Magnetic stiffness is one of the important stability parameters of high temperature superconducting levitation systems. Till to now, great efforts have been made to understand levitation properties including flux penetration, magnetization curves, levitation force, ac susceptibilities, etc. In thispaper we present a quadratic approximation method for the limit of magnetic stiffness in a high temperature superconducting levitation system based on Kim’s critical state model and Ampère law. The system is composed with a cylindrical permanent magnet (PM) and a coaxial high temperature superconductor (HTS). It is found that the limit of magnetic stiffness depends upon both the penetration history of shielding currents distribution in HTS and applied magnetic field gradients. Furthermore, the influence of the physical parameters, such as critical current density in HTS and applied magnetic field, on the limits of magnetic stiffness is investigated in detail. The obtained results display that magnetic stiffness decreases with the increasing of critical current density, since shielding currents have not penetrated into the large portion of the HTS. With the increase of applied magnetic field, the magnetic stiffness obtain a larger magnification factor. It is related to the increase of the shielding current penetration volume and the internal magnetic field in HTS.

中文翻译：

---

物理参数对高Tc超导悬浮系统磁刚度极限的影响

磁刚度是高温超导悬浮系统的重要稳定性参数之一。到现在为止，人们已经做出了很大的努力来理解悬浮特性，包括磁通量穿透，磁化曲线，悬浮力，交流磁化率等。在本文中，我们提出了一种基于高温超导悬浮系统的磁刚度极限的二次近似方法。关于金的临界状态模型和安培定律。该系统由圆柱形永磁体（PM）和同轴高温超导体（HTS）组成。已发现，磁刚度的极限既取决于HTS中屏蔽电流分布的穿透历史，也取决于施加的磁场梯度。此外，物理参数的影响 如高温超导中的临界电流密度和施加的磁场，在磁刚度的极限上进行了详细研究。所获得的结果表明，由于屏蔽电流尚未渗透到HTS的大部分中，因此磁强度随临界电流密度的增加而降低。随着施加磁场的增加，磁刚度获得较大的放大倍数。这与HTS中屏蔽电流的穿透量和内部磁场的增加有关。随着施加磁场的增加，磁刚度获得较大的放大倍数。这与HTS中屏蔽电流的穿透量和内部磁场的增加有关。随着施加磁场的增加，磁刚度获得较大的放大倍数。这与HTS中屏蔽电流的穿透量和内部磁场的增加有关。