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Experimental determination of linear optics including quadrupole rotations

The measured response matrix giving the change in orbit at beam position monitors (BPMs) with changes in steering magnet excitation can be used to accurately determine many important parameters in a storage ring. Using the NSLS X-ray ring measured response matrix we have determined the gradients in all 56 quadrupole magnets; the calibration of the steering magnets and BPMs; the rotational mis-alignments of the quadrupoles, steering magnets, and BPMs about the electron beam direction; the longitudinal magnetic centers of the orbit steering magnets; and the transverse mis-alignments of the sextupoles. Random orbit measurement error of the BPMs propagated to give 0.04% RMS error in determination of individual quadrupole gradients and 0.4 mad RMS error in the determination of quadrupole rotational alignment. Small variations of a few parts in a thousand in the quadrupole gradients within an individual family were resolved. The improved understanding of the X-ray ring has enabled us to better control the electron beam size.