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We discuss effects of Landau damping on the stability of coherent oscillations of short identical colliding bunches. Near the
sum-type resonances n/(2m), where n and m are integers, these oscillations are unstable. Comparing the stopbands
calculated for monochromatic and non-monochromatic bunches, we have found that the beam-beam tunespreads increase the widths of
the stopbands of coherent modes thus, resulting in Landau anti-damping of coherent beam-beam oscillations. The tunesperads
due to octupole fields do not eliminate Landau anti-damping.
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