Study On Magnetic Stiffness Of High-T_c Superconducting Levitation Systems Under Field Cooling Conditions

Magnetic stiffness is one of the important physical parameters to high-Tc superconducting levitation systems(HTS). There are some reletant problems to be solved in application including high temperature superconducing magnetic bearings and high temperature supercondcting maglev. The study on magnetic stiffness plays an important role in superconductivity. Many groups have paid their attention on this area. In this Ph.D. thesis the characteristics of magnetic stiffness of high-Tc superconducting system under two kinds of field cooling conditions are investigated. A few of new relations between magnetic stiffness and the parameters of HTS are found, using the internal current penetration and magnetic field in superconducting bulk, and the results are explained.Based on Kim critical model and Maxwell equations, a semi analytical implicit equation on shielding currents penentration in bulk is presented. The relation between shielding currents and magnetic field is considered in this equation. The chacteristics of magnetic levitation force is showed based on the solution of the equation. Furtherly, the rule on the levitation force including the parameters of HTS are discussed.The traditional program for magnetic stiffness data is analysized. These data may be about experiments or simulations. A new method for data processing is presented, which is named limited-fitting method. The results using this method to gain magnetic stiffness is believed to be effective. Based on the limited-fitting method, the chacteristics of HTS under ascending-descending field cooling condition are showed. The dependences of magnetic stiffness on the parameters of HTS are researched in detail, which can be explained with the change of shielding currents and internal magnetic field.The physical difference between descending-ascending(DA) field cooling condition and ascending-descending one(AD) is provided. We pay more attention to the mechanics behavior of magnetic stiffness of HTS under DA condition and AD one, such as the influence of field cooling heiths. The dependences of magnetic stiffness on critical currents、applied magnet field and thickness etc of HTS are presented. In addition, a preliminary idea about instant cotrolling on high temperature superconducting levitation system is showed considering penetration of shielding currents.Finally, the dynamic characteristics such as angular frequency 、 dynamical magnetic stiffness and relative damping factor are discussed. The dynamical differential equation is solved using the fourth-order Runge-Kutta method based on Kim critical electro-magnetic model and Ampère circular law. The angular frequency and the dynamical magnetic stiffness are found to be changed with time. The Logistic relation is employed to associate the dynamical magnetic stiffness changing with time. The dependence of dynamical magnetic stiffness on field cooling height is investigated. The relative damping factor of high-Tc superconducting system changes with time and field cooling heights. The effect of crtical current density constant intior of HTS on the dynamical magnetic stiffness is given in this thesis.