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A theoretical, numerical and experimental study is presented of the coherent synchro-betatron modes due to the coherent beam-beam interaction. Possible coherent beambeam instability of the head-tail type caused by the combined effect of the impedance elements in the machine and linearized coherent beam-beam interaction is discussed, as well as the ways to stabilize the beam-beam system, including optimal choice of the chromaticity. Special case of linac-ring collision scheme is also described.doi:10.1103/physrevstab.4.024403 fatcat:vu5p46xfqfhuznyrgwnhpaptou