Two examples of integrable systems with round colliding beams

Abstract

The work is devoted to analytical study of application of integrable systems to round colliding beams, aiming at enhancement of the beam-beam limit. Two examples of "integrable" beam-beam forces are presented, relevant to round counter beams with special density distributions. In such systems all the resonances will vanish, hence the beam-beam effects can be suppressed, and the intensities of colliding beams may be strongly increased, at least in the "weak-strong" case.