Analytical estimation of the beam-beam limited dynamic apertures and lifetimes in e+e- circular colliders

Physically speaking, the delta function like beam-beam nonlinear forces at interaction points (IPs) act as a sum of delta function nonlinear multipoles. By applying the general theory established previously, in this paper we examine analytically the beam-beam interaction limited dynamic apertures and the corresponding beam lifetimes for both the round and the flat beams. Relations between the beam-beam limited beam lifetimes and the beam-beam tune shifts are established, which show clearly why experimentally one has always a maximum beam-beam tune shift, ξ_y,max, around 0.045 for e ⁺e^circular colliders, and why one can use round beams to double this value approximately