Crossing in the magnetic force-gap hysteresis curve of magnetic levitation systems with a high-Tc superconductor

For the magnetic levitation system consisting of a high-T_c superconductor and permanent magnet, the relation curve of magnetic force with gap between these two components is known as a hysteresis loop, that is, the approaching and departing portions envelop a complete one, and generally these two portions do not cross each other. However, in some special cases this crossing arises, and makes the complete loop broken. In this paper, by the numerical simulation of the magnetic force-gap curve in large numbers of physical and geometrical parameters, two typical crossings were found. To investigate the crossing and explore its physical causes, for one of the crossings, the current density in the superconductor was further calculated and its magnitude and vector distribution at the gaps nearby where the crossing arises were obtained. Based on these calculation results and an adequate discussion, the conclusion was induced that the crossing in the magnetic force-gap hysteresis curve results from applied magnetic field’s incomplete and insufficient penetrating in superconductor.