IR Optics Measurement with Linear Coupling´s Action-Angle Parameterization

A parameterization of linear coupling in action-angle co-ordinates is convenient for analytical calculations and interpretation of turn-by-turn (TBT) beam position monitor (BPM) data. We demonstrate how to use this parameterization to extract the twiss and coupling parameters in interaction regions (IRs), using BPMs on each side of the long IR drift region. The example of TBT BPM analysis was acquired at the Relativistic Heavy Ion Collider (RHIC), using an AC dipole to excite a single eigenmode. Besides the full treatment, a fast estimate of beta, the beta function at the interaction point (IP), is provided, along with the phase advance between these BPMs. We also calculate and measure the waist of the beta function and the local optics.