Ferromagnetic substrate influences the electromagnetic response of a type-II superconducting film to the applied magnetic field. We present a two-dimensional integrodifferential model for the magnetization of a flat superconductor/ferromagnet bilayer of an arbitrary shape using a thin shell quasistatic model for the ferromagnetic substrate and an infinitely thin approximation for the superconducting layer. An efficient numerical method is developed and used to investigate the effect of a ferromagnetic substrate. In particular, we simulate the thin bilayer magnetization in a parallel field and, for a high field, the critical-state distributions of the superconducting current density. These critical-state distributions are different from those known for a normal external field.

翻译：铁磁基底影响第二类超导薄膜对施加磁场的电磁响应。我们基于铁磁基底薄壳准静态模型与超导层的无限薄近似，针对任意形状的平坦超导/铁磁双层结构，提出了一个二维积分-微分磁化模型。开发了高效数值方法，并用于研究铁磁基底的影响效应。特别地，我们模拟了平行磁场中薄层双层的磁化强度，以及高场条件下超导电流密度的临界态分布。这些临界态分布与已知的法向外部场分布存在差异。