Discreteness-induced resonances and ac voltage amplitudes in long one-dimensional Josephson junction arrays

New resonance steps are found in the experimental current-voltage characteristics of long, discrete, one-dimensional Josephson junction arrays with open boundaries and in an external magnetic field. The junctions are underdamped, connected in parallel, and dc biased. Numerical simulations based on the discrete sine-Gordon model are carried out, and show that the solutions on the steps are periodic trains of fluxons, phase locked by a finite amplitude radiation. Power spectra of the voltages consist of a small number of harmonic peaks, which may be exploited for possible oscillator applications. The steps form a family that can be numbered by the harmonic content of the radiation, the first member corresponding to the Eck step. Discreteness of the arrays is shown to be essential for appearance of the higher order steps. We use a multimode extension of the harmonic balance analysis, and estimate the resonance frequencies, the ac voltage amplitudes, and the theoretical limit on the output power on the first two steps.