Advancements in Optics Control at the CERN Proton Synchrotron

The CERN Proton Synchrotron (PS), operational since 1959, remains a critical component in CERN's accelerator complex, supporting downstream experiments and serving as an injector for larger machines like the SPS and LHC. Despite its foundational role, the PS faces increasing operational challenges, including precise control of tune and chromaticity, reliable horizontal emittance measurements, and resonance management. These difficulties are compounded by its aging infrastructure, non-linear magnetic lattice effects, dispersive contributions, and high-intensity beam demands.

To address these issues, this thesis introduces a suite of advanced diagnostic and control techniques. One major focus is the Pole Face Windings (PFWs), which are essential for managing tune and chromaticity. Historically controlled through static response matrices and basic functions, PFWs have struggled with accuracy, especially during transition crossing. This rigidity has made adapting to new beam cycles labor-intensive. A new machine learning (ML)-based system replaces these outdated controls with a dynamic, physics-aware neural network. A first network predicts tune and chromaticity using PFW settings, magnetic field values, and beam parameters, employing a physics-based loss function to incorporate beam dynamics directly into the training. A second control network allows real-time adjustments, significantly improving precision and flexibility across the magnetic cycle, particularly at high energies where traditional methods falter.

Accurate horizontal emittance measurements are critical, especially for the LHC injector chain. At low energies, the momentum spreads distort these measurements due to dispersion, masking true beam characteristics. To resolve this, zero dispersion optics were developed using Low Energy Quadrupoles (LeQs), enabling clean emittance measurements by removing dispersive contributions at key profile monitors. Experimental validation confirmed that discrepancies previously thought to be emittance blow-up between the PS Booster (PSB) and PS were actually artifacts of dispersion. The measurements also uncovered previously hidden overpopulated beam tails, significant for LHC luminosity performance.

The thesis also developed a numerical deconvolution method for machines unable to implement zero dispersion optics. By combining transverse profile measurements and longitudinal tomography, this method successfully separated convoluted beam distributions. Results matched zero dispersion optics measurements closely and revealed consistent tail populations. This technique, once refined, could be applied to other machines like the PSB and SPS, offering an adaptable approach for precise diagnostics in less flexible lattices. 

In addition to linear diagnostics, the thesis tackled resonance correction through the measurement of Resonance Driving Terms (RDTs). Traditional loss map methods are imprecise and time-consuming. By leveraging forced oscillations from the transverse damper (ADT), RDTs were measured with high resolution from turn-by-turn Beam Position Monitor (BPM) data. These measurements enabled identification and quantification of problematic resonances, including the skew sextupole resonance 3Qy and the 2Qx+1Qy resonance. In one key case, analytical corrections calculated from the RDTs reduced beam losses associated with the 2Qx+1Qy resonance, validating the method’s effectiveness.

Further improvements were made through enhanced BPM calibration using SVD-based cleaning of oscillation data. This step revealed inconsistencies in the PS's magnetic model, particularly in the skew sextupole strengths, which were corrected through model refinement and confirmed by simulation. The study also explored integrating BBQ pick-ups with turn-by-turn data to improve signal-to-noise ratios, though synchronization challenges remain.

Space charge effects were examined in the context of dispersion measurements. It was shown that while space charge influences beam width, it does not affect position-based dispersion measurements, allowing for indirect assessment of space charge dynamics. This distinction enabled the validation of RMS-based space charge models, particularly the KV-distribution model, which showed strong agreement with both simulations and experimental data.

Collectively, these results offer a set of powerful new tools for beam diagnostics, control, and correction in aging yet essential synchrotrons like the PS. Machine learning-based control of non-linear elements such as PFWs enables flexible and precise beam tuning. Zero dispersion optics and numerical deconvolution provide accurate emittance and beam tail measurements, crucial for optimizing luminosity. RDT-based resonance analysis presents a fast, model-driven alternative to traditional loss maps, expanding the reach of resonance correction to machines without AC-Dipoles.