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Feature: Dispersion-function measurement #56

@gubaidulinvadim

Description

@gubaidulinvadim

This use case can now be implemented as all prerequisites are available in pyAML (RF masterclock and BPM array). @simoneliuzzo @kparasch @Amoutardier @gubaidulinvadim This issue might interest you!

Description, motivation and use case

The user wants to measure the dispersion function of the machine.
This measurement requires the implementation of BPMs and an RF master clock (set and get of the RF frequency within a narrow range around the nominal value).

The measurement structure is identical to that of subsection \ref{usecase:chromaticity}.
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 beam orbit (horizontal and vertical local orbit positions at each BPM) is recorded.
For each BPM, then a polynomial fit (usually linear) is made of the local orbit to the RF frequency.
The linear coefficient of this fit (normalised by a coefficient depending on the momentum compaction factor) is a local value of the dispersion.
Dispersion functions (horizontal and vertical) are then obtained at the locations of each BPM.

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