Landau damping of coherent beam-beam modes by overlap with synchrotron side-bands.

For the nominal LHC parameters the coherent beam-beam pi-mode is outside the incoherent continuum and therefore does not experience Landau damping. Mechanisms to restore damping by reducing the degree of symmetry between the two beams are effective, but may not be desirable due to possible side effects. Since the synchrotron tune and the linear beam-beam tuneshift have the same order of magnitude for the LHC, Landau damping could be provided by overlapping the discrete modes with the synchrotron sidebands of the incoherent continuum. In this report we study this damping effect qualitatively and quantitatively with a strong-strong simulation model