Abstract
Based upon the method of current vector potential and the critical state model of Bean, the vertical and lateral forces with different sizes of minor loop are simulated in two typical cooling conditions when a rectangular permanent magnet (PM) above a cylindrical high temperature superconductor (HTS) moves vertically and horizontally. The different values of average magnetic stiffness are calculated by various sizes of minor loop changing from 0.1 to 2 mm. The magnetic stiffness with zero traverse is obtained by using the method of linear extrapolation. The simulation results show that the extreme values of forces decrease with increasing size of minor loop. The magnetic hysteresis of the force curves also becomes small as the size of minor loop increases. This means that the vertical and lateral forces are significantly influenced by the size of minor loop because the forces intensely depend on the moving history of the PM. The vertical stiffness at every vertical position when the PM vertically descends to 1 mm is larger than that as the PM vertically ascents to 30 mm. When the PM moves laterally, the lateral stiffness during the PM passing through any horizontal position in the first time almost equal to the value during the PM passing through the same position in the second time in zero-field cooling (ZFC), however, the lateral stiffness in field cooling (FC) and the cross stiffness in ZFC and FC are significantly affected by the moving history of the PM.
Highlights
Since the discovery of high temperature superconductors (HTSs), the interaction between a permanent magnet (PM) and a bulk HTS has achieved attention, mainly due to its promising applications, such as magnetic bearing in flywheel system[1,2,3] and magnetic levitating transporter.[4]
The different values of average magnetic stiffness are calculated by various sizes of minor loop changing from 0.1 to 2 mm
The vertical and lateral forces with different sizes of minor loop are simulated in zero-field cooling (ZFC) and field cooling (FC) when the PM moves vertically and horizontally, respectively
Summary
Since the discovery of high temperature superconductors (HTSs), the interaction between a permanent magnet (PM) and a bulk HTS has achieved attention, mainly due to its promising applications, such as magnetic bearing in flywheel system[1,2,3] and magnetic levitating transporter.[4]. The dimensions of the PM and the HTS were finite.[22,23] The lateral force acting on a cylindrical superconductor in the field of a coaxial cylindrical PM was calculated.[22] The lateral and vertical forces were simulated using the current vector potential method, the hybrid finite and boundary element method and the critical state model.[23] The vertical and lateral forces were calculated using the modified frozen-image method when a PM above an HTS traverses in arbitrary directions.[24] To our knowledge, no theoretical calculation has been carried out to predict the effect of minor loop size on the magnetic forces. Most theoretical studies of magnetic stiffness were usually obtained by taking the derivative of vertical or lateral forces with respect to displacement.[20,25,26,27,28]. A numerical study on the magnetic forces with different sizes of minor loop has been performed by using the method of current vector potential (T) and the critical state model of. The magnetic stiffness under the different moving mode and cooling conditions is presented
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