1. Introduction
According to the baseline design of the China Fusion Engineering Test Reactor (CFETR), the toroidal field at the major radius is $ B_{t}=6.5 T @ 7.2 \mathrm{~m} $ and the minor radius a = 2.2 m. The peak field ($B_p$) on the TF coil reaches 14.5 T, with an operation current of 95.6 kA [1], [2], bringing great challenges for the TF coil manufacture in terms of transverse electromagnetic (EM) load. One of the most critical problems is how to achieve an optimum and stable performance of the cable-in-conduit conductor (CICC).
The performance of ITER-grade Nb3Sn strand ($J_{c} \sim 1000 \mathrm{~A}. $/mm2 @12 T, 4.2 K) is not adequate to meet the CFETR requirements, since its critical current density ($J_{c}$) is too low at a magnetic field of 14.5 T. Thus high-$J_{c}$ Nb3Sn strand ($J_{c}$ > 2000 A/mm2 @12 T, 4.2 K) was taken into consideration. Under operation conditions, the conductor is locally exposed to an extremely high electro-magnetic (EM) load (∼1400 kN/m), 1.77 times that of the ITER TF conductor. Such high EM load on the cable can damage the internal structure of the superconducting strand, which then causes irreversible performance degradation to the conductor. Based on previous research [3], [4], [5], [6], the short twist pitch (STP) cable structure shows high transverse stiffness, which better withstands the EM load and prevents irreversible degradation of the Nb3Sn conductor. The combination of high-$J_{c}$ Nb3Sn strand and the STP cable pattern might be a solution for the CFETR. However, it is unknown if the STP cable structure still works for the high-$J_{c}$ Nb3Sn strand, since the internal layout of the strand is quite different from ITER class strands. For investigating the feasibility of this solution, a high-$J_{c}$ Nb3Sn conductor sample (named CFTF-STP-01) was manufactured with the identical structure of CFETR-CSMC conductor and tested in SULTAN facility at SPC, Switzerland. The used high-$J_{c}$ strand with a current density of 2000 A/mm2 at 12 T, 4.2 K was manufactured by WST.
The test campaign includes DC and AC tests. In the DC tests, the evolution of the current sharing temperature ($T_{cs}$) was investigated at different levels of cyclic EM loading. The EM load was stepwise divided into three levels: partial load levels (35 kA × 4.5 T, 40.5 kA × 7.78 T), standard load level (45 kA × 10.8 T, similar to that of the CFETR CSMC), and overload levels (58.1 kA × 10.8 T, 80.0 kA × 10.8 T), which aim to explore the possible starting point of the conductor performance degradation. The overview of the $T_{cs}$ evolution is shown in Fig. 1 and the detailed test results are presented in [7]. From Fig. 1, it can be seen that no performance degradation was observed on the partial and standard load levels. However, when the load was increased to 130%, the $T_{cs}$ decreased slightly with cycles but then increased again after a warm-up and cool-down (WUCD) cycle. Finally, the 177% load led to a severe decrease of $T_{cs}$, suggesting that irreversible deformation, causing a change in the strain state, or even damage has occurred in the superconducting strands. The conductor strain distribution measurement showed that the strain distribution expanded to the tensile region after cycling [7], which is a sign of Nb3Sn strain alteration or damage. Based on the test results, it seems that the STP cable pattern is working well for high-$J_{c}$ Nb3Sn strand within a limited range of EM loading. The actual load limit is somewhere between 58.1 kA × 10.8 T and 80.0 kA × 10.8 T, for this conductor sample.
Fig. 1. Overview of the $T_{cs}$ evolution of CFTF-STP-01 sample, cycled under various EM loads, with 100% full loading corresponding to the peak CFETR-CSMC load. |
It is not possible to find the exact EM load limit of this conductor by re-testing it, since the degradation is irreversible. But the magnetic field distribution on the conductor sample offers scope to explore the limitation by metallographic investigation. As the magnetic field distribution along the longitudinal direction varies gradually, so is the EM load, which means that segments subjected to different EM loads can be extracted from the conductor sample. First, metallographic observation can prove whether the strand sub-element in such segment has been subjected to cracks under the specific EM load. Secondly, previous studies [8], [9], [10], [11] showed that under different EM loads, the conductor cross-section exhibits a difference in geometric features, i.e. strand movements caused by Lorentz force change the local void fraction, giving a deviation of the center of mass of the strands and inter-strand contact status. We attempt to achieve two goals through these studies:
I. Establish a correlation between the geometric features changes of the conductor cross-section caused by the electromagnetic force and the conductor performance.
II. Narrow the range of the EM load limit, which causes irreversible degradation of this conductor sample.
The sample preparation, observation method, data processing approach, results, and discussions will be presented in the following sections.
2. Experimental procedures
After testing in the SULTAN facility, the sample is disassembled into two legs and sent back to ASIPP. The sample conductors were secured well in the box to guarantee that the samples won’t get damaged during transportation.
The right leg conductor of the sample was selected as the sample for metallographic investigation, several short segments were extracted from the leg for transverse cross-section geometry observation and crack distribution statistics on strand sub-elements. The segments extracting principle and analysis methods will be presented in the following sections.
2.1. Segment extraction
The magnetic field along the conductor in the SULTAN magnet varies in longitudinal direction. The positions of the segments were determined by the EM loads the segments were subjected to, as shown in Fig. 2.
Fig. 2. The magnetic field profile along the length of the test sample and segment positions. |
As shown in Fig. 2, the EM loads applied on the segments SM1 to SM6 correspond to 177% to 32% of the full CFETR-CSMC load, with an operating current of 80 kA. The extra two segments SM1-R and SM2-L were extracted for narrowing the range of critical EM load which causes irreversible degradation. The extracting activities were performed very carefully and strictly in accordance with the following steps:
(1) Determine the position of each segment with first locating the central field by using the voltage-taps on the conductor sample as a reference. Then, according to the distance between segment and central field point, as shown in Fig. 2, the central line of each segment is marked on the conductor. The central distance of SM1 to SM1_R and SM2 to SM2_L is 150 mm respectively, close to 1/3 of the central distance between SM1 and SM2.
(2) Determine the direction of the EM or Lorentz force, that points in the same direction as the helium outlet tube, which has been checked with the SULTAN facility. The direction of the Lorentz force was marked on each segment using electric discharge machining (EDM) lettering before cutting, to avoid missing of the marks in the extracting process.
(3) Extracting the segment in two steps, (1) cut the segment from the conductor with a length of 60 mm, by electric saw; (2) remove 5 mm extra length from both ends of each segment, by EDM cutting. This is to prevent the impact of electric saw cutting on the geometric feature of the transverse cross-section. The final length of the segment is 50 mm.
2.2. Transverse cross-section analysis
In order to observe for crack formation in the strand sub-elements, the CICC jacket shall be removed and the cable is split in longitudinal direction. Thus the image of the transverse cross-section of each segment must be scanned before crack observation.
The transverse cross-section was imaged using an ultra-high-resolution scanner, the DPI of the image is 6400 (10,000x20,000 pixels). The obtained image was then converted into a binary image (as shown in Fig. 3), with the open-source software package Fiji [12]. This software can determine the local void fraction, measure the geometric center coordinates of each individual strand, which are very useful in the strand center of mass deviation analysis and inter-strand contact count.
Fig. 3. The image of the transverse cross-section of the segment (a) and the binary image of its bundle region (b). |
2.3. Crack distribution statistics
The crack observation in the Nb3Sn filaments is very challenging and the operation process needs to be performed very careful to prevent secondary damage to the filaments. In previous studies [8], [9], the strands were extracted from the cable to perform metallographic analysis. The extraction and sampling processes need very precise and complicated procedures, the Nb3Sn strands in the cable are sintered (especially for the STP cable) after heat treatment. The first step is releasing the sintering with a chemical solution, then several strands are selected and marked from different positions in the cable, finally solidifying and polishing the selected sample strands in longitudinal orientation. The solidifying and polishing process is complex because the extracted strands are spatially twisty and it is difficult to obtain a longitudinal cross-section. After trials, we decided to give up the extraction approach and turned to cut the segment integrally, as shown in Fig. 4, the split face is in the middle of the conductor and parallel to the Lorentz force direction. After cutting, it was found that a small part of the strands present almost transverse cross-section, due to the short twist pitch, but most of the strands show practically longitudinal cross-section. This allowed to observe the morphology of the sub-element in the strand from the high-pressure (HP) region to the low-pressure (LP) region. Here the HP and LP region refer to the 0° and 180° to the Lorentz force vector, as shown in Fig. 4(b). The HP region is formed as the strands migrate in the direction of the Lorentz force and so is the LP region.
Fig. 4. Longitudinal cut of the CICC section for filament crack metallography, with LP and HP, low pressure and high pressure side respectively. |
It is necessary to point out that this approach can be adopted for high-$J_{c}$ Nb3Sn strand but not for the ITER-grade single barrier Nb3Sn strand. After heat-treatment, the Nb filaments in the sub-element of the high-$J_{c}$ Nb3Sn strand are sintered, almost as a single filament, with a diameter of ∼80 µm. Thus, an optical microscope can be used to observe the morphology of the sub-elements, the range of motion of the microscope lens can cover the segment cross-section. The Nb filaments in the ITER-grade single barrier Nb3Sn strand are much smaller than that of the high-$J_{c}$ Nb3Sn strand and resolution of the optical microscope is not enough for accurate filament morphology observation. Also, it is not possible to put the whole segment into the sample chamber of a SEM.
Before dissecting, the segments were solidified by resin, to prevent strand movement during the dissection process. The resin impregnation process was performed in vacuum. After solidification, the jacket was removed from the segment by milling, because the jacket cannot be cut by a diamond wire saw. The cable then was dissected by a diamond wire saw. Finally, the faces of the split sections were polished with metallographic abrasive.
3. Results
3.1. Geometric analysis of the transverse cross-section
The geometric analysis of the transverse cross-section, including the local void fraction variation, deviation of the center of mass of the strands and inter-strand contact was performed, the results are presented in the following sections. These results are also compared with ITER CS conductors, which are analyzed in [9]. The parameters of the conductors in comparison are listed in Table 1.
Table 1. The main parameters of the conductors in comparison. |
| Sample ID | Cable type | Triplet configuration | Twist pitch (mm) | Void fraction (%) | Maximum EM load, B×I (N/m) |
|---|---|---|---|---|---|
| CFTF-STP-01 | STP-High-$J_{c}$ | $ 2 \times s c+1 C u $ | 25/50/92/155/450 | 32.5 | 10.8 T × 80.0 kA |
| CSJA 2-2 | Baseline—BR | $ 2 \times s c+1 C u $ | 45/84/145/251/453 | 33.4 | 10.8 T × 45.1 kA |
| CSIO 1-2 | Baseline—IT | $ 2 \times s c+1 C u $ | 45/85/147/248/424 | 33.4 | |
| CSIO 2-2 | Short—IT | $ 2 \times s c+1 C u $ | 22/45/81/159/443 | 32.5 | |
| CSJA 3-1 | Short—BR | $ 2 \times s c+1 C u $ | 22/45/81/159/443 | 32.5 |
3.1.1. Local void fraction variation
The overall void fractions and local void fractions of the eight segments were measured. The measured global void fractions of the segments are 32.5 ± 0.25%, close to the target value. For each cross-section, 12 local void fractions were measured, i.e., each petal was separated into two parts and analyzed. The area out of the petal wrap was not taken into account when measuring the local void fractions. The results are shown in Fig. 5, where the horizontal axis coordinate ϴ refers to the angle between the Lorentz force direction and the center of the measured region, as shown in Fig. 4(b).
Fig. 5. The void fraction deviation from the global void fraction as a function of the angle with the Lorentz Force direction, where 0° is the Lorentz Force direction. |
Fig. 5 shows the void fraction deviation from the global void fraction as a function of the angle to Lorentz Force direction. To avoid visual confusion due to the large number of data points, the plots are represented in two figures. For SM5 and SM6, the void fraction deviations do not fluctuate significantly with the angle. From SM4 to SM1, the void fraction deviations begin to fluctuate with the angle, with largest effect for the SM1 segment. The results indicate that the strands migrate to the HP region under Lorentz force, leading to a void fraction expansion in the LP region and compression in the HP region. The migration of the strands reduces the inter-strand support in the LP region, which increases the bending strain on the strands. In the HP region, the inter-strand contacts pressure at the contact point increases. Both of them will impact the conductor performance [13], [14].
3.1.2. Deviation of the center of mass of the strands
The coordinates of the individual strand centers in the conductor cross-section can be determined by the Fiji software. The geometric strand centers were averaged and compared to the center of the conductor, which in this paper is defined as the geometric center of the inner hole of the jacket.
The results are shown in Fig. 6. All the results look logical except for the SM6 segment, it has a very big offset in the direction perpendicular to the Lorentz force. The reason for this is unknown yet, maybe it is caused during the sample manufacture or from the image processing. Apart from SM6 in Fig. 6, the impact of the Lorentz force on the cable structure is evident, the strands were significantly moved by the Lorentz force.
Fig. 6. The average strand center of mass offset of the conductor cross-sections. |
Fig. 7 makes a comparison among the conductors from Table I, the plot shows the components of the offset in Lorentz force direction versus the transverse Lorentz force. Compared with the classical “normal” twist pitch (NTP) conductor, the average strand center of mass offset of the STP conductor is significantly lower, even with twice the EM load, indicating that the STP cable structure has greater stiffness. Also, it seems that the movement of the strands changes suddenly (see the solid blue line in Fig. 7.) when the EM load reaches a certain value, which is represented obviously in the results of the last two segments. It is speculated that the strand movement is constrained by the sintering and inter-strand contact friction at lower EM loads. When the EM load reaches a certain critical value, the constraints are broken and this leads to an avalanche in movement of strands.
Fig. 7. The average strand center of mass offset in Lorentz force direction as a function of transverse Lorentz force, the value under the load of 45 kA × 10.8 T is also compared with those of other conductor samples in [8]. |
3.1.3. Inter-strand contact
The third way to assess the movements of strands in the cross-section is by counting the contact points between the strands. If the strands move to one area, the density of the strands in this area will increase and the number of contact points between strands will also increase.
Due to that the geometric centers of strands had been obtained, it can be determined whether there is contact between two strands, is decided by calculating the central distance between the two strands. Theoretically, if two strands contact each other, their center distance should be less than or equal to the strand diameter (see in Fig. 8, case I). But in the conductor cross-section, the shape of the strand cross-section is oval, as shown in case II, III, and IV. Case III shows an extreme situation in which the distance is maximum, and most of the contacts between the strands are as shown in case IV, $ d \leq d^{\prime} \leq k \bullet d $, where the coefficient k should be $ 1 / \cos \theta $, for this sample, the $k$ is 1.04∼1.05. Thus the $d’$ is uncertain and this uncertainty will influence the contact counting results. One way to reduce the uncertainty is adjusting the $d′$ to make a best fit between the calculated and manually counted numbers of the contact point, in one of the cross-sections. The fitted d′ is 1.038, which will be used for the contact points calculation in all cross-sections. Although this method is still not precise enough, we pay more attention to statistical results.
Fig. 8. The sketch map of the contact situation between the strands in the conductor transverse cross-section. |
Fig. 9 shows the transverse cross-sections of SM1 to SM6 segments, with the strands marked by different colors according to the number of strands in contact with them. The number ranges from 0 to 5, which refers to no other strands in contact or up to five strands in contact with this strand. Intuitively, the light region of SM1, SM1-R, and SM2-L is larger than that of other segments, especially for SM1. meanwhile, the light region on the HP side is larger than that of the LP side for these three segments. For other segments from SM2 to SM6, the light regions are smaller, and there is not much difference between the HP and LP side. Fig. 10 shows the statistical outcome, the strands with more than two neighbors in contact (i.e., light colors) on the HP side and LP side are compared for each segment, which confirms the findings above.
Fig. 9. Transverse cross-sections of the segment, the strands are colored according to their neighbor number in the contact. |
Fig. 10. The statistical results of inter-strand contact in the cross-section for each segment., The vertical axis represents the number of strands with more than two neighbors in contact, in HP and LP side respectively. |
These results indicate that under high EM force, the strands move to the HP region and the segregated copper strands were subjected to more plastic deformation. However, compared with the CSIO1-2 sample (in [8] Fig. 12(b)), the difference in the number of contact points of strands in the HP region and LP region is not that big, once again, demonstrating that the STP cable structure can restrain strand movement in the cable.
3.2. Crack observation
The cross-section of a segment after cutting and polishing is shown in Fig. 11 with the strands fixed well by the resin after VPI, avoiding secondary strand damage effectively. The cross-section can be easily scanned with an optical microscope.
Fig. 11. The longitudinal cross-section of a segment, the strands are fixed by the resin, and the jacket is removed after VPI. |
The cross-sections of all segments were observed, it was found that the formation of cracks on the sub-elements of the high-$J_{c}$ Nb3Sn strand is quite different from that on the ITER Nb3Sn filaments. In previous studies [8], [9], [11], it was seen that the Nb3Sn filaments are ‘fractured’ by bending strain (shown in Fig. 12(a)) and the path for superconducting current transport is blocked. But here, no total ‘fractured’ sub-element was found in all of the segments, instead, in the cross-sections of SM1, many longitudinal cracks were found (as shown in Fig. 12(b)) can be found. This kind of crack was also found in the cross-sections of SM1-R, SM2-L and SM2, but the amount is much lower than that of SM1. Table 2 is the statistics of strand damage of SM1, SM1-R, SM2-L and SM2, the total strand number refers to the number of strand which can be seen in the longitudinal cross-section shown in Fig. 11, the damaged strand number refers to the number of strand that cracks can be found on the sub-elements of which.
Fig. 12. (a) Tensile and contact stress fracture observed on ITER Nb3Sn filaments [8], (b) Longitudinal cracks found on the sub-element in the cross-section of SM1 segment, near the boundary between the Nb barrier and the sintered Nb3Sn mass, (c) Nb barrier - Nb3Sn mass boundary without cracks, in the cross-section of SM3 segment. |
Table 2. Statistics of strand damage. |
| HP side | LP side | |||
|---|---|---|---|---|
| Total strand number | Damaged strand number | Total strand number | Damaged strand number | |
| SM1 | 47 | 21 | 47 | 26 |
| SM1-R | 36 | 3 | 40 | 1 |
| SM2-L | 42 | 2 | 44 | 0 |
| SM2 | 45 | 5 | 42 | 2 |
The cracks are are aligned in longitudinal direction and concentrated near the ‘boundary’ between the Nb barrier and the sintered Nb3Sn mass (i.e. Cu-Nb matrix before heat-treatment), and look more like ‘disintegration’. No similar cracks were found near the ‘boundary’ of the sub-elements in other segments, as shown in Fig. 12(c). This kind of crack does not have the features of cracks on the filament of ITER-class Nb3Sn strand, caused by tensile and contact stress fracture, which were described and defined in [8]. The longitudinal cracks were found in the PIT Nb3Sn strand subjected to the transverse compression [15], but it seems that the cracks penetrate the sub-element, no such penetrating crack can be observed in this case. There is no visible distinction between the cracks in the HP and LP region, thus the formation mechanism of this kind of crack is not well identified and it is not clear if they are a significant factor in causing conductor performance degradation.
Further work would be required to understand the formation mechanism of this kind of crack, and more important, whether this type of cracks will propagate further inwards the sub-element under continued cyclic high EM loads (only 200 times an EM peak load of 80 kA × 10.8 T was applied) then become the penetrating crack.
4. Conclusion
The SULTAN test results indicate that the performance of the CFTF-STP-01 conductor sample, made of high-$J_{c}$ Nb3Sn strand and with STP cable pattern, has degraded considerably under a high EM design load of 80 kA × 10.8 T. From eight extracted segments, subjected to different EM loads, the geometry of the transverse cable cross-section and Nb3Sn crack density was analyzed.
A good correlation was found between the decrease of the current sharing temperature, location of cracks, and deformation of the cable cross section. The observed cracks in the sub-elements of the high-$J_{c}$ Nb3Sn strand are aligned in longitudinal direction, no transverse crack formation was observed.
The critical EM load after which irreversible degradation of the conductor starts, is between 850 kN/m and 870 kN/m.
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.
Acknowledgements
This work was in part supported by the National Key R & D Program of China (Grant No. 2017YFE0301404), and the Comprehensive Research Facility for Fusion Technology Program of China under Contract No. 2018-000052-73-01-001228
