Stratonovich expansion and beam-beam interaction

A general approach is proposed for the study of coherent phenomena in electron storage rings due to a localized nonlinear force. The approach is based on expanding the distribution function into a series using generalized Hermite polynomials in two dimensions (Stratonovich expansion). When the series is terminated at the lowest order, it gives the Gaussian approximation. The approach is applied to strong-strong and weak-strong beam-beam interactions in e/sup +/e/sup -/ colliding storage rings at the next-to-lowest order approximation and shows improved quantitative agreement with the multiparticle tracking.<>