| Summary: | We have modified the beam-beam simulation code CBI to handle asymmetric beams and used it to look at energy transparency and symmetries in the beam-beam interaction. We find that even a small violation of energy transparency, or of the symmetry between the two beams, changes the character of the collective (coherent) motion; in particular, period-n oscillations are no longer seen. We speculate that the one-time observation of these oscillations at LEP, and the more ubiquitous observation of the flip-flop instability in colliders around the world, may be a consequence of breaking the symmetry between the electron and positron beams. We also apply this code to the asymmetric collider PEP-II, and find that for the nominal parameters of PEP-II, in particular, the nominal tune-shift parameter of ξ_{0}=0.03, there are no collective beam-beam issues. Collective quadrupole motion sets in only at ξ_{0}=0.06 and above, consistent with earlier observations for symmetric beams.
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