Please wait a minute...
Chin. Phys. B, 2021, Vol. 30(12): 127401    DOI: 10.1088/1674-1056/ac0697

Angular dependence of vertical force and torque when magnetic dipole moves vertically above flat high-temperature superconductor

Yong Yang(杨勇)1,2,†, Shuai-Jie Yang(杨帅杰)1, Wen-Li Yang(杨文莉)1, and Yun-Yi Wu(吴云翼)3,4
1 School of Mechano-Electronic Engineering, Xidian University, Xi'an 710071, China;
2 Shaanxi Key Laboratory of Space Extreme Detection, Xi'an 710071, China;
3 China Three Gorges Science and Technology Research Institute, Beijing 100036, China;
4 Physikalisches Institut B, RWTH Aachen, Aachen 52056, Germany
Abstract  The interaction between a permanent magnet (PM) assumed as a magnetic dipole and a flat high-temperature superconductor (HTS) is calculated by the advanced frozen-image model. When the dipole vertically moves above the semi-infinite HTS, the general analytical expression of vertical force and that of torque are obtained for an arbitrary angle between the magnetization direction of the PM and the c axis of the HTS. The variations of the force and torque are analyzed for angle and vertical movements in both zero-field cooling (ZFC) condition and field cooling (FC) condition. It is found that the maximum vertical repulsive or attractive force has the positive or negative cosine relation with the angle. However, the maximum torque has the positive or negative sine relation. From the viewpoint of the rotational equilibrium, the orientation of the magnetic dipole with zero angle is deemed to be an unstable equilibrium point in ZFC, but the same orientation is considered as a stable equilibrium point in FC. In addition, both of the variation cycles of the maximum force and torque with the angle are π.
Keywords:  high-temperature superconductor      magnetic dipole      frozen-image model      angle  
Received:  10 March 2021      Revised:  16 April 2021      Accepted manuscript online:  29 May 2021
PACS:  74.72.-h (Cuprate superconductors)  
  84.71.Ba (Superconducting magnets; magnetic levitation devices)  
  85.25.Am (Superconducting device characterization, design, and modeling)  
  85.70.Rp (Magnetic levitation, propulsion and control devices)  
Fund: Projects supported by the National Natural Science Foundation of China (Grant No. 11572232) and the China Three Gorges Corporation Research Project (Grant No. 202103407).
Corresponding Authors:  Yong Yang     E-mail:

Cite this article: 

Yong Yang(杨勇), Shuai-Jie Yang(杨帅杰), Wen-Li Yang(杨文莉), and Yun-Yi Wu(吴云翼) Angular dependence of vertical force and torque when magnetic dipole moves vertically above flat high-temperature superconductor 2021 Chin. Phys. B 30 127401

[1] Wang J, Wang S, Zeng Y, et al. 2002 Physica C 378-381, Part 1 809
[2] Mattos L S, Rodriguez E, Costa F, Sotelo G G, de Andrade R and Stephan R M 2016 IEEE Trans. Appl. Supercond. 26 3600704
[3] Hong W, Xin Y, Wang C, Wen Y, Zhao C and Li W 2020 IEEE Trans. Appl. Supercond. 30 3603210
[4] Werfel F N, Floegel-Delor U, Rothfeld R, Riedel T, Goebel B, Wippich D and Schirrmeister P 2012 Supercond. Sci. Technol. 25 014007
[5] Miyazaki Y, Mizuno K, Yamashita T, Ogata M, Hasegawa H, Nagashima K, Mukoyama S, Matsuoka T, Nakao K, Horiuch S, Maeda T and Shimizu H 2016 Cryogenics 80 234
[6] Espenhahn T, Wunderwald F, Möller M, Sparing M, Hossain M, Fuchs G, Abdkader A, Cherif C, Nielsch K and Hühne R 2020 J. Phys. D:Appl. Phys. 53 035002
[7] Ozturk K, Kabaer M, Abdioglu M, Patel A and Cansiz A 2016 J. Alloys Compd. 689 1076
[8] Ai L, Zhang G, Li W, Liu G and Liu Q 2018 Physica C 550 57
[9] Yang W, Liao D, Ji Y and Yao L 2018 J. Appl. Phys. 124 213901
[10] Yu Z, Zhang G, Qiu Q, Zhang D, Sun X, Wang S, Liu Y, Feng W, Li W and Ai L 2019 J. Supercond. Nov. Magn. 32 1605
[11] Yang Y and Wu Y 2020 J. Appl. Phys. 128 053905
[12] Huang C, Xu B and Zhou Y 2020 J. Appl. Phys. 127 193907
[13] Antončík F, Lojka M, Hlásek T, Bartůněk V, Valiente-Blanco I, Perez-Diaz J L and Jankovský O 2020 Supercond. Sci. Technol. 33 045010
[14] Shi D, Qu D, Sagar S and Lahiri K 1997 Appl. Phys. Lett. 70 3606
[15] Tent B A, Qu D and Shi D 1998 Physica C 309 89
[16] Yang W, Zhou L, Feng Y, Zhang P, Chen S, Wu M, Zhang C, Wang J, Du Z, Wang F, Yu Z, Wu X, Gawalek W and Gorner P 1998 Physica C 307 271
[17] Yang W, Feng Y, Zhou L, Zhang P, Wu M, Chen S, Wu X and Gawalek W 1999 Physica C 319 164
[18] Zhao B, Deng Z, Hu Z, Liu Y, Zhang S and Zheng J 2020 IEEE Trans. Appl. Supercond. 30 6800305
[19] Ruiz-Alonso D, Coombs T A and Campbell A M 2005 Supercond. Sci. Technol. 18 S209
[20] Gou X, Zheng X and Zhou Y 2007 IEEE Trans. Appl. Supercond. 17 3795
[21] Zheng X and Yang Y 2007 IEEE Trans. Appl. Supercond. 17 3862
[22] Ma G, Wang J and Wang S 2010 IEEE Trans. Appl. Supercond. 20 2219
[23] Navau C, Del-Valle N and Sanchez A 2013 IEEE Trans. Appl. Supercond. 23 8201023
[24] Badía-Majós A, Aliaga A, Letosa-Fleta J, Alfonso M M and Roche J P 2015 IEEE Trans. Appl. Supercond. 25 3601810
[25] Sass F, Dias D H N, Sotelo G G and de Andrade Junior R 2018 Supercond. Sci. Technol. 31 025006
[26] Navau C and Sanchez A 2001 Phys. Rev. B 64 214507
[27] Valle N D, Sanchez A, Pardo E, Chen D X and Navau C 2007 Appl. Phys. Lett. 90 042503
[28] Bernstein P, Noudem J and Dupont L 2016 Supercond. Sci. Technol. 29 075007
[29] Bernstein P, Colson L, Dupont L and Noudem J 2017 Supercond. Sci. Technol. 30 065007
[30] Davis L C, Logothetis E M and Soltis R E 1988 J. Appl. Phys. 64 4212
[31] Alqadi M K 2015 Chin. Phys. B 24 118404
[32] Kordyuk A A 1998 J. Appl. Phys. 83 610
[33] Hull J R and Cansiz A 1999 J. Appl. Phys. 86 6396
[34] Yang Y and Zheng X 2007 J. Appl. Phys. 101 113922
[35] Zhang X, Zhou Y and Zhou J 2008 Physica C 468 401
[36] Wu X, Xu K, Cao Y, Hu S, Zuo P and Li G 2013 Physica C 486 17
[37] Cansiza A, Yildizerb İ and McGuiness D T 2019 Cryogenics 98 60
[38] Bernstein P and Noudem J 2020 Supercond. Sci. Technol. 33 033001
[39] Alzoubi F Y, Al-khateeb H M, Alqadi M K and Ayoub N Y 2005 Supercond. Sci. Technol. 18 1329
[40] Coffey M W 2000 Journal of Superconductivity 13 381
[41] Coffey M W 2002 Journal of Superconductivity 15 257
[42] Alqadi M K, Alzoubi F Y and Al-khateeb H M 2006 Mod. Phys. Lett. B 20 1549
[43] Al-khateeb H M, Alqadi M K, Alzoubi F Y and Ayoub N Y 2007 Chin. Phys. Lett. 24 2700
[44] Palaniappan D 2009 J. Supercond. Nov. Magn. 22 471
[45] Diez-Jimenez E, Valiente-Blanco I and Perez-Diaz J 2013 J. Supercond. Nov. Magn. 26 71
[46] Alqadi M K, Alzoubi F Y, Al-khateeb H M and Ayoub N Y 2009 Physica B 404 1781
[47] Sivrioglu S and Cinar Y 2007 Supercond. Sci. Technol. 20 559
[48] Sivrioglu S and Basaran S 2015 IEEE Trans. Appl. Supercond. 25 3601507
[49] Basaran S and Sivrioglu S 2017 Supercond. Sci. Technol. 30 035008
[1] Unified entropy entanglement with tighter constraints on multipartite systems
Qi Sun(孙琪), Tao Li(李陶), Zhi-Xiang Jin(靳志祥), and Deng-Feng Liang(梁登峰). Chin. Phys. B, 2023, 32(3): 030304.
[2] Entanglement and thermalization in the extended Bose-Hubbard model after a quantum quench: A correlation analysis
Xiao-Qiang Su(苏晓强), Zong-Ju Xu(许宗菊), and You-Quan Zhao(赵有权). Chin. Phys. B, 2023, 32(2): 020506.
[3] Transformation relation between coherence and entanglement for two-qubit states
Qing-Yun Zhou(周晴云), Xiao-Gang Fan(范小刚), Fa Zhao(赵发), Dong Wang(王栋), and Liu Ye(叶柳). Chin. Phys. B, 2023, 32(1): 010304.
[4] Probabilistic quantum teleportation of shared quantum secret
Hengji Li(李恒吉), Jian Li(李剑), and Xiubo Chen(陈秀波). Chin. Phys. B, 2022, 31(9): 090303.
[5] Energy levels and magnetic dipole transition parameters for the nitrogen isoelectronic sequence
Mu-Hong Hu(胡木宏), Nan Wang(王楠), Pin-Jun Ouyang(欧阳品均),Xin-Jie Feng(冯新杰), Yang Yang(杨扬), and Chen-Sheng Wu(武晨晟). Chin. Phys. B, 2022, 31(9): 093101.
[6] Nonreciprocal coupling induced entanglement enhancement in a double-cavity optomechanical system
Yuan-Yuan Liu(刘元元), Zhi-Ming Zhang(张智明), Jun-Hao Liu(刘军浩), Jin-Dong Wang(王金东), and Ya-Fei Yu(於亚飞). Chin. Phys. B, 2022, 31(9): 094203.
[7] Characterizing entanglement in non-Hermitian chaotic systems via out-of-time ordered correlators
Kai-Qian Huang(黄恺芊), Wei-Lin Li(李蔚琳), Wen-Lei Zhao(赵文垒), and Zhi Li(李志). Chin. Phys. B, 2022, 31(9): 090301.
[8] Dynamically tunable multiband plasmon-induced transparency effect based on graphene nanoribbon waveguide coupled with rectangle cavities system
Zi-Hao Zhu(朱子豪), Bo-Yun Wang(王波云), Xiang Yan(闫香), Yang Liu(刘洋), Qing-Dong Zeng(曾庆栋), Tao Wang(王涛), and Hua-Qing Yu(余华清). Chin. Phys. B, 2022, 31(8): 084210.
[9] Precisely controlling the twist angle of epitaxial MoS2/graphene heterostructure by AFM tip manipulation
Jiahao Yuan(袁嘉浩), Mengzhou Liao(廖梦舟), Zhiheng Huang(黄智恒), Jinpeng Tian(田金朋), Yanbang Chu(褚衍邦), Luojun Du(杜罗军), Wei Yang(杨威), Dongxia Shi(时东霞), Rong Yang(杨蓉), and Guangyu Zhang(张广宇). Chin. Phys. B, 2022, 31(8): 087302.
[10] Purification in entanglement distribution with deep quantum neural network
Jin Xu(徐瑾), Xiaoguang Chen(陈晓光), Rong Zhang(张蓉), and Hanwei Xiao(肖晗微). Chin. Phys. B, 2022, 31(8): 080304.
[11] Direct measurement of two-qubit phononic entangled states via optomechanical interactions
A-Peng Liu(刘阿鹏), Liu-Yong Cheng(程留永), Qi Guo(郭奇), Shi-Lei Su(苏石磊), Hong-Fu Wang(王洪福), and Shou Zhang(张寿). Chin. Phys. B, 2022, 31(8): 080307.
[12] Bifurcation analysis of visual angle model with anticipated time and stabilizing driving behavior
Xueyi Guan(管学义), Rongjun Cheng(程荣军), and Hongxia Ge(葛红霞). Chin. Phys. B, 2022, 31(7): 070507.
[13] Robustness of two-qubit and three-qubit states in correlated quantum channels
Zhan-Yun Wang(王展云), Feng-Lin Wu(吴风霖), Zhen-Yu Peng(彭振宇), and Si-Yuan Liu(刘思远). Chin. Phys. B, 2022, 31(7): 070302.
[14] Heralded path-entangled NOON states generation from a reconfigurable photonic chip
Xinyao Yu(于馨瑶), Pingyu Zhu(朱枰谕), Yang Wang(王洋), Miaomiao Yu(余苗苗), Chao Wu(吴超),Shichuan Xue(薛诗川), Qilin Zheng(郑骑林), Yingwen Liu(刘英文), Junjie Wu(吴俊杰), and Ping Xu(徐平). Chin. Phys. B, 2022, 31(6): 064203.
[15] Water contact angles on charged surfaces in aerosols
Yu-Tian Shen(申钰田), Ting Lin(林挺), Zhen-Ze Yang(杨镇泽), Yong-Feng Huang(黄永峰), Ji-Yu Xu(徐纪玉), and Sheng Meng(孟胜). Chin. Phys. B, 2022, 31(5): 056801.
No Suggested Reading articles found!