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

Numerical methods are used to analyze the Ginzburg-Landau equations for a superconducting plate carrying transport current in a magnetic field. Critical current is calculated as a function of the applied magnetic field strength for superconducting plates with different thicknesses. The relations between the field dependence of critical current and the distributions of order parameter, magnetic field, and supercurrent in a plate are analyzed. The field-dependent critical currents computed for plates are used to determine the critical current as a function of the applied magnetic field strength and local magnetic field and current distributions for multilayers in parallel magnetic fields. The constituent superconducting layers are assumed to interact only via magnetic field. 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 zero applied magnetic field. The method can be used to analyze experimental results.