[Paper Review] Simulation of an Intra-Pulse Interaction Point Feedback for Future Linear Colliders

Daniel Schulte|ArXiv.org|Aug 18, 2000

Particle Accelerators and Free-Electron Lasers2 references3 citations

TL;DR

This paper proposes an intra-pulse feedback system for future linear colliders (NLC and CLIC) that corrects beam position and angle jitter at the interaction point using beam-beam kick measurements. By measuring the kick angle from beam-beam interactions and applying corrective kicks with a feedback loop, it reduces luminosity loss by a factor of 6 in NLC and 3 in CLIC, even for large offsets.

ABSTRACT

In future normal-conducting linear colliders, the beams will be delivered in short bursts with a length of the order of 100 ns. The pulses will be separated by several ms. In order to maintain high luminosity, feedback is necessary on a pulse-to-pulse basis. In addition, intra-pulse feedback that can correct beam positions and angles within one pulse seem technically feasible. The likely performances of different feedback options are simulated for the NLC (Next Linear Collider) and CLIC (Compact Linear Collider).

Motivation & Objective

• To address luminosity degradation in future linear colliders caused by beam position and angle jitter at the interaction point.
• To design and simulate a real-time intra-pulse feedback system that corrects beam jitter within a single pulse.
• To evaluate the performance of position and angle feedback systems using beam-beam kick measurements as error signals.
• To determine optimal feedback gains and hardware requirements for achieving significant luminosity recovery.
• To assess the feasibility of correcting large beam offsets (up to 12σ_y) and mitigate the impact of BPM resolution and noise.

Proposed method

• Uses beam-beam interaction to generate a kick angle proportional to beam offset at the interaction point, which serves as a feedback error signal.
• Employs a feedback loop with a BPM to measure beam position and a kicker to apply corrective kicks, with a total delay τ_d ≈ 20 ns for NLC and 15 ns for CLIC.
• Models the feedback gain g such that δy = g × (θ / σ_y') × σ_y, optimizing g to minimize luminosity loss.
• Simulates luminosity loss as a function of beam offset and angle error using the Guinea-Pig beam-beam simulation code.
• Introduces an angle feedback system using BPMs at (n + ½)π and kickers at nπ phase advance to measure and correct beam angle errors.
• Combines position and angle feedback to correct both offset and angular jitter simultaneously, reducing total luminosity loss.

Experimental results

Research questions

• RQ1 Can intra-pulse feedback using beam-beam kick measurements effectively reduce luminosity loss due to beam jitter in linear colliders?
• RQ2 What is the optimal feedback gain g that minimizes luminosity loss for position and angle errors?
• RQ3 How does BPM resolution and bunch-to-bunch jitter affect feedback performance and luminosity recovery?
• RQ4 Can feedback recover luminosity for large beam offsets (e.g., 12σ_y) when nominal luminosity would otherwise be nearly zero?
• RQ5 Is correcting only the measured kick angle sufficient, or is a dedicated angle feedback necessary to mitigate angular jitter?

Key findings

• With optimal feedback gain g = 0.06, luminosity loss due to a 2σ_y position offset is reduced by a factor of 6 in NLC compared to no feedback.
• For a 12σ_y offset, the feedback system recovers 73% of nominal luminosity in NLC, whereas without feedback, luminosity drops to only 3.5% of nominal.
• The BPM resolution requirement is not stringent: a 15 µm resolution induces only 0.07% additional luminosity loss on average.
• In CLIC, luminosity loss is reduced by a factor of 3 with feedback, and the luminosity loss for σ_y offset is ΔL/L = 1.2×10⁻⁴ with optimal gain.
• Angle feedback is essential: correcting only the kick angle from beam-beam interaction fails to reduce luminosity loss when initial angle errors are large.
• Combined position and angle feedback reduces luminosity loss independently of initial angle error, achieving significant recovery even under combined jitter.