Coherent Beam-Beam Oscillations at the LHC

The transverse coherent motion of the two colliding LHC beams is studied by multi-particle tracking, where the beam-beam force is calculated assuming a Gaussian beam distribution with variable barycentres and rms beam sizes. The simulation yields the coherent and incoherent oscillation frequencies, the emittance growth of either beam, and evidence for the existence or lack of Landau damping. The transverse beam sizes change with the fractional part of the tune as expected from the dynamic beta effect. For head-on collisions, we find that the pi-mode frequency lies outside of the continuum frequency spread if the ratio of the beam-beam parameters exceeds 0.6, in accordance with predictions [1]. For smaller ratios, the pi-mode is Landau damped. When long range interactions are also included, undamped coherent modes do still exist outside the continuum, both with and without alternating crossing planes at two interaction points. However, the simulation shows that separating the tunes of the two beams can restore the Landau damping.