Critical state in thin superconductors: a Josephson junction array analogy

Abstract

The Josephson junction array is numerically simulated to study the vortex dynamics in a thin superconductor in a transverse magnetic field. The non-local interaction between currents and fields is incorporated in the dynamics by considering the full inductance matrix of the array. The field and the current distribution in the array are obtained for various applied fields which shows striking similarity with that obtained in the critical state model for a superconductor in the 2D limit (thin film geometry). The cross-over from a non-linear distribution of the field for the 2D limit (demagnetisation factor N → 1) to a linear distribution for the 3D case (N = 0) is studied phenomenologically by increasing the thickness of the superconducting islands forming the array. Increasing the thickness of the array effectively reduces the strength of the non-local interaction between currents and fields. The M-H curve and the field distribution within the array are calculated for field independent and field dependent critical currents of the Josephson junction. We also probe in detail the evolution of the field and the current distribution towards their equilibrium values after an external field is applied. The results are discussed and compared with analytical results of the critical state model for a thin superconducting strip in a transverse magnetic field.