A Hierarchy of Models for Superconducting Thin Films

A hierarchy of models for type-II superconducting thin films is presented. Through appropriate asymptotic limits this hierarchy passes from the mesoscopic Ginzburg-Landau model to the London model with isolated vortices as δfunction singularities, to vortex-density models and finally to macroscopic critical-state models. At each stage it is found that a key nondimensional parameter is Λ = λ2/dL where λ is the penetration depth of the magnetic field, a material parameter, and d and L are a typical thickness and lateral dimension of the film respectively. The models simplify greatly if this parameter is large or small.