Surface Tension and Kinetic Coefficient for the Normal/Superconducting Interface: Numerical Results vs. Asymptotic Analysis

The dynamics of the normal/superconducting interface in type-I superconductors has recently been derived from the time-dependent Ginzburg-Landau theory of superconductivity. In a suitable limit these equations are mapped onto a ``free-boundary'' problem, in which the interfacial dynamics are determined by the diffusion of magnetic flux in the normal phase. The magnetic field at the interface satisfies a modified Gibbs-Thomson boundary condition which involves both the surface tension of the interface and a kinetic coefficient for motion of the interface. In this paper we calculate the surface tension and kinetic coefficient numerically by solving the one dimensional equilibrium Ginzburg-Landau equations for a wide range of $\kappa$ values. We compare our numerical results to asymptotic expansions valid for $\kappa\ll 1$, $\kappa\approx 1/\sqrt{2}$, and $\kappa\gg 1$, in order to determine the accuracy of these expansions.