Critical state in type-II superconductors of arbitrary shape

The well-known Bean critical state equations in general are not sufficient to describe the critical state of type-II superconductors when the sample shape is not symmetric. We show how one can find the critical state in superconductors of arbitrary shapes. Analyzing a simple example of nonsymmetry, we demonstrate that in the general case, a perturbation of the current distribution in the critical state propagates into the sample smoothly in a diffusive way. This is in contrast to the usual Bean critical state where the current distribution changes abruptly at a narrow front.