Error Determination in Sextupole Magnet Calibration and Alignment Measurements and Application to Horizontal Beam Size Calculations at the Cornell Electron-positron Storage Ring

TL;DR

This paper presents detailed measurements and modeling of sextupole magnets in CESR, improving calibration accuracy and alignment, which are crucial for precise horizontal beam size measurements in particle accelerators.

Contribution

It introduces new beam-based calibration and alignment methods for sextupole magnets, enhancing measurement precision for beam size analysis.

Findings

Calibration differences of 3.1% on average from previous values

Alignment offsets with RMS spreads of about 1 mm

Achieved 10% precision in horizontal beam size measurement

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 ($K_2$ 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 $\Delta K_2$. High accuracy was achieved by fitting to difference phase and coupling functions as $K_2$ 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~$\mu$radian in the horizontal angle change produced in the sextupole for a typical strength change of \mbox{$\Delta K_2 \, L$ = 1 m$^{-2}$}, where $L$ 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.