Optics-measurement-based Beam Position Monitor Calibration.

Accurate measurements of the focusing properties of an accelerator are essential for proper operation of a synchrotron, both for the machine protection and for the performance of the experiment. Measurement of linear optics functions based on turn-by-turn measurements has been developed continuously in pursuit of more accurate results. Optics functions that describe the focusing properties of the machine can be obtained from different observables: phase and amplitude of the transverse betatron oscillations and the change of the tune by modulating the current of quadrupoles (K-modulation) . Reconstruction of linear optics using the phase, in combination with K-modulation, have been the main approaches for obtaining the $\beta$-function in accelerators all over the world. Measurements of optics functions based on the amplitude, denoted as from amplitude, have not been used as widely as the other methods since it requires accurate beam-position-monitor (BPM) calibration. BPMs are key elements in accelerator operation, providing essential information about different beam parameters that are directly related to the accelerator performance. BPMs are calibrated before its installation in the accelerator to obtain an accurate conversion from an induced voltage to the centre of charge position. This calibration procedure can only be performed when the accelerator is in a period of non-activity and does not completely reproduce the exact conditions that occur during the machine operation. The studies presented in this thesis have served as improvement of the from amplitude approach, $\beta^{A}$, and they can be summarized in two groups: developing of the uncertainty associated to the $\beta^{A}$-function and mitigation of the BPM calibration factors effects. First, a study of the error-bar associated with the measured A-function is introduced using an analytical formalism that has been contrasted with simulations and experimental results. Second, a study of the BPM calibration factors based on optics measurements has been developed as part of this research. Discrepancies observed during the optics measurements at the Large Hadron Collider (LHC) and the Proton Synchrotron Booster (PSB) between different $\beta$-reconstruction approaches, show that the impact of the BPM calibration factors on the optics functions was higher than expected from the design values and tolerances. Measurement of the optics functions allows obtaining extra information on BPM calibration together with its associated uncertainty and resolution. This thesis summarizes the development of two different techniques to compute the BPMs calibration factors based on optics measurements accurately. These approaches have been developed using as a test bench the LHC and the PSB, and it is foreseen to extrapolate them to future accelerators. In case of LHC, the optics developed for computing the calibration factors only allows to accurately calibrate a limited range of BPMs located in the vicinity of the experiments denoted as IRs. The implementation of this approach in LHC and PSB is introduced in this thesis. Together with a summary of the hardware and software upgrades needed for its implementation. In case of LHC, calibration factors have been implemented in different machine configurations, in which the -function can be measured accurately using the three different approaches previously introduced: $\beta$, $\beta^{A}$ and K-modulation. In LHC IRs BPMs a systematic deviation of the BPM calibration was observed when reconstructing the $\beta$-function using the $\beta^{A}$-method with respect to the results obtained using the approach. By compensating the effect of the calibration factors in the measured $\beta^{A}$-function, the average accuracy of the $\beta$-function has improved in a 6% in Beam 1 and 4% in Beam 2 with respect to the direct measured A-function. On the other hand, in case of PSB, the validation of the calibration optics has been performed using the nominal optics used during the routine operations. Calibrating the BPMs using an optics-based approach has allowed decreasing the -function error bar, previously computed using the approach, by a factor of three.