Beam Dynamics in Future Colliders with Crab Crossing

Overview

Crab crossing is a technique used in high-luminosity colliders to restore head-on collisions when beams cross at an angle. While it improves luminosity, it introduces complex synchrobetatron coupling and nonlinear beam-beam interactions that must be carefully controlled.

Key Challenges

• Synchrobetatron resonances: The crab cavity RF fields couple transverse and longitudinal motion, exciting resonances that can drive beam instabilities.
• Beam-beam effects: beam-beam forces are modified by the crossing angle and crab cavity parameters.
• Diffusions: Combined nonlinearities excites nonlinear resonances and create slow deterioration of beam quality.

Approach

We use Frequency Map Analysis (FMA) and other techniques to identify and quantify resonance driving terms in the presence of crab crossing. The figure above shows a representative FMA result from our published study, revealing resonance islands and chaotic regions in the crab-crossing configuration.

Analytical models based on the Hamiltonian formalism complement tracking simulations, allowing us to predict which parameter regimes are safe for collider operation.

Relevance

This work directly informs the design of the High-Luminosity LHC (HL-LHC) and the Electron–Ion Collider (EIC), both of which rely on crab crossing for peak luminosity performance.