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.
Highlights
The crab waist (CW) collision scheme was proposed by Raimondi [1] to enhance the luminosity of electronpositron colliders
Frequency map analysis [6,7] turned out to be very useful for CW investigations, as it 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
The frequency map analysis (FMA) technique played an important role in these studies, as it gave us the key information which would be difficult to obtain in a different way
Summary
The crab waist (CW) collision scheme was proposed by Raimondi [1] to enhance the luminosity of electronpositron colliders. The CW transformation provides effective suppression of betatron coupling resonances (together with their synchrobetatron satellites), increasing the y limit by a factor of about 3 It was predicted by simulations and observed experimentally at the DAÈNE È factory [4,5]. Frequency map analysis [6,7] turned out to be very useful for CW investigations, as it 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 We applied this technique to see how CW works at the DAÈNE È factory, where a very good agreement between simulations and experimental data has been obtained [8,9]. The FMA technique played an important role in these studies, as it gave us the key information which would be difficult to obtain in a different way
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