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Characteristics of Critical Current of HTS Conductor on Round Core
Available online at www.sciencedirect.com
ScienceDirect Physics Procedia 81 (2016) 125 – 128
28th International Symposium on Superconductivity, ISS 2015, November 16-18, 2015, Tokyo, Japan
Characteristics of critical current of HTS Conductor on Round Core X. Zhan*, L. Ren, Z. Wang, Y. Xu ( R&D Center of Applied Superconductivity, State Key Lab. of AEET, Huazhong University of Science and Technology, Wuhan 430074, China )
Abstract The bend and transposition of high-temperature superconductors (HTS) have great influence on the characteristics of critical current. For Conductor on Round Core (CORC), twist pitch and diameter will influence the characteristics of critical current. The influence of twist pitch and diameter on the critical current characteristics of CORC was studied. In this paper, the simulation of magnetic field distribution of the conductor using FEM was accomplished, and the critical current of the conductor was calculated and discussed in different twist pitch and diameter. Then, the sample of HTS CORC was fabricated, and the critical current was measured at liquid nitrogen temperature and self-field. The test results correspond with simulation. © Published by Elsevier B.V. B.V. This is an open access article under the CC BY-NC-ND license ©2016 2016The TheAuthors. Authors. Published by Elsevier (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the ISS 2015 Program Committee. Peer-review under responsibility of the ISS 2015 Program Committee Keywords: CORC;HTS;Critical current; Electromagnetic design
1. Introduction With the development of HTS, advantages of HTS in the large fusion magnet design and manufacture will be significant. The bases of realizing HTS applied for fusion magnet are high current conductors [1]. The cabling method of high current conductors is usually a parallel arrangement of tapes. If bundling HTS tapes together directly to form high current conductors, it will generate high AC loss which disturbs working state of the conductors [2]. So it is necessary to consider the transposition of conductors for reducing AC loss, but the characteristics of critical current will be influenced by transposition. Twisting could not be directly implemented owing to the craftsmanship
* Corresponding author. Tel.: +86-27-8754-4755; fax: +86-27-8754-0937. E-mail address: [email protected]
1875-3892 © 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the ISS 2015 Program Committee doi:10.1016/j.phpro.2016.04.017
126
X. Zhan et al. / Physics Procedia 81 (2016) 125 – 128
of HTS tape itself. It is demanded to design a more reasonable structure of large current conductor. In 2010, University of Colorado presented CORC (Conductor on Round Core) design of spiral-winding tapes on a small round former [3-4]. In this paper, the magnetic field distribution of this kind conductor in different twist pitch and diameter (77K) is simulated and critical current is calculated. The measure experiment of critical current is carried out to verify simulation results. 2. Model of conductor structure In this paper, 4 tapes of SuperPower SCS4050 are spiral-winded uniformly on a round epoxy former which does not share current, so the effect of former could be ignored. The width of SuperPower SCS4050 tape without insulation is 4mm, thickness is 0.1mm, the critical current at 77K and self-field is 117A, and the total current of 4 tapes without degradation is 468A. Fig. 1(a) shows the structure of conductor. COMSOL Multiphysics mf module is used for simulation. It is based on Ampere’s law: ×H=J where H is magnetic field intensity, J is current density. In this paper, diameter is from 16mm-60mm, twist pitch is from 50mm-250mm. The least bending diameter of SuperPower SCS4050 is 11mm and the critical tension strain is 0.45%. We consider extreme condition that diameter is 16mm and twist pitch is 50mm, the strain can be calculated from equations (2) in reference [5] and is -0.25%, and there is nearly no reduction in Ic. Moreover, the actual strain of tape will be reduced when a small gap exists between conductor and former. So the influence of magnetic field on critical current is dominating relative to strain The tetrahedron is used to generate mesh of conductor in detail and mesh of air roughly. Fig. 1(b) presents the mesh shape of conductor. For simplicity we consider the tape as YBCO superconductors, and define resistivity for different materials in the model. For air, we use ρ=1000 Ω m; for superconductors, we use the E-J power law: E= E=E0(J/Jc)n, where Jc is defined as the current when E0=1×10-4 V/m is reached under DC I-V measurements, n=30, Jc=2.5×108A/m2, single coil module is used to apply current load for conductor. Critical current is calculated by obtaining max magnetic flux density and load curve of conductor, combined with critical current curve of tape. The point of intersection between load curve and critical current curve corresponds to the critical current of conductor. Because it is a homogeneous 3D model, it is very hard to identify which component is longitudinal or lateral, we use Bnorm = (Bx2 + By2+ Bz2)1/2 as magnetic flux density. Ic (1μV/cm criterion) of SuperPower SCS4050 in different magnetic field angle (77K) is presented in Fig. 1(c), critical current curve in perpendicular field (90°) is adopted in this paper. (a)
0°
30°
200
400
45°
60°
90°
(c) 120
(b)
110
Ic/A
100 90 80
70 60 0
600
800
1000
B/Gs
Fig. 1. (a) Conductor on Round Core; (b) Mesh shape of conductor; (c) The curve of critical current of SuperPower SCS4050
3. Results and Discussion The steady-state current of each tape is 60A DC. Table 1 shows max magnetic flux density and critical current of the conductor in different twist pitch when diameter is 16mm, Fig. 2(a) presents curve of critical current with different twist pitch. As twist pitch increases, the maximum magnetic flux density decreases gradually, the critical current Ic increases gradually. The results show that the variation trend of critical current Ic is not linear. The critical current Ic increases sharply when twist pitch is between 0-100mm, while decreases slowly when twist pitch is between 100mm-250mm and tends to 388A gradually at last. When twist pitch is 250mm, the maximum magnetic
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X. Zhan et al. / Physics Procedia 81 (2016) 125 – 128
flux density is 221.52Gs; the critical current Ic is 388A, decreasing by 80A compared with 468A and dropping by 17%. When twist pitch is 50mm, the maximum magnetic flux density is 404.94Gs; the critical current Ic is 336A, decreasing by 132A compared with 468A and dropping by 28%. Besides, it is found that the smaller the twist pitch is, the more uniform magnetic field distribution of tapes is. Table 2 shows max magnetic flux density and critical current of the conductor when twist pitch is 150mm, Fig. 2(b) presents curve of critical current with different diameter. The steady-state current of each tape is 60A DC when diameter is between 15mm-35mm, reducing to 50A when diameter is between 40mm-60mm for preventing exceeding critical current of conductor. As the diameter increases, the maximum magnetic flux density increases gradually, the critical current Ic decreases almost linearly. When diameter is 15mm, the maximum magnetic flux density is 246.73Gs; the critical current Ic is 378A, decreasing by 90A compared with 468A and dropping by 19%. When diameter is 60mm, the maximum magnetic flux density is 367.74Gs; the critical current Ic is 324A, decreasing by 144A compared with 468A and dropping by 31%. Furthermore, it is noticed that uniformity of magnetic field distribution is not affected by diameter. Table 1. Max magnetic flux density in different twist pitch when diameter is 16mm twist pitch/mm 50 100 120 150 180 200 250
Max B/Gs 404.94 291.47 275.13 252.08 241.40 228.80 221.52
Ic/A 336 364 369 376 380 384 388
Table 2. Max magnetic flux density in different diameter when twist pitch is 150mm diameter/mm 15 20 25 30 40 45 50 55 60
critical current Ic
400
(b)
380
390
370
380
360
370
350
Ic/A
Ic/A
(a)
Max B/Gs 246.73 275.89 301.90 325.24 305.94 328.93 348.56 356.57 367.74
360
critical current Ic
340
350
330
340
320
330
Ic /A 378 368 361 355 345 339 333 328 324
310 0
50
100
150
200
250
300
10 15 20 25 30 35 40 45 50 55 60 65
twist pitch/mm
diameter/mm
Fig. 2. (a) Critical current Ic in different twist pitch (diameter 16mm); (b) Critical current Ic in different diameter (twist pitch 150mm)
The simulation results could be analyzed qualitatively. The smaller twist pitch is, the more significant the coupled effect of magnetic field which gives rise to the increase of magnetic flux density is. For magnet field of a hollow cylinder in perpendicular field, it could be explained by reference [6]:
Hp =
2 μ J (R − Ri ) π 0 c o
1
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X. Zhan et al. / Physics Procedia 81 (2016) 125 – 128
Where H p is perpendicular magnetic, Ri is inside radius, Ro is outside radius μ0 is permeability of vacuum, J c is current density. In this situation ( Ri is zero), the magnetic field intensity increases linearly and the critical current decreases linearly as diameter increases. For the design of CORC, smaller twist pitch and larger diameter are expected if conductor needs to reach higher critical current regardless of strain effect et al. 4. Experiment For verifying the accuracy of simulation results, the sample of CORC (twist pitch 150mm, diameter 16mm) is manufactured. Fig. 3(a) shows the sample of CORC, each tape is wound by hand. The material of round core is epoxy resin, voltage contact is soldered on the middle surface of every tape, and terminal tapes are soldered to brass which is used as current contacts. If one of 4 tapes quenches, the state of conductor is counted as quench. The critical current is measured by the four-probe method at a quench criterion of 1 μV/cm and 4 μV is determined (distance between voltage contacts is 4cm). For this experiment, current source is used as a source and the current ramping speed is 1 A/s. Fig. 3(b) presents quench curve of one tape. The initial voltage is 7 μV and the voltage value of quench is 11 μV because of contact resistance. The critical current of sample is 375 A, the critical current in simulation is 376 A, the difference is 1 A and the experimental error is 0.26%. The experiment results are in accordance with simulation results, verifying the accuracy of simulation results. voltage signal of tape
(b) 14 12 10
V/μV
(a)
8 6 4 0
100
200
300
400
I/A Fig. 3. (a) Prototype of CORC; (b) The quench curve of tape
5. Conclusion The influence of twist pitch and diameter on the critical current characteristics of CORC (twist pitch is from 50mm-250mm, diameter is from 15mm-60mm) has been studied. The simulation results show that the larger twist pitch and the smaller diameter are, the higher the critical current is. A prototype of CORC (twist pitch 150mm, diameter 16mm) has been fabricated, and the critical current is tested. The test value 375 A is close to the simulation result 376 A. Acknowledgements This work was supported in part by Fundamental Research Funds for the Central Universities, HUST under Grant 2014TS145 and Specialized Research Fund for ITER under Grant 2011GB113004 References [1] [2] [3] [4] [5] [6]
Bromberg, Leslie, et al. Fusion Engineering and Design 54.2 (2001): 167-180. Berger, A. D, Massachusetts Institute of Technology, (2012) 55-70. Van der Laan D C, Lu X F, Goodrich L F. Superconductor Science and Technology, 24. 4 (2011) 1-6. Van der Laan D C, P D Noye. Superconductor Science and Technology, 26.4 (2013) 2-9. Van der Laan D C, Superconductor Science and Technology. 22.6 (2009) 1-5. Carr W J Jr, AC Loss and Macroscopic Theory of Superconductors, 2nd edn, Taylor & Francis, New York, 2001.
ScienceDirect Physics Procedia 81 (2016) 125 – 128
28th International Symposium on Superconductivity, ISS 2015, November 16-18, 2015, Tokyo, Japan
Characteristics of critical current of HTS Conductor on Round Core X. Zhan*, L. Ren, Z. Wang, Y. Xu ( R&D Center of Applied Superconductivity, State Key Lab. of AEET, Huazhong University of Science and Technology, Wuhan 430074, China )
Abstract The bend and transposition of high-temperature superconductors (HTS) have great influence on the characteristics of critical current. For Conductor on Round Core (CORC), twist pitch and diameter will influence the characteristics of critical current. The influence of twist pitch and diameter on the critical current characteristics of CORC was studied. In this paper, the simulation of magnetic field distribution of the conductor using FEM was accomplished, and the critical current of the conductor was calculated and discussed in different twist pitch and diameter. Then, the sample of HTS CORC was fabricated, and the critical current was measured at liquid nitrogen temperature and self-field. The test results correspond with simulation. © Published by Elsevier B.V. B.V. This is an open access article under the CC BY-NC-ND license ©2016 2016The TheAuthors. Authors. Published by Elsevier (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the ISS 2015 Program Committee. Peer-review under responsibility of the ISS 2015 Program Committee Keywords: CORC;HTS;Critical current; Electromagnetic design
1. Introduction With the development of HTS, advantages of HTS in the large fusion magnet design and manufacture will be significant. The bases of realizing HTS applied for fusion magnet are high current conductors [1]. The cabling method of high current conductors is usually a parallel arrangement of tapes. If bundling HTS tapes together directly to form high current conductors, it will generate high AC loss which disturbs working state of the conductors [2]. So it is necessary to consider the transposition of conductors for reducing AC loss, but the characteristics of critical current will be influenced by transposition. Twisting could not be directly implemented owing to the craftsmanship
* Corresponding author. Tel.: +86-27-8754-4755; fax: +86-27-8754-0937. E-mail address: [email protected]
1875-3892 © 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the ISS 2015 Program Committee doi:10.1016/j.phpro.2016.04.017
126
X. Zhan et al. / Physics Procedia 81 (2016) 125 – 128
of HTS tape itself. It is demanded to design a more reasonable structure of large current conductor. In 2010, University of Colorado presented CORC (Conductor on Round Core) design of spiral-winding tapes on a small round former [3-4]. In this paper, the magnetic field distribution of this kind conductor in different twist pitch and diameter (77K) is simulated and critical current is calculated. The measure experiment of critical current is carried out to verify simulation results. 2. Model of conductor structure In this paper, 4 tapes of SuperPower SCS4050 are spiral-winded uniformly on a round epoxy former which does not share current, so the effect of former could be ignored. The width of SuperPower SCS4050 tape without insulation is 4mm, thickness is 0.1mm, the critical current at 77K and self-field is 117A, and the total current of 4 tapes without degradation is 468A. Fig. 1(a) shows the structure of conductor. COMSOL Multiphysics mf module is used for simulation. It is based on Ampere’s law: ×H=J where H is magnetic field intensity, J is current density. In this paper, diameter is from 16mm-60mm, twist pitch is from 50mm-250mm. The least bending diameter of SuperPower SCS4050 is 11mm and the critical tension strain is 0.45%. We consider extreme condition that diameter is 16mm and twist pitch is 50mm, the strain can be calculated from equations (2) in reference [5] and is -0.25%, and there is nearly no reduction in Ic. Moreover, the actual strain of tape will be reduced when a small gap exists between conductor and former. So the influence of magnetic field on critical current is dominating relative to strain The tetrahedron is used to generate mesh of conductor in detail and mesh of air roughly. Fig. 1(b) presents the mesh shape of conductor. For simplicity we consider the tape as YBCO superconductors, and define resistivity for different materials in the model. For air, we use ρ=1000 Ω m; for superconductors, we use the E-J power law: E= E=E0(J/Jc)n, where Jc is defined as the current when E0=1×10-4 V/m is reached under DC I-V measurements, n=30, Jc=2.5×108A/m2, single coil module is used to apply current load for conductor. Critical current is calculated by obtaining max magnetic flux density and load curve of conductor, combined with critical current curve of tape. The point of intersection between load curve and critical current curve corresponds to the critical current of conductor. Because it is a homogeneous 3D model, it is very hard to identify which component is longitudinal or lateral, we use Bnorm = (Bx2 + By2+ Bz2)1/2 as magnetic flux density. Ic (1μV/cm criterion) of SuperPower SCS4050 in different magnetic field angle (77K) is presented in Fig. 1(c), critical current curve in perpendicular field (90°) is adopted in this paper. (a)
0°
30°
200
400
45°
60°
90°
(c) 120
(b)
110
Ic/A
100 90 80
70 60 0
600
800
1000
B/Gs
Fig. 1. (a) Conductor on Round Core; (b) Mesh shape of conductor; (c) The curve of critical current of SuperPower SCS4050
3. Results and Discussion The steady-state current of each tape is 60A DC. Table 1 shows max magnetic flux density and critical current of the conductor in different twist pitch when diameter is 16mm, Fig. 2(a) presents curve of critical current with different twist pitch. As twist pitch increases, the maximum magnetic flux density decreases gradually, the critical current Ic increases gradually. The results show that the variation trend of critical current Ic is not linear. The critical current Ic increases sharply when twist pitch is between 0-100mm, while decreases slowly when twist pitch is between 100mm-250mm and tends to 388A gradually at last. When twist pitch is 250mm, the maximum magnetic
127
X. Zhan et al. / Physics Procedia 81 (2016) 125 – 128
flux density is 221.52Gs; the critical current Ic is 388A, decreasing by 80A compared with 468A and dropping by 17%. When twist pitch is 50mm, the maximum magnetic flux density is 404.94Gs; the critical current Ic is 336A, decreasing by 132A compared with 468A and dropping by 28%. Besides, it is found that the smaller the twist pitch is, the more uniform magnetic field distribution of tapes is. Table 2 shows max magnetic flux density and critical current of the conductor when twist pitch is 150mm, Fig. 2(b) presents curve of critical current with different diameter. The steady-state current of each tape is 60A DC when diameter is between 15mm-35mm, reducing to 50A when diameter is between 40mm-60mm for preventing exceeding critical current of conductor. As the diameter increases, the maximum magnetic flux density increases gradually, the critical current Ic decreases almost linearly. When diameter is 15mm, the maximum magnetic flux density is 246.73Gs; the critical current Ic is 378A, decreasing by 90A compared with 468A and dropping by 19%. When diameter is 60mm, the maximum magnetic flux density is 367.74Gs; the critical current Ic is 324A, decreasing by 144A compared with 468A and dropping by 31%. Furthermore, it is noticed that uniformity of magnetic field distribution is not affected by diameter. Table 1. Max magnetic flux density in different twist pitch when diameter is 16mm twist pitch/mm 50 100 120 150 180 200 250
Max B/Gs 404.94 291.47 275.13 252.08 241.40 228.80 221.52
Ic/A 336 364 369 376 380 384 388
Table 2. Max magnetic flux density in different diameter when twist pitch is 150mm diameter/mm 15 20 25 30 40 45 50 55 60
critical current Ic
400
(b)
380
390
370
380
360
370
350
Ic/A
Ic/A
(a)
Max B/Gs 246.73 275.89 301.90 325.24 305.94 328.93 348.56 356.57 367.74
360
critical current Ic
340
350
330
340
320
330
Ic /A 378 368 361 355 345 339 333 328 324
310 0
50
100
150
200
250
300
10 15 20 25 30 35 40 45 50 55 60 65
twist pitch/mm
diameter/mm
Fig. 2. (a) Critical current Ic in different twist pitch (diameter 16mm); (b) Critical current Ic in different diameter (twist pitch 150mm)
The simulation results could be analyzed qualitatively. The smaller twist pitch is, the more significant the coupled effect of magnetic field which gives rise to the increase of magnetic flux density is. For magnet field of a hollow cylinder in perpendicular field, it could be explained by reference [6]:
Hp =
2 μ J (R − Ri ) π 0 c o
1
128
X. Zhan et al. / Physics Procedia 81 (2016) 125 – 128
Where H p is perpendicular magnetic, Ri is inside radius, Ro is outside radius μ0 is permeability of vacuum, J c is current density. In this situation ( Ri is zero), the magnetic field intensity increases linearly and the critical current decreases linearly as diameter increases. For the design of CORC, smaller twist pitch and larger diameter are expected if conductor needs to reach higher critical current regardless of strain effect et al. 4. Experiment For verifying the accuracy of simulation results, the sample of CORC (twist pitch 150mm, diameter 16mm) is manufactured. Fig. 3(a) shows the sample of CORC, each tape is wound by hand. The material of round core is epoxy resin, voltage contact is soldered on the middle surface of every tape, and terminal tapes are soldered to brass which is used as current contacts. If one of 4 tapes quenches, the state of conductor is counted as quench. The critical current is measured by the four-probe method at a quench criterion of 1 μV/cm and 4 μV is determined (distance between voltage contacts is 4cm). For this experiment, current source is used as a source and the current ramping speed is 1 A/s. Fig. 3(b) presents quench curve of one tape. The initial voltage is 7 μV and the voltage value of quench is 11 μV because of contact resistance. The critical current of sample is 375 A, the critical current in simulation is 376 A, the difference is 1 A and the experimental error is 0.26%. The experiment results are in accordance with simulation results, verifying the accuracy of simulation results. voltage signal of tape
(b) 14 12 10
V/μV
(a)
8 6 4 0
100
200
300
400
I/A Fig. 3. (a) Prototype of CORC; (b) The quench curve of tape
5. Conclusion The influence of twist pitch and diameter on the critical current characteristics of CORC (twist pitch is from 50mm-250mm, diameter is from 15mm-60mm) has been studied. The simulation results show that the larger twist pitch and the smaller diameter are, the higher the critical current is. A prototype of CORC (twist pitch 150mm, diameter 16mm) has been fabricated, and the critical current is tested. The test value 375 A is close to the simulation result 376 A. Acknowledgements This work was supported in part by Fundamental Research Funds for the Central Universities, HUST under Grant 2014TS145 and Specialized Research Fund for ITER under Grant 2011GB113004 References [1] [2] [3] [4] [5] [6]
Bromberg, Leslie, et al. Fusion Engineering and Design 54.2 (2001): 167-180. Berger, A. D, Massachusetts Institute of Technology, (2012) 55-70. Van der Laan D C, Lu X F, Goodrich L F. Superconductor Science and Technology, 24. 4 (2011) 1-6. Van der Laan D C, P D Noye. Superconductor Science and Technology, 26.4 (2013) 2-9. Van der Laan D C, Superconductor Science and Technology. 22.6 (2009) 1-5. Carr W J Jr, AC Loss and Macroscopic Theory of Superconductors, 2nd edn, Taylor & Francis, New York, 2001.