Theory of flux penetration into thin films with field-dependent critical current

A theoretical analysis is presented for the critical state of an infinitely long type-II superconducting strip characterized by an arbitrary critical current density ${\mathit{J}}_{\mathit{c}}$(B). An analytical framework is developed, and numerical solutions are presented for the quasistatic current-density and flux-density profiles, as well as the hysteretic magnetization curves. The field dependence of the critical current density significantly affects the shape of the magnetization curves.