Possible Phase Loop for the Global Decoupling

Abstract

The two eigentunes Q I and Q II , two eigenmode amplitude ratios R I and R II , and two eignmode phase differences ∆φ I and ∆φ II , are defined as the coupling observables for the linear weak difference betatron coupling. Simulations were carried out to investigate their behaviors in global decoupling scans. It was found that the amplitude ratios R I,II are more sensitive than the tune split when the decoupling scan is approaching the global uncoupled point, and that the phase differences ∆φ I,II tell the right global decoupling direction, the right strength combination of the skew quadrupoles or families. The analytical solution to these six coupling observables is calculated through both the strict matrix approach and the perturbation Hamiltonian approach. The constant phase differences in the right decoupling direction hint a possible global decoupling phase loop. Dedicated beam experiments were carried out at the Relativistic Heavy Ion Collider (RHIC). The preliminary results from the beam experiments are presented. These six parameters can be used for the global decoupling in feedback mode, especially on the non-stop energy ramp.

Matrix perturbation approach to the weak linear coupling

“…They imply three possible loops for the global decoupling [8]. In [8], the analytical solutions to the six weak linear difference coupling observables are obtained through the Hamiltonian perturbation theory [9,10,11]. C. Gardner also obtained similar expressions for the amplitude ratios and the phase differences through the direct matrix approximation under the weak coupling [12].…”

“…(89) play important roles in the linear difference coupling observations. They imply three possible loops for the global decoupling [8]. In [8], the analytical solutions to the six weak linear difference coupling observables are obtained through the Hamiltonian perturbation theory [9,10,11].…”

Simultaneous Tune and Coupling Feedback in RHIC, and Possible Implications for LHC Commissioning

“…Earlier efforts [2,3] were hampered by large betatron coupling, as well as the requirement for large dynamic range. Both problems have been addressed, the first by continuous measurement of coupling [4,5], and the second by an improved analog front end [6,7]. With these improvements, simultaneous tune and coupling feedback were successfully implemented during RHIC Run 6.…”

Continuously Measure Global Difference Coupling using a Phase-Locked-Loop Tune Meter in the RHIC

“…In applying tune feedback on the RHIC ramp, we sometimes experienced a mix-up of the PLL eigentune tracking under the coupled situation [7,8]. To solve this problem to ensure a robust PLL tune measurement system, continuous coupling measurements and corrections are needed [14,15].…”

“…In addition, a formalism was developed to properly parameterize this measurement [15,16]. According to this formalism, the global coupling coefficient can be determined from the measurements of the eigenmode projection parameters.…”