Dynamical analysis to the levitated systems of high temperature superconductors with hysteresis

Dynamic behavior and penetration history of shielding currents distribution associated with the hysteresis of magnetic levitation force are investigated to the vertically mechanical oscillation of a permanent magnet (PM) which is magnetically levitated over a YBCO superconductor based on Bean’s critical-state model and Ampére circulation theorem. After the shielding current distribution is analytically derived out from the Maxwell’s equations of the electromagnetic system to each monotonic procedure of the hysteresis, the dynamic differential equation of the levitation is solved to the damped free vibration of the system using the adaptive Runge–Kutta approach of order 4. The obtained results display that the partially wiping-out phenomenon of shielding currents always happens in the interior of the superconductor such that the PM experiences a damped vibration. It is found that the damping generated from the hysteresis in the superconductor is time-changeable in the whole response, and that the frequency of vibration or magnetic stiffness increases with time during the first four periods of the response, as well as that the maximum penetration depth, δp, of the shielding currents at the end of each procedure of the hysteresis decays with time or turning number, Ntur, i.e., δp=eα0-α1Nturδp=eα0-α1Ntur where α0 and α1 are the fitting coefficients.