Beam Dynamics Studies to Develop a High-energy Luminosity Model for the LHC

Luminosity, the key figure of merit of a collider as the LHC, depends on the brightness of the colliding beams. This makes the intensity dependent beam-beam effect the dominant performance limiting factor at collision. The parasitic interactions due to the electromagnetic mutual influence of the beams in the interaction region of a collider induce a diffusive behaviour in the tails of the beam. The evolution of charge density distribution is studied to model the beam tails evolution in order to characterize beam lifetime and luminosity. To achieve this, tools are developed for tracking distributions of arbitrary number of single particles interacting with the opposing strong-beam, to analyse the halo formation processes due to the combined effect of beam-beam and machine non-linearities. This paper presents preliminary results of the simulations, both for the LHC Run I and nominal LHC parameters. The former will be used to benchmark simulations while the latter aims at supporting luminosity estimate for the Run II.