The Large Hadron Collider (LHC), the largest particle accelerator ever built, is presently under commissioning at the European Organization for Nuclear Research (CERN). It will collide beams of protons, and later Pb ions, at ultrarelativistic energies. Because of its unprecedented energy, the operation of the LHC with heavy ions will present beam physics challenges not encountered in previous colliders. Beam loss processes that are harmless in the presently largest operational heavy-ion collider, the Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory, risk to cause quenches of superconducting magnets in the LHC. Interactions between colliding beams of ultrarelativistic heavy ions, or between beam ions and collimators, give rise to nuclear fragmentation. The resulting isotopes could have a charge-to-mass ratio different from the main beam and therefore follow dispersive orbits until they are lost. Depending on the machine conditions and the ion species, these losses could occur in localized spots, where the induced heating risks to the quench the superconducting magnets. In this thesis, I study first electromagnetic processes between \pb ions at the interaction points of the LHC through simulations. The beam-induced heat load from ions that have undergone bound free pair production (BFPP), which is the potentially most dangerous loss mechanism, is predicted to be 40% above the quench level although uncertainties are large. Measurements with Cu beams at RHIC show that localized losses from the collisions exist, although it is difficult to disentangle the losses from BFPP and electromagnetic dissociation (EMD). Furthermore, residual ion fragments created in the collimation system of the LHC could induce quenches and I present the first measurements of such beam losses together with detailed simulations. The results reveal qualitative differences in loss behaviour between heavy ions and protons and serve both as an evaluation of the principles of ion collimation and as an experimental benchmark of the ICOSIM program. Finally, simulations of the ion luminosity time evolution at RHIC and LHC are presented and I show details of a physical model for collisions on a particle level. This model is combined with routines for intrabeam scattering and optical tracking, written by others, to a particle tracking code. The program gives a very good agreement with experimental data from RHIC over a wide range of physics stores with different conditions. The same code is then used to predict the luminosity time evolution in the LHC
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