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

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