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Description
Linear optics parameters are often estimated using readily available turn-by-turn (TbT) data. In-plane beta functions are the most common measurement objectives that can be estimated from TbT data amplitudes or phases. In addition to estimating uncoupled twiss parameters, TbT data can also be utilized for characterizing coupled linear motion. This paper investigates several methods for constructing a full normalization matrix at each beam position monitor (BPM). BPMs provide information on beam transverse coordinates, but direct measurement of transverse momenta is not available. To estimate momenta, one can use a pair of BPMs or fit data from several BPMs. After obtaining coordinates and momenta, the one-turn matrix or its power can be fitted at each BPM to obtain coupled twiss parameters. Another approach involves fitting linear coupled invariants expressed in terms of normalization matrix. In this study, a special form of a normalization matrix, which is non-singular in the zero coupling limit, is derived and utilized to obtain linear invariants. Likewise, the normalization matrix can be fitted to minimize coupling in normalized coordinates. Coupled twiss parameters can be obtained from normalization matrix. This paper presents the results of applying and comparing these methods to model and measured VEPP-4M TbT data.
