Numerical simulation of vortex dynamics in type-II superconductors in oscillating magnetic field using time-dependent Ginzburg–Landau equations

Abstract

Time-dependent Ginzburg-Landau equations were solved by the finite difference scheme for a superconducting sample in steady and oscillating magnetic fields for 3D geometry. The dynamic behaviour of penetrating and leaving magnetic vortices in superconductor with the oscillating magnetic field was simulated. Carrier concentration density and the average magnetization of the sample were studied as a function of the external oscillating magnetic field. Anomalies in carrier concentrations at certain magnetic field values were observed and discussed. It was also observed that the area swept by magnetization versus external magnetic field is magnetic oscillation frequency dependent, which increases with increasing frequencies. It was suggested that this effect may cause instability in the superconducting characteristics of the sample over a number of cycles. Calculated energy patterns showed consistency with vortex patterns in the steady magnetic field. Magnetic oscillations initiated oscillations in energy components, ripples in superconducting energy are subjected to the entrance and leaving of vortices, while instability observed in interaction energy is referred to vortex relaxation time.

Effect of Background Magnetic Field on Type-II Superconductor under Oscillating Magnetic Field Simulated Using Ginzburg-Landau Model

“…The frequency of this variation depends on the speed of the HTS on PM guideway (i.e., speed of the vehicle). The magnetic field in such a case is not exactly oscillating (which was reported earlier [18]), but it is (practically) a constant magnetic field having small jitters (or oscillations) in its amplitude appearing due to imperfections in PM guideway. In this work, we studied such a magnetic field and compared the results with results reported earlier for perfectly oscillating magnetic fields [18].…”

“…The magnetic field in such a case is not exactly oscillating (which was reported earlier [18]), but it is (practically) a constant magnetic field having small jitters (or oscillations) in its amplitude appearing due to imperfections in PM guideway. In this work, we studied such a magnetic field and compared the results with results reported earlier for perfectly oscillating magnetic fields [18]. To investigate this type of energy loss, we studied the behavior of type-II superconductor exposed to an oscillating magnetic field simulated using time-dependent Ginzburg-Landau (TDGL) equations [15,26,27] near critical temperature with and without an additional static background magnetic field.…”

“…Link variable schemes [16,17,36] are the most commonly used schemes to solve coupled GL equations. In the present work, in order to investigate carrier concentration, magnetization, and vortex dynamics in superconductor, we used coupled nonlinear TDGL equations (8) and (9) solved by finite difference scheme using link variables, described by Winiecki and Adams [16], implemented in three-dimensional code we have developed [18]. Equations (8) and (9) along with boundary condition equations (5) and (6) form the basis of the present work.…”

“…Gorkov [15] proved that close to critical temperatures microscopic BCS theory also reduces to GL theory. Various numerical methods, including finite difference [16][17][18], finite element [19][20][21], and spectral method [22], have been developed for the solution of this model. In this report, we used the semiimplicit finite difference method with staggered grid scheme.…”

Phase-Field Simulation of Superconductor-Ferromagnet Bilayer-Based Cryogenic Strain Sensor

“…To study the vortex structure in type-II superconductors, the phenomenological Ginzburg-Landau theory was used. Time-dependent Ginzburg-Landau (TDGL) equations, developed by GoR'Kov and Eliashberg [20], were used with the version of equations reported in references [21][22][23]. Gibbs free energy within the domain of Ginzburg-Landau model, in terms of superconducting order parameter ψ (primary order parameter) and magnetic vector potential A (secondary order parameter), is given as ( 1)…”