Experimental observations and theoretical models for beam-beam phenomena

The beam-beam interaction in storage rings exhibits all the characteristics of nonintegrable dynamical systems. Here one finds all kinds of resonances, closed orbits, stable and unstable fixed points, stochastic layers, chaotic behavior, diffusion, etc. The storage ring itself being an expensive device nevertheless while constructed and put into operation presents a good opportunity of experimentally studying the long-time behavior of both conservative (proton machines) and nonconservative (electron machines) dynamical systems - the number of bunch-bunch interactions routinely reaches values of 10/sup 10/-10/sup 11/ and could be increased by decreasing the beam current. At the same time the beam-beam interaction puts practical limits for the yield of the storage ring. This phenomenon not only determines the design value of main storage ring parameters (luminosity, space charge parameters, beam current), but also in fact prevents many of the existing storage rings from achieving design parameters. Hence, the problem has great practical importance along with its enormous theoretical interest. A brief overview of the problem is presented.