Application of frequency map analysis to beam-beam effects study in crab waist collision scheme

Abstract

We applied frequency map analysis (FMA)—a method that is widely used to explore dynamics of Hamiltonian systems—to study beam-beam effects in a novel crab waist collision approach. The “crab” focusing of colliding beams results in significant suppression of betatron coupling resonances induced by beam-beam interaction. Application of FMA provides visible information about all working resonances, their widths, and locations in the planes of betatron tunes and betatron amplitudes, so the process of resonances suppression due to the beams crabbing is clearly seen. However, our numerical simulations and further analysis showed that effectiveness of crab waist is considerably restricted in the cases when the colliding beams are not flat. The FMA technique turned out to be very helpful in these studies, as it gave us the key information which would be difficult to obtain in a different way.