Landau damping and the head–tail instability of the coupled synchro-betatron coherent oscillations

Within the hollow-bunch approximation we study variations in the stability conditions of the coupled synchro-betatron coherent oscillations due to common effects of the lattice chromaticity and of the Landau damping of such oscillations. We assume that the Landau damping of coherent oscillations is provided by octupole fields of the ring lattice. 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 is ignored in this paper.