Error Determination in Sextupole Magnet Calibration and Alignment Measurements and Application to Horizontal Beam Size Calculations at the Cornell Electron-positron Storage Ring
arXiv:2409.19728
Abstract
We report on measurements and modeling studies performed from 2021 to 2024 on the 76 sextupole magnets in the Cornell Electron-positron Storage Ring CESR. Beam-based, magnet-specific calibrations ( value versus excitation current) were measured. It was found that the new calibrations differ from those previously in use by an average of 3.1% with an RMS spread of 12%. The uncertainties in the calibration correction factors average 1.7% with an RMS spread of 1.0%. Sextupole alignment values relative to the reference orbit were measured by combining the measured beam position with the quadrupole and skew quadrupole terms caused by a sextupole strength change . High accuracy was achieved by fitting to difference phase and coupling functions as was varied. The horizontal (vertical) average offset values were found to be -0.01 (0.03)~mm with RMS spread of 1.1 (0.9)~mm with some exceptionally large values of a few millimeters. Typical uncertainties are 0.01-0.02~mm. The above measurements were motivated by the precision required in measuring horizontal beam size at each sextupole. A precision of 10\% for a \mbox{1-mm} beam size requires uncertainties of better than 0.1~radian in the horizontal angle change produced in the sextupole for a typical strength change of \mbox{ = 1 m}, where is the length of the sextupole, as well as 10\% in the difference of the squared horizontal and vertical beam positions relative to the center of the sextupole. These precision values were achieved by the analysis of difference functions. However, a small source of horizontal angle change of unknown origin, independent of the sextupole strength, requires a sextupole strength range larger than now available to measure accurately the typical horizontal beam size at CESR.
62 pages, 56 figures, 25 citations