Independent component analysis for beam measurements

Abstract

Independent component analysis (ICA) has been used for data mining in many branches of science. In beam physics, ICA can be applied to analyze turn-by-turn beam position monitor data of beam motion. The narrow-band filtering of ICA provides us methods to identify and extract information on the linear betatron and synchrotron motion, effects of wake fields, etc. We show that the ICA is also a powerful tool to measure nonlinear magnetic field in accelerators. Numerical simulations are used to demonstrate the ability to obtain sextupole strengths at high precision. The methods can be extended to other higher order multipoles.

Uncovering beam position monitor noise at the Relativistic Heavy Ion Collider

“…It is highly efficient in separating narrow-band source signals from sampled data. 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].…”

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

“…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.…”

Independent component analysis applied to long bunch beams in the Los Alamos Proton Storage Ring

“…ICA's major advantage over the typical BSS method, principal component analysis (PCA), which is the BSS foundation of the well-known model independent analysis (MIA) [2], is that it is more robust to noise, coupling, and nonlinearity [3][4][5]. Because of its robustness and generality, ICA has been widely applied in different fields, such as image feature extraction, audio separation, brain imaging, telecommunications, and econometrics [1], but using ICA for beam analysis is relatively new [3][4][5][6][7][8].…”

“…In PCA, the separated source signals are uncorrelated, while the source signals from ICA are independent, which mathematically is a much stronger property. It is easy to show that uncorrelatedness is not sufficient to cleanly separate source signals [1], especially in the presence of coupling and nonlinearity [3][4][5].…”

“…Multi-BPM ICA has been used to measure the transverse betatron phase and amplitude functions, dispersion function, linear coupling, sextupole strength, and nonlinear beam dynamics [3][4][5].…”