Mode coupling instability of colliding beams in the HL-LHC

The coupling between the coherent beam-beam modes and the head-tail modes can result in strong instabilities under the effect of electromagnetic wake fields. This mode coupling phenomenon was modelled and observed in the Large Hadron Collider (LHC) for the dipole mode. In the High Luminosity upgrade (HL-LHC), the low β function at the interaction point may generate coupling instabilities of higher-order head-tail modes which would not be stabilised by the transverse feedback. This paper describes the development of an efficient 6D model of the coherent beam-beam interactions in order to assess the beam stability in configurations relevant for the HL-LHC. After having described the limit of the simulation method, we show that the mechanism of Landau damping by the synchrotron sidebands of the incoherent spectrum is sufficient to stabilise the beam in the operational scenario of HL-LHC, including a backup scenario without crab-cavity featuring a large Piwinski angle.