Manipulation of Fluxoid by Electromagnetic Perturbation

Abstract

yDepartment of Electrical Engineering, Kyoto UniversityKatsura, Nishikyo, Kyoto 615-8510, JapanContact email(TH): hikihara.takashi.2n@kyoto-u.ac.jpAbstract —The Time-Dependent Ginzburg-Landau(TDGL) equation is known as a nonlinear equation thatenables us to reproduce variously-scaled physical phenom-ena represented by the Ginzburg-Landau equation. In thispaper, we numerically discuss the dynamics of uxoidsin type-II superconductors based on the TDGL equation.In particular, we discuss the dynamics of trapping of auxoid at a pinning point and the release by an externalperturbation by electromagnetic wave. The manipulationof uxoid by the perturbation gives us an approach toquantum systems by classical dynamics.1. IntroductionType-II superconductors show the mixing state of uxpenetrated into bulk/lm. The ux is spatially quantizedin the superconductor [1]} The quantized ux is calleduxoid. Fluxoids are pinned at low potential wells causedby impurities in the superconductor. The normal conduc-tion particles, clacks, and so on become the impurities ofcrystal. The pin is surrounded by superconducting current,which traps a uxoid in it. The gradient of potential aroundthe pin becomes negative. That is, the uxoid is attracted.In addition, the force strongly depends on the magneticcharacteristics of superconductor, so that the hysteric char-acteristics appear in the pinning force and magnetic eldrelationship. The hysteric characteristics produce the pos-sibility of high potential magnets which can be applied inmagnetic levitation systems [2]. The application of bulksuperconductor is clear but the physics of the uxoid is notthe level of analysis in nonlinear dynamics.The distribution of magnetic ux for type II supercon-ductor can be described by Time-Dependent Ginzburg-Landau (TDGL) equation [3]} There have been amount ofsimulations based on the equation for estimating uids andphysics of ux pinning [4, 5]. This paper focuses on thedynamics of uxoid in type II superconductor by numeri-cal simulations of TDGL equation. In particular, the ma-nipulation of uxoid is considered through a perturbationby electromagnetic wave.2. TDGL Equation and Model of Type II Superconduc-torFor the analysis of uxoid in a thin lm consisting oftype II superconductor, a mathematical model based onTDGL equation is introduced. Figure 1 approximates a2D model of superconducting thin lm. The thin lm is asquare with L