Estimates of the upper critical field for the Ginzburg—Landau equations of superconductivity

摘要

In this paper we study the effects of an applied magnetic field on a superconductor and estimate the value of the upper critical magnetic field H_(C_3) at which superconductivity can nucleate. In the case of a spatially homogeneous applied field. we show that H_(C_3) approx= k/#beta#0, the ratio of the Ginzburg—Landau parameter k and the first eigenvalue #beta#0 of a twisted Laplacian operator, and that superconductivity nucleates at the boundary when the applied field is close to H_(C_3). In the case of a spatially non-homogeneous applied field, we give an estimate for the upper critical value and find that superconducting properties may persist only in the interior or the domain. In addition, we show that the order parameter concentrates at the minimum points of the applied field.