Tune modulation effects in the High Luminosity Large Hadron Collider

Several transverse noise sources, such as power supply ripple, can potentially act as an important limiting mechanism for the luminosity production of the Large Hadron Collider (LHC) and its future High-Luminosity upgrade (HL-LHC) [High Luminosity Large Hadron Collider (HL-LHC): Technical Design Report V0.1, CERN-2017-007-M [http://cds.cern.ch/record/782076?ln=en]]. In the presence of non-linearities, depending on the spectral components of the power supply ripple spectrum and the nature of the source, such a mechanism can increase the tune diffusion of the particles in the distribution through the excitation of sideband resonances in the vicinity of the resonances driven by the lattice nonlinearities. For the HL-LHC, due to the reduction of the beam size in the interaction points (IP) of the high luminosity experiments (IP1 and 5), increased sensitivity to power supply ripple is anticipated for the quadrupoles of the inner triplets. The modulation that may arise from the power supply ripple will be combined with the tune modulation that intrinsically emerges from the coupling of the transverse and longitudinal plane for off-momentum particles through chromaticity. This paper aims to study the impact of tune modulation effects on the transverse beam motion resulting from the interplay between quadrupolar power supply ripple and synchro-betatron coupling in the presence of strong head-on and long-range beam-beam interactions. A power supply ripple threshold for acceptable performance is estimated with single-particle tracking simulations by investigating the impact of different modulation frequencies and amplitudes on the dynamic aperture. The excitation of sideband resonances due to the tune modulation is demonstrated with frequency maps and the higher sensitivity to specific modulation frequencies is explained. Finally, a power supply ripple spectrum consisting of several tones is considered to determine whether their presence will limit the luminosity production in the HL-LHC era.