APS : Harmonic analysis of nonstationary signals with application to LHC beam measurements

Russo, G.; Maclean, E.H.; Giovannozzi, M.; Franchetti, G.

doi:10.1103/PhysRevAccelBeams.27.094001

Article
Report number	arXiv:2409.05406
Title	Harmonic analysis of nonstationary signals with application to LHC beam measurements
Author(s)	Russo, G. (CERN ; Frankfurt U.) ; Franchetti, G. (Darmstadt, GSI) ; Giovannozzi, M. (CERN) ; Maclean, E.H. (CERN)
Publication	2024-09-01
Imprint	2024-09-09
Number of pages	19
In:	Phys. Rev. Accel. Beams 27 (2024) 094001
DOI	10.1103/PhysRevAccelBeams.27.094001 (publication)
Subject category	physics.acc-ph ; Accelerators and Storage Rings
Accelerator/Facility, Experiment	CERN LHC
Abstract	Harmonic analysis has provided powerful tools to accurately determine the tune from turn-by-turn data originating from numerical simulations or beam measurements in circular accelerators and storage rings. Methods that have been developed since the 1990s are suitable for stationary signals, i.e., time series whose properties do not vary with time and are represented by stationary signals. However, it is common experience that accelerator physics is a rich source of time series in which the signal amplitude varies over time. Furthermore, the properties of the amplitude variation of the signal often contain essential information about the phenomena under consideration. In this paper, a novel approach is presented, suitable for determining the tune of a non-stationary signal, which is based on the use of the Hilbert transform. The accuracy of the proposed methods is assessed in detail, and an application to the analysis of beam data collected at the CERN Large Hadron Collider is presented and discussed in detail.
Copyright/License	publication: © 2024 authors (License: CC BY 4.0) preprint: (License: CC BY 4.0)

$Simulated signals representing the oscillation of the barycenter of a kicked beam as a result of energy damping (A), chromatic decoherence (B), nonlinearities (C), and acceleration (D). These signals are shown as functions of the number of turns $n$ (up to the maximum of $1024$ turns). For each signal, the characteristic scaling factor $\lambda$ has been varied in the interval shown on the color scale.$ $The tune error $\Delta \nu(N)$ is computed (from left to right) for the signals with amplitude variation from energy damping (A), chromatic decoherence (B), nonlinearities (C), and acceleration (D). Two methods have been used, namely, the interpolated {DFT} (top) and the interpolated {DFT} with Hanning filter (bottom). {The scaling of the tune error corresponding to the case $\lambda=0$ is represented by the back dashed lines with a dependence as $1/N^2$ (top) and $1/N^4$ (bottom). When $\lambda \neq 0$ the colored curves representing the tune error show a very different scaling with respect to the case of stationary signals.}$ $The tune error $\Delta \nu(N)$ is computed (from left to right) for the signals with amplitude variation from energy damping (A), chromatic decoherence (B), nonlinearities (C), and acceleration (D). Two methods have been used, namely, the interpolated {DFT} (top) and the interpolated {DFT} with Hanning filter (bottom). {The scaling of the tune error corresponding to the case $\lambda=0$ is represented by the back dashed lines with a dependence as $1/N^2$ (top) and $1/N^4$ (bottom). When $\lambda \neq 0$ the colored curves representing the tune error show a very different scaling with respect to the case of stationary signals.}$ Show more plots

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Journalen skapades 2024-10-09, och modifierades senast 2024-10-11

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