Abstract
The beam-beam interaction is one of the most severe limitations on the performance of circular colliders, as it is an unavoidable strong nonlinear effect. As one aspires for greater luminosity in future colliders, one will simultaneously achieve stronger beam-beam interactions. We study the limitations caused by strong incoherent head-on beam-beam interactions, using a new code (cabin) that calculates on a graphics processing unit (GPU), allowing for a detailed description of the long-term particle trajectories in 6D phase space. The evolution of the beam emittance and beam intensity has been monitored to study the impact quantitatively, while frequency map analysis has been performed to understand the impact qualitatively. Results from cabin have shown good quantitative agreement with dedicated experiments in the Large Hadron Collider (LHC). For large beam-beam tune shifts, alternatives to the LHC tunes have been found to improve the beam quality. Schemes devised to cancel beam-beam driven resonances, by use of specific intermediate phase advances between the interaction points, work very well with zero crossing angle, and the accuracy required is achievable. Due to lack of symmetry, these schemes have an almost negligible impact with a significant crossing angle. The hourglass effect has been found to reduce the detrimental effects caused by the chromaticity and vice versa. The optimal level of the hourglass effect has been achieved when ${\ensuremath{\beta}}^{*}=1.5{\ensuremath{\sigma}}_{s}$. The ultimate parameters of the Future Circular Hadron Collider (FCC-hh) seem within reach, in absence of residual odd resonances.
Highlights
With the hard collisions at an interaction point in a circular collider, multiple small angle deflections occur
The total beam-beam tune shift is relatively small in the Large Hadron Collider (LHC) today, and a working point close to the nominal ðQx; QyÞ 1⁄4 ð0.31; 0.32Þ preserves the beam quality sufficiently well
The experiment tested collisions at different working points between individual bunches of higher intensity and smaller normalized emittance than the ones produced for regular operation with bunch trains, but close to the bunch brightness expected for the high-luminosity upgrade of the Large Hadron Collider (HL-LHC) project
Summary
With the hard collisions at an interaction point in a circular collider, multiple small angle deflections occur This phenomenon, known as the beam-beam interaction, is caused by the electromagnetic fields from the opposing beam [1]. The interaction force is strongly nonlinear, resulting in the possibility of betatron resonances [2] These resonances can cause a strong diffusion of the particles, or even make the beam unstable and lost within a short amount of time. This paper studies the impact of strong head-on beam-beam interactions with a crossing angle. The discovered trends will be explained by the underlying mechanisms through frequency analysis [14], and compared to relevant previous studies [10,13,15].
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