Simulations of Coherent Beam-Beam Modes at the LHC

The transverse coherent oscillations of the two colliding LHC proton beams are studied via multi-particle tracking, using the beam-beam force of a Gaussian distribution with variable barycenters and rms sizes. In addition to head-on collisions, our simulation optionally includes the effect of long-range collisions and an external impedance. Simulation results are the coherent and incoherent oscillation frequencies, the emittance growth of either beam, and evidence for the existence or absence of Landau damping. We find that with equal beam sizes and equal tunes Landau damping acts on the coherent modes for current ratios smaller than 60%. For equal current ratio, Landau damping of the coherent dipole oscillations is lost. However it can be restored by separating the tunes, provided the external impedance is sufficiently small.