The Large Hadron Collider (LHC) stores and collides the most energetic and intense particle beams ever produced. Even minute fractional beam losses in LHC hardware can affect operational efficiency and, in extreme cases, cause severe damage. To mitigate this, the LHC employs a sophisticated multi-stage collimation system. With the High-Luminosity upgrade (HL-LHC), the stored beam energy will increase such that the collimation system's integrity may be challenged in the event of failures of critical components.

Particles at large transverse amplitudes, the transverse beam halo, pose a particular risk to machine protection during fast beam loss events. Understanding the transverse halo population is therefore essential, as is assessing the need for active halo removal. One proposed solution is the installation of Hollow Electron Lenses (HELs), which generate a hollow electron beam co-axial and counter-rotating with the circulating hadron beam. The hollow geometry selectively perturbs halo particles while leaving the beam core unaffected. HELs were incorporated into the HL-LHC baseline in 2019 to mitigate halo effects, but production delays have postponed their availability, and they will not be available for the HL-LHC operation start, currently foreseen for mid-2030. Consequently, it is necessary to reassess HL-LHC limitations arising from an over-populated beam halo and define interim mitigation strategies.

This thesis focuses on characterising the transverse beam halo in the LHC, using both theoretical models and experimental data. Dedicated new measurements probe potential physical drivers of halo population and assess the impact of upgraded beam parameters, featuring higher intensities and brightness, approaching HL-LHC conditions. Novel transverse halo models are derived from these studies, providing the most accurate representation to date. Using LHC halo measurements, an estimate of the stored energy in the halo under HL-LHC operation is obtained, allowing evaluation of intensity limitations and providing a quantitative basis for halo removal requirements and active control system specifications.

Building on these halo models, fast-failure scenarios in the HL-LHC are re-assessed, clarifying the criticality of failures in combination with expected halo populations. Halo mitigation using HELs is studied numerically, evaluating efficiency and impact on both the halo and the beam core, which must remain unaffected. Due to the complexity of beam dynamics, these effects are investigated through detailed tracking simulations. The results establish a framework for understanding transverse halo behaviour, assessing halo criticality in HL-LHC operation, and guiding the development of mitigation strategies using HELs.