Boundary-Layer Behavior in the Superconductor Transition Problem

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Abstract
A superconducting material may be isothermally transformed to a normal conductor by raising the magnetic field to a value greater than a certain critical field. When this is done, the transition takes place along an interface, determined by the critical field value and by a magnetic-flux condition. In the present paper, the effect on the transition rate of magnetic-field penetration into the superconductor is studied. This involves the solution of a free-boundary problem in which the free boundary divides two regions, each governed by a different parabolic differential equation. The problem is solved by using the asymptotic techniques of singular perturbation theory. A boundary layer is shown to exist along the moving interface on the superconducting side. The presence of the boundary layer slows the motion of the free boundary. Also included in the solution is a study of the effect of the magnitude of the initial field on the starting motion of the free boundary. Finally, some numerical results are presented.

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