[Paper Review] Characterization and control of linear coupling using turn-by-turn beam position monitor data in storage rings

Yongjun Li, Lingyun Yang+1 more|arXiv (Cornell University)|Jun 19, 2017

Electromagnetic Simulation and Numerical Methods3 citations

TL;DR

This paper presents a method to characterize and control linear betatron coupling in storage rings using turn-by-turn (TbT) beam position monitor (BPM) data by extracting symplectic Lie generators that directly reveal coupling terms. By adjusting non-dispersive skew quadrupoles based on these terms, the method reduces vertical emittance to the diffraction limit in the NSLS-II storage ring, enabling automated feedback with minimal operational disruption.

ABSTRACT

We introduce a new application of measuring symplectic generators to characterize and control the linear betatron coupling in storage rings. From synchronized and consecutive BPM (Beam Position Monitor) turn-by-turn (TbT) readings, symplectic Lie generators describing the coupled linear dynamics are extracted. Four plane-crossing terms in the generators directly characterize the coupling between the horizontal and the vertical planes. Coupling control can be accomplished by utilizing the dependency of these plane-crossing terms on skew quadrupoles. The method has been successfully demonstrated to reduce the vertical effective emittance down to the diffraction limit in the newly constructed National Synchrotron Light Source II (NSLS-II) storage ring. This method can be automatized to realize linear coupling feedback control with negligible disturbance on machine operation.

Motivation & Objective

• To develop a real-time method for characterizing linear betatron coupling in electron storage rings using TbT BPM data.
• To enable automated coupling correction via skew quadrupole adjustments without disrupting routine machine operations.
• To reduce vertical effective emittance to the diffraction limit in high-brilliance light sources like NSLS-II.
• To provide a direct, data-driven alternative to conventional orbit response matrix fitting and LOCO-based methods.

Proposed method

• Extract one-turn maps from synchronized, consecutive TbT BPM readings at multiple locations along the ring.
• Compute symplectic Lie generators from the one-turn maps using the matrix logarithm to obtain quadratic Lie generators.
• Identify the four plane-crossing terms (e.g., xy, xp_y, p_x y, p_x p_y) in the Lie generator as direct indicators of linear coupling.
• Use the dependence of these coupling terms on skew quadrupole strengths to design a control law for correction.
• Implement iterative correction via skew quadrupole adjustments based on real-time Lie generator updates.
• Validate the method using multiple diagnostics: RDT spectra, beam profiles, and beam lifetime measurements.

Experimental results

Research questions

• RQ1 Can symplectic Lie generators extracted from TbT BPM data directly and accurately characterize linear coupling in storage rings?
• RQ2 How can the coupling terms in the Lie generator be used to control coupling via non-dispersive skew quadrupoles?
• RQ3 Can coupling correction be automated and integrated into routine machine operation with minimal disruption?
• RQ4 What is the impact of coupling correction on vertical emittance, beam profile, and beam lifetime?

Key findings

• The vertical effective emittance was reduced from 32.0 pm·rad to 6.4 pm·rad after three iterative corrections, approaching the diffraction limit.
• The horizontal betatron mode frequency peak in the vertical spectrum was effectively suppressed post-correction, confirming reduced coupling.
• Beam transverse profiles showed a significant reduction in tilt angle and vertical size, with the pinhole camera capturing a 4.5× decrease in vertical beam size.
• Beam lifetime increased linearly with vertical beam size reduction, confirming improved stability and reduced Touschek loss.
• The method enabled feedback control with data access and correction completed in seconds, suitable for real-time automation during routine operation.
• Independent component analysis (ICA) validation confirmed the accuracy of the Lie generator-based coupling characterization.