Generalization of Landau's laminar model to superconducting plate with finite thickness

Landau's laminar model is generalized to the case of a plate with finite thickness d by considering the mutual influence of its both-side surfaces. By using a modified Schwartz-Christoffel transformation and a conformal mapping, the parametric expression of N-S boundaries has been derived. The quantities, such as domain period and fraction of the normal phase, which realize the feature of laminae are given in the form of parametric expression. The computed result based on free energy minimization depends on characteristic parameter Δ/d, where Δ is the surface energy parameter. It is also shown that the present result agrees with the experimental result by Davies on the reduction of the critical field of a thin plate in a perpendicular magnetic field. (auth.)