Time behaviour of order parameter perturbations near the surface of a superconductor

Abstract

The time-dependent Ginzburg-Landau (GL) equations have been used for calculating some problems associated with the possibility of creation and penetration of flux lines near the surface of superconductors. Using the solutions of the static GL equations and modifying the time-dependent GL equation for the order parameter by simple coordinate transformations, the time behaviour of special forms of order parameter perturbations (pointlike, linear, laminar) is obtained in analytical form, suitable for further use in the iteration procedure, outlined also in this paper. All the treated perturbation forms are suitable for obtaining analytical solutions, at least for small times after the perturbation. The correctness of the used approximations is verified for the laminar perturbation. Some preliminary results for this form of perturbations, as well as for linear perturbations parallel to the vector potential, are also given.