CRITICAL-STATE IN THIN SUPERCONDUCTORS - A JOSEPHSON-JUNCTION ARRAY ANALOGY

The Josephson junction array is numerically simulated to study the vor tex 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 obta ined 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 lin ear distribution for the 3D case (N=0) is studied phenomenologically b y increasing the thickness of the superconducting islands forming the array. Increasing the thickness of the array effectively reduces the s trength of the non-local interaction between currents and fields. The M-H curve and the field distribution within the array are calculated f or field independent and field dependent critical currents of the Jose phson junction. We also probe in detail the evolution of the field and the current distribution towards their equilibrium values after an ex ternal field is applied. The results are discussed and compared with a nalytical results of the critical state model for a thin superconducti ng strip in a transverse magnetic field. (C) 1997 Elsevier Science B.V .