Tune modulation effects in the High Luminosity Large Hadron Collider

Abstract

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 resonances 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.

Origin of the 50 Hz harmonics in the transverse beam spectrum of the Large Hadron Collider

“…First, one must observe that the frequencies of the lines are not affected by the tune change. This fact proves that the harmonics are the result of a dipolar field error rather than a tune modulation [44]. Second, a comparison prior and after the trim leads to the conclusion that the amplitude of the lines in the vicinity of the betatron tune is strongly enhanced.…”

“…From the FMAs, it is observed that the dipolar noise results in an increase of the particles' diffusion, first, by enhancing the strength of some of the nominal resonances and second, through the excitation of additional resonances. In contrast to quadrupolar modulations [44], which lead to the excitation of sideband resonances, the location of the resonances in the presence of a modulated dipolar field error is equal to the frequency of the excitation. As the noise is injected in the horizontal plane, they appear as vertical lines in fixed positions for the low (black) and high (blue) frequency cluster.…”

“…Given that these frequency maps are performed in 5D, the modulation induced from the synchrotron motion to the off-momentum particles through chromaticity is not illustrated [44]. This effect leads to the excitation of synchrotron sideband resonances, which overlap with the nominal and the dipolar resonances, further increasing the tune diffusion of the particles in the distribution.…”

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

“…The aim of the present paper is to determine whether the 50 Hz harmonics act as a limiting factor to the beam performance of the LHC, as well as its future upgrade, the High-Luminosity LHC (HL-LHC) [8], using single-particle tracking simulations with power supply ripple in the form of dipolar excitations. The impact of power supply ripple that results in a tune modulation is discussed in a previous paper [9]. First, the motion of a particle in the presence of a modulated dipolar field error is described using a linear formalism (Section II).…”