Numerical Simulation of Phase Transitions in Type-II Annular Superconductor Using Time-dependent Ginzburg-Landau Equations

Time-dependent Ginzburg-Landau equations were solved by finite element method in two-dimensional space for order parameter and energy components of the annular superconducting sample in steady magnetic fields. Vortices preferred to penetrate from the inner surface of the annulus due to lesser energy required at the concave surface. A transition magnetic field strength was observed in spatial averages of carrier concentration and energy components, showing small bumps and abrupt variations, indicating phase transition from a non-vortex to vortex state. These effects were observed to repeat with every subsequent entry of a set of vortices into the sample; transition magnetic field strength was found to depend inversely on the annular width of the sample. The present work gives a better understanding of energy variations during phase transition from non-vortex to vortex state and predicts that vortex state can be avoided by tuning the wire thickness in practical applications, e.g., superconducting electromagnets.