Aplication of Frequency Map Analysis to Beam-Beam Effects Study in Crab Waist Collision Scheme

TL;DR

This paper demonstrates how Frequency Map Analysis can effectively study beam-beam effects and resonance suppression in Crab Waist collision schemes, providing clear visualization of resonance behaviors.

Contribution

It introduces the application of Frequency Map Analysis to analyze beam-beam interactions in Crab Waist collision schemes, highlighting its effectiveness in visualizing resonance suppression.

Findings

FMA reveals all relevant resonances and their properties.

Crab Waist focusing suppresses betatron coupling resonances.

FMA provides clear visualization of resonance dynamics.

Abstract

We applied Frequency Map Analysis (FMA) - a method that is widely used to explore dynamics of Hamiltonian systems - to beam-beam effects study. The method turned out to be rather informative and illustrative in the case of a novel Crab Waist collision approach, when "crab" focusing of colliding beams results in significant suppression of betatron coupling resonances. 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.