Equilibrium Beam Distribution and Halo in the LHC

The equilibrium LHC beam distribution at large amplitudes is a crucial input to the collimation and machine protection design, as well as to background studies. Its estimation requires a knowledge of the diffusion rates at which beam particles are transported to large transverse or longitudinal amplitudes. Important known mechanisms of particle diffusion include Touschek scattering, synchrotron radiation, intrabeam scattering (IBS) the nonlinear motion due to the long-range (LR) beam-beam (BB) collisions at top energy, persistent-current field errors during injection and at the start of acceleration, and Coulomb scattering off the residual gas. We summarize the expected contributions from different sources, introduce a diffusion model, and illustrate the evolution of the beam distribution at 7 TeV.