Simple models describing the time-evolution of luminosity in hadron colliders

In recent years, several studies have been performed to describe the evolution of the losses in circular proton machines. Considerations based on single-particle, non-linear beam dynamics allowed building models that, albeit simple, proved to be in good agreement with measurements. These initial results have been generalised, thus opening the possibility to describe the luminosity evolution in a circular hadron collider. In this paper, the focus is on the derivation of scaling laws for the integrated luminosity, taking into account both burn off and additional pseudo-diffusive effects. The proposed models are applied to the analysis of the data collected during the LHC Run I and the outcome is discussed in detail.