Chaotic Motions in Dynamic High-Tc Superconducting Levitation System with Thermal Effects
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Chaotic Motions in Dynamic High‑Tc Superconducting Levitation System with Thermal Effects Yi Huang1 · Zhong‑Cheng Qin1 · Fu‑Jin Ma1 Received: 5 December 2018 / Accepted: 8 June 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract The chaotic motions were shown by the vibrations of a bulk permanent magnet (PM) supported by a cylindrical high-Tc superconductor (HTSC) under external disturbance in very early experiments. There are few theoretical studies on the nonlinear behaviors of the HTSC levitation system as the complex interaction between the HTSC and PM. In this paper, we developed a numerical program to analyze the nonlinear vibrations of the levitated PM coupled with the electromagnetic force, taking into account the heat diffusion on HTSC. When the levitation system displayed chaotic oscillations by vertical excitation, the electromagnetic and thermal characteristics of the HTSC will change. The dynamic responses are shown by comparing the calculation results in which the thermal effects are taken into account and not. The numerical results display the displacements of PM, magnetic levitation forces, the acceleration, and the maximum Lyapunov exponent. The results show that the thermal effect will influence the stability of the levitation system. Keywords Levitation system · Thermal effects · High-temperature superconductor · Chaotic motions
1 Introduction The high-Tc superconductor (HTSC) has been one of the most interesting research topics as it can obtain high critical current density and high trapped field in many magnetic devices, such as magnetic bearings [1], traffic system [2], and trapped field magnets [3]. The passive levitation system with the HTSC is an essential practical application due to its self-stability without energy input. The strong electromagnetic forces between an HTSC and a permanent magnet (PM) caused by flux pining can
* Yi Huang [email protected] 1
College of Science, Guangxi University for Nationalities, Nanning 530006, Guangxi, People’s Republic of China
13
Vol.:(0123456789)
Journal of Low Temperature Physics
make the levitation system self-regulate. Thus, obtaining a higher magnetic force and higher stabilization is essential. Since the motions of flux-line lattices inside the HTSC are related to the critical current density and the magnetic force [4], the levitation system consisting of an HTSC and a PM in the stable case has been comprehensively investigated for decades. For example, the flux flow and flux creep caused by the motions of flux lattices are essential reasons for the time decay of the levitation force [5, 6] and the drift phenomenon [7, 8]. Moon et al. [9, 10] observed period doubling and chaotic oscillations by vertical vibrations of the HTSC levitation system. Philippe [11] analyzed the nonlinear motions of superconducting levitation systems under external excitations by the complex relation between HTSC and PM. Huang [12] experimentally researched on the bifurcation of the levitation system in the vertical directio
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