Measurement of global betatron coupling with skew quadrupole modulation

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.