  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
multi-mode 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.
