Fluxons in a superlattice of Josephson junctions: Dynamics and radiation

We study the dynamics of a homopolar coherent array of fluxons in a planar superlattice of long Josephson junctions coupled through lateral idle regions. These regions introduce dispersion, which in effect destroys the Lorentz invariance of the usual sine-Gordon equation. Thus, the system is described by an effectively non-local equation. We use a collective coordinate approach to determine the fluxon width resulting uniform coherent fluxon motion, as well as the fluttering frequency as a function of the momentum, which is an integral of the motion. At relatively high fluxon velocities Cherenkov radiation appears as oscillations following the propagating fluxon. We obtained analytical formulae for the wavevector, frequency, amplitude and form of the emitted radiation. The analytical results are in fair agreement with numerical simulations. At very high fluxon velocities, the radiation strongly modifies the I-v characteristics leading to resonant structures, known as Cherenkov steps. The coherency of the emitted radiation makes possible the use of such devices as rf oscillators in the gigahertz region, where they can compete with semiconductor based oscillators.