First-stage magnetization and metastable migration field in a type I superconducting slab

The penetration of the field in the edge of a type I superconducting slab, placed in a uniform magnetic field, perpendicular to its plane, is analyzed by means of a suited complex potential, derived from general methods used in Dirichlet's type problems. The way of taking into account the singularities of the field distribution at the ends of the edge structure in the intermediate state, and the boundary conditions are discussed. A computational method is described for calculating the potential and flux profiles along the edges and thereby, the thermodynamic potential of the system. The first stage magnetization law together with the equilibrium dimensions of the edge structure and the previously defined migration threshold are deduced from the theory