Abstract
Independent component analysis (ICA) is a powerful blind source separation (BSS) method. Compared to the typical BSS method, principal component analysis, ICA is more robust to noise, coupling, and nonlinearity. The conventional ICA application to turn-by-turn position data from multiple beam position monitors (BPMs) yields information about cross-BPM correlations. With this scheme, 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. We apply ICA in a new way to slices along the bunch revealing correlations of particle motion within the beam bunch. We digitize beam signals of the long bunch at the Los Alamos Proton Storage Ring with a single device (BPM or fast current monitor) for an entire injection-extraction cycle. ICA of the digitized beam signals results in source signals, which we identify to describe varying betatron motion along the bunch, locations of transverse resonances along the bunch, measurement noise, characteristic frequencies of the digitizing oscilloscopes, and longitudinal beam structure.
Highlights
Independent component analysis (ICA) is a powerful blind source separation (BSS) method [1]
Direct evidence of the 32 MHz oscilloscope clock independent components (ICs) is found in the FFT of the digitized beam signal, Fig. 11, which shows the revolution harmonics separated by the revolution frequency
The 32 MHz signal has been observed for several years in FFTs of SRWM41’s sum and difference signals, which are traditionally digitized with the LeCroy LC684DXL oscilloscope, but its source was not identified because the FFT signal analysis approach only provides the source signal frequency
Summary
Independent component analysis (ICA) is a powerful blind source separation (BSS) method [1]. ICA and PCA separate data into source signals without a beam dynamics model or knowledge of measurement details. They require additional information from a model and additional assumptions of the source signals other than the original PCA assumption. We choose to use ICA for two reasons: no imposed data model and no additional assumptions of the source signals other than independence. Digitized signal bins are spatially distributed along the beam bunch, giving adequate spatial structure and providing ICA with enough raw data.
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