Developing a Resonance Correction Scheme in the LHC

Non-linear errors in the magnetic field of the Large Hadron Collider (LHC) at CERN often lead to undesirable resonances and instabilities in the particle motion, which can negatively affect the operations of the accelerator. This project focuses on developing a new correction scheme with a response matrix approach to optimize the values of the skew sextupolar correctors of the LHC at injection, in order to mitigate the impact of resonance driving terms (RDTs). So far, no correction has been introduced to actively compensate these RDTs. In particular, we investigate the RDTs related to the $3Q_y$ resonance, which has been proposed to be connected to emittance growth in the LHC, leading to a loss of luminosity in the detectors. Starting from a basic linear model of the LHC, we gradually introduce more complex errors and demonstrate that this correction scheme is more effective than the standard correction. The correction scheme also proves to be effective for more advanced non-linear models, also considering alignment errors.