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Use case implementation: chromaticity correction

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Overdue by 3 month(s)
Due by October 15, 2025
Last updated Jan 22, 2026
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More information available in: User specification document (8.1.3), Requirement specification document (A.3.5).

This use case is supposed to give access (get and set) to the storage ring chromaticity or to the booster chromaticity at a given time along the ramp.
The user would like to get the value of the chromaticity and set it to a desired value (not necessarily the model one).
This measurement requires implementing a betatron tune monitor (for chromaticity measurement) and at least two families of sextupole magnets (for changing chromaticity in both transverse planes) with a corresponding response matrix, and having a measured of estimated value of momentum compaction factor and beam energy (usually simulator values are good enough).
Depending on the way to measure chromaticity, we may need access to the RF master clock (varying the main RF frequency around the nominal value), analysis of the bunch spectrum of betatron oscillations, or calculation of chromaticity based on the lattice.
Here, only the method using the RF master clock is described.

The measurement of chromaticity is done in the following way.
The user sets the value of the step in RF frequency ($\Delta f$, a small value of a few \unit{\Hz}) and the number of such steps.
Then the RF frequency is changed between $f_0$, $f_0 - n_\text{steps}\Delta f$ to $f_0 + n_\text{steps}\Delta f$ and back to $f_0$ (we do this path to avoid any large change in the RF frequency).
At each value of RF frequency, a betatron tune value (horizontal and vertical) is recorded and stored.
A betatron tune in each plane $Q_{x, y}$ as a function of RF frequency is fitted to a polynomial of a user-specified order (typically $<=4$).
The polynomial coefficients, normalised with a coefficient depending on momentum compaction factor and beam energy, are the values of chromaticity.
Typically, only the linear coefficient is of interest in the horizontal and vertical planes.

To set the chromaticity, one requires a response matrix of chromaticity to sextupole magnet strength/currents.
Such a matrix can be measured or estimated from a simulator model of the accelerator and stored in a file.
Knowing the desired chromaticity values, we can find the required sextupole families' settings by using the inverse of this response matrix.
Then the required strength/currents are applied to the magnets.

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