Impact of the 50 Hz harmonics on the beam evolution of the Large Hadron Collider.

Since the beginning of the Large Hadron Collider (LHC) commissioning, spectral components at harmonics of the mains frequency (50~Hz) have been observed in the transverse beam spectrum. This paper presents an overview of the most important observations, collected during the latest physics run of the LHC in 2018, which clearly indicate that the harmonics are the result of a real beam excitation rather than an instrumental feature. Based on these findings, potential sources of the perturbation are discussed and a correlation with noise originating from the magnets' power converters is presented. As many of these tones reside in the vicinity of the betatron tune, their presence can be detrimental for the quality of the tune measurement and its tracking during operation, potentially leading to proton losses. A quantitative characterisation of the machine noise spectrum, together with an understanding of the noise source is an essential ingredient to 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 noise spectrum as extracted from experimental observations. The methods and results of the tracking studies are reported and discussed in this paper.