Solvable model of beam-beam effects in e+e- colliding storage rings

A solvable model is constructed for the strong-beam--strong-beam phenomenon. The model represents the extreme case where the radiation effect is quite strong. Although it does not present a quantitatively accurate description of the beam behavior for realistic ring parameters, it qualitatively well illustrates several common characteristic features of the observed phenomenon: saturation of the beam-beam parameter, universality of its saturated value, blowup of one of the beams (spontaneous symmetry breakdown), flip-flop hysteresis (cusp catastrophe), and so on