Coherent instability of weak-strong beam-beam interactions

With HERA as a model, the collective (coherent) beam-beam instability in the case of weak-strong or very unsymmetrical beam-beam interactions was studied with a self-consistent beam-beam simulation by using the particle-in-cell method. It was found that when the beam-beam parameter of the weak lepton beam exceeds a threshold that corresponds to an overlap of the weak beam with low-order single-particle beam-beam resonances, the onset of the coherent beam-beam instability results in a significant emittance growth of the strong proton beam. After the onset of the coherent beam-beam instability, both the beams could develop a spontaneous coherent oscillation and the quasi-equilibrium distribution of the lepton beam deviates from a Gaussian distribution with a formation of a beam halo. The collective instability of weak-strong beam-beam interactions has been confirmed in a beam experiment on HERA. The phenomena observed in the experiment qualitatively agree with the numerical prediction.