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. Sim-ulation results are the coherent and incoherent oscillation frequencies, the emittance growth of either beam, and ev-idence for the existence or absence of Landau damping. We find that with equal beam sizes and equal tunes Landau damping is lost for current ratios larger than 60%. How-ever, Landau damping of the coherent dipole oscillations can be restored by separating the tunes, provided the exter-nal impedance is sufficiently small.