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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

Minor loop dependence of the magnetic forces and stiffness in a PM-HTS levitation system