A study of beam-beam effects in hadron colliders with a large number of bunches

A particle beam is a collection of a large number of charges and represents an electromagnetic potential for other charges, therefore exerting forces on itself and other beams. The control of this so called Beam-Beam Interactions (BBIs) in particle colliders is fundamental to preserve beam stability and achieve the collider maximal luminosity. In the case of the Large Hadron Collider (LHC) at CERN, these forces are experienced as localized periodic distortions when the two beams cross each other in the four experimental areas. The forces are most important for high density beams, i.e. high intensity and small beam sizes. Each LHC beam is composed of 2808 bunches, each containing $10^{11}$ protons and with a transverse size of 16~$\mu $m at the interaction points. These extreme parameters are the key to obtain high ``luminosity'', i. e. the number of collisions per second needed to study rare physics phenomena. The BBI is therefore often the limiting factor for the luminosity of colliders. Within all BB effects, this thesis covers coherent and incoherent beam-beam effects in hadron colliders with particular enphasis on those with a large number of bunches, like the LHC. We have developed complementary numerical tools to study the effects of BBIs on the particle beams. The use of new parallel algorithms was fundamental to allow the scale of the calculations. The objectives are a better understanding of these effect s and if necessary to propose changes to the LHC beam parameters to keep detrimental effects small. We have demonstrated the numerical predictibility of bunch to bunch differences and for the first time compared the results to analytical predictions and experimental data from the Relativistic Heavy Ion Collider (RHIC). Beam-beam transfer function measurements had been reproduced and understood in terms of coherent beam-beam modes. An implementation of the measurement devices had been suggested in order to avoid misinterpreted diagnostics. An emittance growth caused by the BBIs had been observed and characterized with numerical studies and explained with a simple physical picture. A study of the parametrical dependency of this effect defines qualitatively the expected limiting factors to avoid detrimental deterioration of the beams. The variation of the LHC tune spectra for different collision symmetries and in the presence of long range as well as head-on collisions had been presented and explained. This will be of fundamental importance to correctly interprete the observations of single bunch measurements during the operation of the collider and to push the performances.