Transverse mode coupling instability of colliding beams

In high brightness circular colliders, coherent and incoherent beam dynamics are dominated by beam-beam interactions. It is generally assumed that the incoherent tune spread introduced by the beam-beam interactions is sufficiently large to cure any instabilities originating from impedance. However, as the two counterrotating beams interact they can give rise to coherent dipole modes and therefore modify the coherent beam dynamics and stability conditions. In this case, coherent beam-beam effects and impedance cannot be treated independently and their interplay should be taken into account in any realistic attempt to study the beam stability of colliding beams. Due to the complexity of these physics processes, numerical simulations become an important tool for the analysis of this system. Two approaches are proposed in this paper: a fully self-consistent multiparticle tracking including particle-in-cell Poisson solver for the beam-beam interactions and a linearized model taking into account finite bunch length effects. To ensure the validity of the results a detailed benchmarking of these models was performed. It will be shown that under certain conditions coherent beam-beam dipole modes can couple with higher order headtail modes and lead to strong instabilities with characteristics similar to the classical transverse mode coupling instability originating from impedance alone. Possible cures for this instability are explored both for single bunch and multibunch interactions. Simulation results and experimental evidences of the existence of this instability at the LHC will be presented for the specific case of offset collisions.