Tune modulation effects in the High Luminosity Large Hadron Collider

Several transverse noise sources, such as power supply ripples, 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). In the presence of non-linearities, depending on the spectral components of the power supply noise and the nature of the source, such a mechanism can increase the diffusion of the particles in the distribution through the excitation of sideband resonances in the vicinity of the ones driven by the lattice non-linearities. 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 noise effects is anticipated for the quadrupoles of the inner triplets. The modulation that may arise from the power supply ripples 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. To this end, the aim of this paper is to study the impact of tune modulation effects on the transverse beam motion resulting from the interplay between quadrupolar power supply ripples and synchro-betatron coupling. A power supply noise 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 modulation is demonstrated with frequency maps and the higher sensitivity to specific modulation frequencies is explained. Finally, a power supply noise spectrum consisting of several tones is considered in the simulations to determine whether the presence of power supply ripples in the quadrupoles of the inner triplet will limit the luminosity production in the HL-LHC era.