中国物理B ›› 2021, Vol. 30 ›› Issue (12): 127401-127401.doi: 10.1088/1674-1056/ac0697

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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. 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
  • 收稿日期:2021-03-10 修回日期:2021-04-16 接受日期:2021-05-29 出版日期:2021-11-15 发布日期:2021-11-23
  • 通讯作者: Yong Yang E-mail:yangyong@xidian.edu.cn
  • 基金资助:
    Projects supported by the National Natural Science Foundation of China (Grant No. 11572232) and the China Three Gorges Corporation Research Project (Grant No. 202103407).

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. 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
  • Received:2021-03-10 Revised:2021-04-16 Accepted:2021-05-29 Online:2021-11-15 Published:2021-11-23
  • Contact: Yong Yang E-mail:yangyong@xidian.edu.cn
  • Supported by:
    Projects supported by the National Natural Science Foundation of China (Grant No. 11572232) and the China Three Gorges Corporation Research Project (Grant No. 202103407).

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摘要： 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.

关键词: high-temperature superconductor, magnetic dipole, frozen-image model, angle

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.

Key words: high-temperature superconductor, magnetic dipole, frozen-image model, angle

中图分类号:  (Cuprate superconductors)

  • 74.72.-h
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)