Application of independent component analysis to Fermilab Booster

Abstract

Autocorrelation is applied to analyze sets of finite-sampling data such as the turn-by-turn beam position monitor (BPM) data in an accelerator. This method of data analysis, called the independent component analysis (ICA), is shown to be a powerful beam diagnosis tool for being able to decompose sampled signals into its underlying source signals. We find that the ICA has an advantage over the principle component analysis (PCA) used in the model-independent analysis (MIA) in isolating independent modes. The tolerance of the ICA method to noise in the BPM system is systematically studied. The ICA is applied to analyze the complicated beam motion in a rapid-cycling booster synchrotron at the Fermilab. Difficulties and limitations of the ICA method are also discussed.

Application of independent component analysis to ac dipole based optics measurement and correction at the Relativistic Heavy Ion Collider

“…The fast Fourier transform of these source signals reveals the betatron tune f . Using the spatial functions A f1 and A f2 , the betatron amplitude function f;i and phase advance c f;i at the ith BPM can be extracted as [7] …”

“…In addition to its high efficiency in mode separation, the technique of ICA for optics measurement has been proven to be as robust as PCA against BPM noise [7]. ICA has been applied to the free betatron oscillation signal to analyze the transverse betatron amplitude function and phase advance, dispersion function, linear coupling, and sextupole strength [7][8][9]. However, additional considerations on interpretation of source signals are required to apply ICA to ac dipole driven betatron oscillation for optics measurement.…”

“…Both spatial and temporal functions of different source signals extracted from ICA analysis provide information about beam motions from which optical functions can be derived. In addition to its high efficiency in mode separation, the technique of ICA for optics measurement has been proven to be as robust as PCA against BPM noise [7]. ICA has been applied to the free betatron oscillation signal to analyze the transverse betatron amplitude function and phase advance, dispersion function, linear coupling, and sextupole strength [7][8][9].…”

Uncovering beam position monitor noise at the Relativistic Heavy Ion Collider

“…Numerical simulations indicate that the ICA can be used to uncover nonlinear modes for sextupole strength measurement [2], vertical dispersion function measurement, and emittance correction [3]. In actual experimental data analysis, ICA has been successfully utilized to extract characteristic beam motion signals from turn-by-turn (TBT) data for beam optics measurement at the Fermilab booster [4], Los Alamos Proton Storage Ring [5], and Relativistic Heavy Ion Collider (RHIC) [6]. Compared to the singular value decomposition (SVD) -based principle component analysis [7], ICA is more robust in the presence of noise [4].…”

“…In actual experimental data analysis, ICA has been successfully utilized to extract characteristic beam motion signals from turn-by-turn (TBT) data for beam optics measurement at the Fermilab booster [4], Los Alamos Proton Storage Ring [5], and Relativistic Heavy Ion Collider (RHIC) [6]. Compared to the singular value decomposition (SVD) -based principle component analysis [7], ICA is more robust in the presence of noise [4]. ICA can also be used to discover intrinsic problems of beam position monitors (BPMs).…”