Magnetization of a type-I superconducting slab in the thermodynamic and the metastable phases

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Abstract
The first magnetization law of an infinite slab of rectangular cross section, in a perpendicular applied field, is worked out along general ideas previously published. By neglecting penetration in the edges of the slab, assumed of small thickness, the complex potential is obtained in a simple way with the help of two successive Schwarz-Christoffel conformal mappings. The construction of the thermodynamic potential permits a detailed analysis of the ideal thermodynamic behavior which is, then, compared with the real one, based on a migration mechanism. Explicit calculations of the magnetic moment along with the thermodynamic and migration thresholds are carried out. The migration process is shown to give rise to a metastable phase, including a macroscopic current, and responsible for the currently observed hysteretic behavior.