Error analysis of linear optics measurements via turn-by-turn beam position data in circular accelerators

Many advanced techniques have been developed, tested and implemented in the last decades in almost all circular accelerators across the world to measure the linear optics. However, the greater availability and accuracy of beam diagnostics and the ever better correction of linear magnetic lattice imperfections (beta beating at 1% level and coupling at 0.1%) are reaching what seems to be the intrinsic accuracy and precision of different measurement techniques. This paper aims to highlight and quantify, when possible, the limitations of one standard method, the harmonic analysis of turn-by-turn beam position data. To this end, new analytic formulas for the evaluation of lattice parameters modified by focusing errors are derived. The unexpected conclusion of this study is that for the ESRF storage ring (and possibly for any third generation light source operating at ultra-low coupling and with similar diagnostics), measurement and correction of linear optics via orbit beam position data are to be preferred to the analysis of turn-by-turn data.