Intermediate state in a type-I superconducting sphere: Pinning and size effect

Simulations based on the time-dependent Ginzburg-Landau equations show that the magnetization and spatial structure of the intermediate state are strongly affected by both the radius of the sphere and by the concentration of pinning centers. The intermediate state undergoes a transformation from a one-domain structure for a small sphere to a multi-domain structure in big spheres. In spheres where part of the superconducting material is replaced by the 0.5% randomly distributed normal phase (dirty case), the intermediate state demonstrates a pronounced turbulence behavior.