Beam-beam

TL;DR

The paper addresses how beam-beam interactions constrain collider performance by detailing a set of analytic models for the beam-beam force, including head-on and long-range regimes. It introduces key quantities such as the deflection $\Delta p_x$, the linear slope $k_{BB}$, and the beam-beam parameter $\xi$, and discusses coherent averaging with effective beam sizes, as well as the hourglass effect arising from finite bunch length through longitudinal-slice modeling. The contributions provide explicit formulas and concepts for predicting orbit and optics changes, highlighting potential deviations from idealized shifts and informing mitigation strategies. These insights are essential for guiding the design and optimization of modern colliders to maximize luminosity while controlling nonlinear effects and radiative losses.

Abstract

The interaction of the two beams in a collider leads to a variety of effects that may limit the performance of the machine. This lecture introduces the basic aspects necessary to understand the design of modern colliders.

Figures (5)

• Figure 1: List of circular colliders FCCBenediktwikilist
• Figure 2: Illustration for the computation of the force experienced by a particle with position $x$ with respect to the center of a uniformly charge cylinder (blue). The co-axial cylinder considered to apply Gauss law is drawn in red.
• Figure 3: Illustration of the beam-beam force for different configurations. The linear and $1/r$ approximations are marked in dashed red in Figs. \ref{['fig-force-gauss']} and \ref{['fig-force-LR']} respectively.
• Figure 4: Illustration of the hourglass effect and its model based on longitudinal slices.
• Figure 5: Illustration of the collision of a particle (red dot) with a bunch (blue) featuring a large crossing angle. The trajectories are marked with red and blue arrows respectively, while the $x$ and $z$ axis of the co-moving reference frame are marked in purple.