Characterization and control of linear coupling using turn-by-turn beam position monitor data in storage rings

We introduce a new application of measuring symplectic generators to characterize and control the linear betatron coupling in storage rings. From synchronized and consecutive BPM (Beam Position Monitor) turn-by-turn (TbT) readings, symplectic Lie generators describing the coupled linear dynamics are extracted. Four plane-crossing terms in the generators directly characterize the coupling between the horizontal and the vertical planes. Coupling control can be accomplished by utilizing the dependency of these plane-crossing terms on skew quadrupoles. The method has been successfully demonstrated to reduce the vertical effective emittance down to the diffraction limit in the newly constructed National Synchrotron Light Source II (NSLS-II) storage ring. This method can be automatized to realize linear coupling feedback control with negligible disturbance on machine operation.