Diffusion model of the hollow electron lens for HL-LHC

In the upcoming years, various upgrades and improvements are planned for the CERN Large Hadron Collider (LHC) and represent the mandate of the High-Luminosity project. The upgrade will allow for a total stored beam energy of about 700 MJ, which will need, among others, an extremely efficient collimation system. This will be achieved with the addition of a hollow electron lens (HEL) system to help control the beam-halo depletion and mitigate the effects of fast beam losses. In this master thesis, we present a diffusion model of the HEL for HL-LHC. In particular, we explore several scenarios to use such a device, focusing on the halo depletion efficiency given by different noise regimes.