Compared with the critical current of three side-by-side tapes, the critical current decreased by 13.74% due to this winding mode.This was the phenomenon of critical current attenuation generated by its self-field, which was closely related to the geometrical structure of helical conductor.However, the issue of critical current attenuation under strong magnetic field would still need more experiments to verify.

Distribution/redistribution of current
In the structure with three tapes side by side, the current distribution in the CORC coil depended on the resistance of the joints [15,42].As the current increased, the feedback voltage of the three channels did not increase simultaneously, as shown in figure 13.The current was not evenly distributed in the three tapes.However, as the current continued to increase, the rise of the current in the highest current tape slowed down and the current in the remaining two tapes continued to rise due to the increase in the resistivity of the tape with the most current.Therefore, the current in each tape was redistributed near the critical current so that the current in each tape tended to be saturated.In multilayer joint design, the problem of uneven current distribution could be improved using step design [43,44].In this study, the insulation of the tapes was used to ensure that the current of each layer was equal.

AC losses
The round coil wound by the in-situ winding method can avoid the slight damage caused by the strain of the tape material during the bending process, even if this damage does not appear as a critical current attenuation under certain parameters.Under the periodic electromagnetic environment, it is subjected to periodic Lorentz force, which causes the strain to be concentrated and distributed, resulting in an irreversible critical current attenuation.Local hot spots at the damage location will increase the AC loss of the coil.

Conclusions
In this work, a six-layer CORC coil has been fabricated using an in-situ winding technology.The critical current of each layer was 427 A at 77 K.The critical current decay of the conductor was 13.74%.The stress distribution on the tapes generated by the bending-winding process was analyzed.The proposed in-situ winding method can avoid the initial stress generated by the conventional winding process, thus improving the stability of the coil under a strong magnetic field.Subsequently, AC losses of coils wound with different structures have been studied.The use of a series crimping joint enabled the conductor to use a less powerful current source to generate a large equivalent current (equivalent overall critical current about 2562 A).We measured the central magnetic field and the distribution of the magnetic field in space.The measurement showed that the magnetic field is consistent with the calculation of the equivalent ring current.In the future, more experiments and theoretical analyses will be carried out to further verified the feasibility of the method.Overall, the coils wound by in-situ winding technology can avoid the stress generated when CORC conductor is forced to bend, obtain larger current density in a smaller space, and achieve a larger central magnetic field.Therefore, the in-situ winding technology could be potentially applied to make high-field coils in largescale fusion reactors.

Figure 2 .
Figure 2. In-situ winding process: (a) the three tapes were combined into a unit using Kapton tapes, (b) densely wrapped around the copper frame, (c) multi-layer cross winding structure.

Figure 3 .
Figure 3. (a) Structure of a single-layer CORC coil.(b) Overall view of the six-layer CORC coil sample.

Figure 5 .
Figure 5. (a) Strain distribution in the winding process.(b) Strain distribution after bending.

Figure 6 .
Figure 6.Measurement: critical current of the CORC coil.

Figure 7 .
Figure 7. Measurement vs Calculation: magnetic field at the center of the coil with different coil current.

Figure 8 .
Figure 8. Measurement: distribution of the magnetic field in the coil.

Figure 9 .
Figure 9. Experiment: critical current degradation behavior in REBCO tape under external magnetic field.

Figure 10 .
Figure 10.Calculation: transport AC losses of the coil with different winding angles and different layers.

Figure 11 .
Figure 11.Self-field critical current of the REBCO tape varies with temperature.

Figure 13 .
Figure 13.Multi-channel voltage measurements, with the current applied; Tape 1, Tape 2 and Tape 3, the three tapes of the outermost layer in the coil, respectively.

Table 1 .
Winding parameters of each layer of the coil.