Resonance frequencies of a ring fluxon oscillator

The behavior of a long ring Josephson transmission line (fluxon oscillator) is analyzed in the presence of a bias dc current. The conditions of stability for fluxon oscillations and the dependence of their frequnecy on both the intensity of the bias current and the radius of the line are determined analytically. A splitting of the fundamental resonance band is predicted to take place in ring fluxon oscillators with finite radius