Approximate boundary conditions in a circular conductor and their application to nonlinear vibration analyses of high-Tc superconducting levitation system

When a levitated superconductor vibrates, the levitation force has nonlinear relationship among an air gap, amplitude, and frequency, so the usual static analysis for levitation forces is invalid. There are two phenomena of a flux creep and flux flow when the conductor vibrates in a magnetic field. The present article provides an analytical result for the levitation forces of a thick superconducting disc with consideration of the phenomena and effects of flux variations on the critical current. It is significantly difficult to have the analytical result of levitation force by using the exact boundary conditions. This paper presents approximate boundary conditions which give an appropriate result. To validate the proposed boundary conditions, eddy currents in a conductor are first discussed, then the superconductor is discussed. Numerical results for the levitation forces were obtained and compared with the previously published experimental data. The levitation force becomes a restoring force having the nonlinear relationship, so it is difficult to solve vibrations. The present article gives a simplified method for solving nonlinear vibration problems for the levitated conductor. Numerical calculations were carried out for some typical examples