  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.
