Effect of the lattice octupole fields on the synchro-betatron mode coupling instability

Within the framework of a simplifying model and in the first approximation of the perturbation theory we discuss the effect of the Landau damping on the synchro-betatron mode coupling instability of a single bunch in a storage ring. We assume that the required by Landau damping frequency spreads of the betatron and of the synchro-betatron modes are provided by the octupole nonlinearity of the ring lattice focusing. We also assume that the wakefields of the bunch decay substantially during the revolution period of particles along the closed orbit. For this reason, the memory of the bunch wakefields are ignored in this paper.