Linear arrays of Josephson junctions: A stability analysis of characteristic modes

Abstract

We have performed a linear stability analysis of two arrays of resistively shunted Josephson junctions: a ladder array and a so-called modified linear array. We find the periodic solutions to be linearly stable for a wide range of bias currents in the absence of a load. This is contrasted with the well-studied globally coupled linear array, where stability of the periodic solutions is a sensitive function of bias current and load parameters. For the ladder array, we have studied the nature of the mesh currents for the different decay modes. Numerical evidence leads us to conclude that the branches of the ladder parallel to the bias current play an important role in helping to damp out perturbed currents. We also compare the long-time dynamics of these Josephson-junction arrays with that of an RL network, which is a ladder of resistors and inductors, and for which the decay rates and mesh currents are calculated exactly. We find that at long times the dynamics of all three arrays are basically identical.