Perturbative analysis of long Josephson junctions having uniform bias and spatially varying penetration depth

Abstract

The effect that a uniform bias current has on the basic theoretical structure of a simple perturbation theory relating to single fluxon motion on long Josephson junctions is discussed. By including the bias directly into the general framework of the theory, it is possible to arrive at a fundamental limitation on the maximum value for the bias above which the validity of the usual power balance expression relating the loss factors, and the voltage to the applied current cannot be justified. As part of this effort, an interpretive generalization of the original theory is provided. This theory is then used to illustrate the way in which a step-wise variation in the London penetration depth affects the propagation of solitons on long junctions, and the influence that this has on the junction I-V curve. In the process of developing this theory and applying it to this problem, a formal connection was found between certain aspects of this approach and the technique outlined by McLaughlin and Scott. The results of the theoretical calculations are also shown to be in good agreement with experimental data.

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