Not yet reviewed by Pith; the record is open.

At the Large Hadron Collider (LHC), the interplay between a series of effects, including intrabeam scattering (IBS), synchrotron radiation, longitudinal beam manipulations, two beam effects (beam-beam, e-cloud) and machine non-linearities, can change the population of the core and tails and lead to non-Gaussian beam distributions, at different periods during the beam cycle. By employing generalised distribution functions, it can be demonstrated that the modified non-Gaussian beam profiles have an impact in the beam emittance evolution by itself and thereby to the collider luminosity. This paper focuses on the estimation of beam distribution modification and the resulting rms beam size due to the combined effect of IBS and synchrotron radiation by employing a Monte-Carlo simulation code which is able to track 3D generalised particle distributions (SIRE). The code is first benchmarked over classical semi-analytical IBS theories and then compared with measurements from the LHC at injection and collision energies, including projections for the High-Luminosity LHC (HL-LHC) high brightness regime. The impact of the distribution shape on the evolution of the bunch characteristics and machine performance is finally addressed.