A study on HL-LHC beam-beam resonances using a Lie Algebraic Weak-Strong model

Abstract

This thesis studies the resonances driven by beam-beam interactions in the planned High Luminosity upgrade to the Large Hadron Collider (HL-LHC) using a Lie algebraic formalism. With the suggested magnetic lattice for the HL-LHC, using the accelerator code MadX, bunch data (containing information such as shape, phase advance, and bunch separation) for 70 bunches over the two interaction regions (IRs), ATLAS and CMS, was computed. These data are used to create a 70 impulse beam-beam Weak-Strong model combining both long-range and head-on interactions. The effective Hamiltonian and a width formula derived in the thesis are used to analyze the system in betatron frequency space. As algebraically derived in this thesis, resonances of order q can be removed by phase-shifting both vertical and horizontal phase advances between interaction points by π/q. Namely, the 16th order resonances close to the proposed working point of (62.31,60.32) can be weakened by phase advances close to π/16. This Is reflected in frequency space plots of the effective Hamiltonian and of the width formula. Resonances are significantly weakened if phase advances are within 10^(-3) of the ideal ones for resonance cancellation; the phasing needs not be exact. The effect of crossing angle was briefly investigated; according to the effective Hamiltonian and width formula, beam-beam resonances cannot be significantly improved by increasing the tentative crossing angle of 590μrad. However, decreasing the crossing angle significantly strengthens the resonances of the system. A new working point (0.475,0.485) suggested from a study by another author was investigated; it lies away from dangerous resonances according to the tools used in this thesis, and should be investigated further.