Studies of coated and polycrystalline superconductors using the time dependant Ginzburg-Landau equations
Time-dependent Ginzburg-Land au equations are used to model 2D and 3D systems containing both superconductors and normal metals, in which both T(_c) and normal-state resistivity are spatially dependent. The equations are solved numerically using an efficient semi-implicit Crank-Nicolson algorithm. The algorithm, is used to model flux entry and exit in homogenous superconductors with metallic coatings of different resistivities. For an abrupt boundary there is a minimum field of initial vortex entry occurring at a kappa-dependent finite ratio of the normal-state resistivities of the superconductor and the normal metal. Highly reversible magnetization characteristics are achieved using a diffusive layer several coherence lengths wide between the superconductor and the normal metal. This work provides the first TD GL simulation in both 2D and 3D of current flow in polycrystalline superconductors, and provides some important new results both qualitative and quantitative. Using a magnetization method we obtain Jc for both 2D and 3D systems, and obtain the correct field and kappa dependences in 3D, given by F = 3.6 x 10-4 B}l (T) (1- b)2. The pre-factor is different (about 3 to 5 times smaller) from that observed in technological superconductors, but evidence is provided showing that this prefactor depends on the details of 1կ effects at the edges of superconducting grains. In 2D, the analytic flux shear calculation developed by Pruymboom in his thin-film work gives good agreement with our computational results.Visualization of Iぜ and dissipation (including movies in the 2D case) shows that in both 2D and 3D, Jc is determined by flux shear along grain boundaries. In 3D the moving fluxons are confined to the grain boundaries, and cut through stationary fluxons which pass through the grains and are almost completely straight.