Incoherent beam-beam effects for round beams in the Novosibirsk phi-factory project

The goal luminosity in the Novosibirsk phi-factory project is in the rang 1033 1/cm2s and very likely will strongly depend on the beam-beam interaction. Quantitatively this limitation is described via the threshold value of the beam-beam parameter ξ = ξth. Once for phi-factories the luminosity L ∝ ξ2th any effects, which can decrease the perturbations of the beam from its the counter-moving partner and therefore increase ξth, becomes very desirable. The preliminary study, which has been performed as shown in cited references, indicated that from this point of view the most favorable can be the configuration, where the colliding bunches are round and the working point of the ring is placed at the linear coupling resonance line νx = νz. Recently Reference 5 indicated the possibility of a strong suppression of the beam-beam resonance powers for round beams, if the lengths of the colliding bunches exceed the value of the β-function at the interaction point (IP) σs ≥ β* (so-called hour-glass effect). Nevertheless, since the calculations in Reference 5 in fact were done within the approximation σs much-lt β*, they must be confirmed for wider region. In this paper the influence of the indicated factors on the limitation of the beam-beam parameter ξ is discussed for the weak-strong beam case