  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.
