A new method for determining the critical state of three-dimensional superconductors: explanation and examples

A new numerical method for solving the critical state is explained and examples of its use are given. The relation describes three-dimensional superconductors interacting with three-dimensional magnetic fields. The method is based on a constitutive relation between current density and local magnetic flux density. No gauge ambiguities arise. A free energy is constructed that is concomitant with the constitutive relation and it is shown that this model describes both reversible behavior and current saturation. The numerical examples, describing several magnetization experiments, confirm that the currents screen the interior of the superconductor from applied fields in the way suggested by the critical state model. Our experience shows that our approach is simple enough to be implemented with relatively inexpensive, commercial software on desktop computers.