Possible Phase Loop for the Global Decoupling

The two eigentunes QIand QII, two eigenmode amplitude ratios RIand RII, and two eignmode phase differences ΔφIand ΔφII, 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 RI,IIare more sensitive than the tune split when the decoupling scan is approaching the global uncoupled point, and that the phase differences ΔφI,IItell 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.