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The purpose of this work is to compare the dynamics of arrays of Josephson junctions in the presence of a magnetic field in two different frameworks: the so-called XY frustrated model with no self-inductance and an approach that takes into account the self-field generated by the screening currents (considering self-inductances only). We show that, while for a range of parameters the simpler model is sufficiently accurate, in a region of the parameter space solutions arise that are not contained in the XY model equations. \textcopyright{} 1996 The American Physical Society.

We study the phase locking of a long Josephson junction operating in a fluxon oscillator regime to external rf signals whose frequency is an even harmonic of the oscillator frequency. The phenomenon is investigated for different values of the dc bias current in the junction, and around each value the current intervals that allow phase locking are evaluated. These intervals can be well identified even when the drive frequency is sixteen times the fluxon oscillator frequency. The explanation of the numerical data that we obtain is given in terms of analytical approximations for a long Josephson junction model. An equation containing relevant experimental parameters is derived for the current-locking ranges generated by the different harmonics. This equation establishes that the amplitude of these intervals decreases exponentially with the harmonic number and we show how this result can be related to a property of the Fourier spectrum of fluxon oscillations. In all the cases that we analyze very good agreement is found between the numerical evidence and theoretical analysis.

There is experimental evidence in long Josephson junctions of rf-induced dynamical states that are not observed in small junctions. Such states consist of groups of current steps, asymmetrical with respect to the McCumber curve, having amplitudes much larger than the expected rf-induced (Shapiro) steps. Numerical solutions of the model equation (the perturbed sine-Gordon equation) obtained from the multimode expansion are in good agreement (at least qualitatively) with the experimental data. The basic dynamic configuration consists of multifluxon bunches phase locked to the rf signal.