[Applications of nonlinear dynamics to the beam-beam interaction]. Progress report, 1985-1986

The effects of radiation damping and quantum fluctuations were included in four dimensional mapping models of colliding round beams. For nearly flat beams it was found that, in the case of area preserving (two dimensional) mapping models of proton beams, the escape rates of orbits through remnants of K.A.M. tori can be accurately described by empirical formulas. Certain low-period orbits of differential equation models of the beam-beam interaction were obtained numerically and analytically. Analytical results were also derived for four dimensional mapping models of colliding electron beams. An explicit, analytical formula was derived for the electromagnetic ''kick'' interaction between beams with elliptically symmetric charge distribution