Equivalent equations and incoherent lifetime calculated from e/sup +/e/sup /eam-beam simulation

For given tunes (/spl nusub x/, /spl nusub y/, /spl nusub s/), the influence of different terms x/sup k/y/sup l/s/sup m/ in the nonlinear beam-beam forces is different, so only some of them are important as sources of regular (nonstochastic) effects. As for irregular effects, it seems that in e/sup +/e/sup -/ colliders the simultaneous action of both quantum fluctuations and three-dimensional nonlinearities creates effectively an additional stochastic force. The developed program of beam-beam simulation including Fourier analysis of different moments M/sup klm/(t)=x/sup k/(t)y/sup l/(t)s/sup m/(t) permits us to identify both regular and stochastic effective forces in the equivalent equations of the particles' motion. These differential equations can be used, for example, for the calculation of the particles' lifetime.<>