Application of the Green’s Function Method to Some Nonlinear Problems of an Electron Storage Ring Part Iv - Study of a Weak Beam Interaction with a Flat Strong Beam

Attempts to describe analytically the beam-beam interaction in a storage ring are asnumerous as they are disappointing and frustrating. One can find in the literature many different theoretical approaches single resonance models, trapping, linear approximations, resonance overlap models, applications of Lie algebra, etc.? None of them give a satisfactory explanation of the observed phenomena either quantitatively or even qualitatively. At the same time the beam-beam instability is the most common limiting phenomenon for practically all storage rings. At least, it seems that all other observed instabilities are understood much better than the beam-beam instability and one or another cure has been found for them. This justifies endless continuous attempts (including the present one) to describe theoretically the beam-beam phenomenon.