Numerical Study of the Influence of Defect on the Material Side in Vortex-Antivortex Formation Based on TDGL Equation

Abstract

Dynamics of vortex-antivortex (VAV) annihilation due to a defect in the side of material has been successfully studied using TDGL Equation. This study was to find out how is the potential curve (V-t) when VAV annihilation occurs. Type II superconductor with κ = 1.3 and size of Lx × Ly = 50ξ0 × 50ξ0 was used here. This study was based on a numerical solution of the TDGL Equation by means of finite difference method with FTCS (Forward Time Centered Space) Scheme. The external current density J e = J e i was applied to the material without applying external magnetic field He . That is the way to bring up antivortex on the bottom of material and vortex on the upper of material. The defects were prepared with the size of 0.3ξ0 × 1ξ0. The defect on the material gives effect to the presence of vortex and antivortex. VAVs can only enter the material through the defect and not enter through another side. This is showing that the defect on the material provides the force which causes VAV more easily enter the material at the defect than another side. VAVs will enter continuously until they will meet each other and the annihilation of VAV occurs in the middle of the material. The sharp pulses (the high peak pulse) appeared during the vortex and antivortex annihilating each other. Besides, the small pulses raised the vortex and antivortex when they entered the material. When annihilation occurred, the potential curve produced the very high potential value for a moment and returned to its normal potential state. The presence of the defect on the material can increase superconductivity of material as well.