A survey of phase-locking in the dc and ac-driven Josephson transmission line

We present a review of the dynamical states of the long Josephson junction when dc and ac currents are considered as bias terms. When only the dc terms are present, depending on the value of the external magnetic field, the excitations consists of fluxon oscillations, cavity modes and travelling waves interactions with the Josephson effect. These three different modes generate well identified singularities in the current-voltage characteristics. We also report on the effect that ac current terms applied to the transmission line can have on these current singularities. In this case a theoretical analysis, based on the nature of dc excitations, has provided predictions for the ranges of locking of the external signal to junction’s oscillations. These predictions are in good agreement with experimental and numerical data that have been reported in the literature.