  Harmonics of the mains frequency (50 Hz) have been systematically observed in
the transverse beam spectrum of the Large Hadron Collider (LHC) since the start
of its operation in the form of dipolar excitations. In the presence of strong
non-linearities such as beam-beam interactions, as many of these power supply
ripple tones reside in the vicinity of the betatron tune they can increase the
tune diffusion of the particles in the distribution, leading to proton losses
and eventually to a significant reduction of the beam lifetime. The aim of this
paper is to determine whether the 50~Hz harmonics have an impact on the beam
performance of the LHC. A quantitative characterization of the ripple spectrum
present in the operation of the accelerator, together with an understanding of
its source is an essential ingredient to also evaluate the impact of the 50~Hz
harmonics on the future upgrade of the LHC, the High Luminosity LHC (HL-LHC).
To this end, simulations with the single-particle tracking code, SixTrack, are
employed including a realistic ripple spectrum as extracted from experimental
observations to quantify the impact of such effects in terms of tune diffusion,
Dynamic Aperture and beam lifetime. The methods and results of the tracking
studies are reported and discussed in this paper.
