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Stability of dynamic coherent states in intrinsic Josephson-junction stacks near internal cavity resonance

Stacks of intrinsic Josephson junctions in the resistive state can by efficiently synchronized by the internal cavity mode resonantly excited by the Josephson oscillations. We study the stability of dynamic coherent states near the resonance with respect to small perturbations. Three states are considered: the homogeneous and alternating-kink states in zero magnetic field and the homogeneous state in the magnetic field near the value corresponding to half flux quantum per junction. We found two possible instabilities related to the short-scale and long-scale perturbations. The homogeneous state in modulated junction is typically unstable with respect to the short-scale alternating phase deformations unless the Josephson current is completely suppressed in one half of the stack. The kink state is stable with respect to such deformations and homogeneous state in the magnetic field is only stable within a certain range of frequencies and fields. Stability with respect to the long-range deformations is controlled by resonance excitations of fast modes at finite wave vectors and typically leads to unstable range of the wave-vectors. This range shrinks with approaching the resonance and increasing the in-plane dissipation. As a consequence, in finite-height stacks the stability frequency range near the resonance increases with decreasing the height.