Limiting Models for Josephson Junctions and Superconducting Weak Links

One of the broadest applications of superconductivity is the technology based on Josephson junction devices. These junction devices are formed by placing a thin layer of normal (nonsuperconducting) material between layers of superconducting material. We consider various limiting cases for models of the junction device based on the Ginzburg–Landau equations. Examples include a model for large values of the Ginzburg–Landau parameter, κ, in the high-field regime and a model for a thin normal layer. Convergence analysis for the simplified models is established and numerical simulations are presented.