Abstract
Measurement of the residual betatron coupling with skew quadrupole modulation is a new diagnostics technique. It was developed and tested at the Relativistic Heavy Ion Collider (RHIC) as a promising method for measuring coupling on the ramp. By modulating the strengths of skew quadrupole families, the two tunes' responses are precisely measured with the phase lock loop system. The projection ratio of the residual coupling coefficient onto the coupling modulation direction can be determined. In this article, the analytical solution to the skew quadrupole modulation is given. Dedicated beam studies were carried out in RHIC Run'04 and the results are presented. The ability to measure coupling on the ramp opens the possibility of continuously correcting coupling during acceleration.
Highlights
For a hadron machine like the Relativistic Heavy Ion Collider (RHIC), the working points are constrained into a very narrow space
We proposed the skew quadrupole modulation technique to replace the skew quadrupole scan
The RHIC phase lock loop (PLL) system is used for fast tune measurement during the skew quadrupole modulation
Summary
For a hadron machine like the Relativistic Heavy Ion Collider (RHIC), the working points are constrained into a very narrow space. Skew quadrupole strength scan is the conventional method to measure and correct the global coupling [1,2,3,4]. Before the skew quadrupole scan, the two tunes should be pushed to the linear difference coupling resonance. The analytical solution to the tune split during the modulation was found, based on the Hamiltonian perturbation theory of linear difference coupling. Different data processing methods were found to extract the residual coupling’s projection ratio onto the coupling modulation direction. This technique has several advantages compared to the skew quadrupole scan.
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