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Linear optics parameters are often estimated using readily availableturn-by-turn (TbT) data. In-plane beta functions, which are the most commonmeasurement objectives, can be estimated from the amplitudes or phases of TbTdata, providing an overall characterization of the linear lattice. In additionto estimating uncoupled Twiss parameters, TbT data can also be utilized forcharacterizing coupled linear motion. We investigate several methods forconstructing a full normalization matrix at each beam position monitor (BPM).BPMs provide information on beam centroid transverse coordinates, but directobservation of transverse momenta is not available. To estimate momenta, onecan use a pair of BPMs or fit data obtained from several BPMs. By using bothcoordinates and momenta, it is possible to fit the one-turn matrix or its powerat each BPM, allowing for the computation of coupled Twiss parameters. Anotherapproach involves the minimization of peak coupling amplitudes in the spectrumof normalized complex coordinates. Similarly, the normalization matrix can beestimated by fitting linear coupled invariants. In this study, we derive andutilize a special form of the normalization matrix, which remains non-singularin the zero coupling limit. Coupled Twiss parameters can be obtained from thenormalization matrix. The paper presents the results of applying and comparingthese methods to both modeled and measured VEPP-4M TbT data, demonstratingeffective estimation of coupled Twiss parameters.

Coupled Twiss Parameters Estimation from TbT Data