Coherent beam-beam effects

We have performed a strong-strong simulation to investigate the effect of a beam-beam interaction on the motion of circulating beams in a 50 GeV × 50 GeV muon-collider ring. The phase-slip factor η ₁ in the muon-collider ring is approximately -1 × 10 ^-6 so that the synchrotron motion is nearly frozen during the muon-storage time. Thus, the energy variation of a particle in the beam due to the beam-beam interaction accumulates from turn to turn, resulting in increase in the energy spread of the beam. Through the strong-strong simulation, we have investigated the parametric dependencies of the energy spread and the beam size induced by the beam-beam interaction on various parameters. It is shown that the induced energy spread due to the beam-beam interaction affects the growth of the beam size. It is also shown that compensation of the energy spread by introducing one additional rf cavity in the ring can reduce the growth of the beam size