On the Landau Damping and Decoherence of Transverse Dipole Oscillations in Colliding Beams

Coherent transverse dipole oscillations in colliding head-on non-rigid bunches are studied using the Vlasov equation. The corresponding eigenvalue problem is solved numerically in the case of round Gaussian bunches of equal size but with not necessarily equal intensities. Transition from the weak-strong to the strong-strong cases is found at the intensity ratio of about 60% when a discrete p-mode frequency emerges from continuum of eigenfrequencies related to the beam-beam tunespread in the weaker bunch. In the strong-strong case the large coherent beam-beam tuneshift dominates over interchange processes between coherent and incoherent motion; it can switch off Landau damping of dipole transverse oscillations, slows down incoherent emittance growth due to external kicks on the beams. The consequences for the transverse feedback operation in collision are discussed.