Harmonic analysis of non-stationary signals with application to LHC beam measurements

TL;DR

This paper introduces a new Hilbert transform-based method for harmonic analysis of non-stationary signals, specifically applied to beam data from the CERN Large Hadron Collider, improving tune detection accuracy.

Contribution

A novel approach using the Hilbert transform for analyzing non-stationary signals in accelerator physics, addressing limitations of existing stationary signal methods.

Findings

Effective in analyzing non-stationary beam signals

Improves tune detection accuracy in LHC data

Demonstrated on CERN LHC beam measurements

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.