Calculation of critical states of superconducting multilayers based on numerical solution of the Ginzburg-Landau equations for superconducting plates

Abstract

The numerical method is used to analyze the critical state of superconducting multilayers. The method is based on self-consistent solutions of the Ginzburg-Landau system of nonlinear equations, which describe the behavior of a superconducting plate carrying transport current in a magnetic field, provided that there are no vortices inside the plate. The field-dependent critical currents computed for plates are used to determine the critical current as a function of the applied magnetic field strength, local magnetic field, and current distributions for multilayers in parallel magnetic fields. The mutual influence of the superconducting layers is assumed to be realized only via a magnetic field. The method makes it possible to account for the peak effect in multilayered superconductors. Our results give an alternative approach to explain different scaling laws that describe flux pinning in the two most common commercial superconductors, NbTi and ${\mathrm{Nb}}_{3}\mathrm{Sn}$. A simple method is proposed for analyzing the critical states of multilayers in magnetic fields of arbitrary strength, based on elementary transformations of the critical current-density distribution over individual layers in a zero applied magnetic field.