Continuous measurement of global difference coupling using a phase-locked-loop tune meter in the Relativistic Heavy Ion Collider

We present a new technique to continuously measure and compensate the global difference coupling coefficient through the continuous measurements of eigenmode projection parameters, using a high resolution phase-locked-loop tune meter. First, four eigenmode projection parameters are defined as the observables for weak difference coupling. Then, their analytical expressions are obtained using the strict matrix treatment and the Hamiltonian perturbation theory of linear coupling. From these parameters, the complex global coupling coefficient can be fully determined and compensated. This method was successfully demonstrated in the Relativistic Heavy Ion Collider (RHIC) 2006 run.