Application of Independent Component Analysis for Beam Diagnosis

The independent component analysis (ICA) is applied to analyze simultaneous multiple turn-by-turn beam position monitor (BPM) data of synchrotrons. The sampled data are decomposed to physically independent source signals, such as betatron motion, synchrotron motion and other perturbation sources. The decomposition is based on simultaneous diagonalization of several unequal time covariance matrices, unlike the model independent analysis (MIA), which uses equal-time covariance matrix only. Consequently the new method has advantage over MIA in isolating the independent modes and is more robust under the influence of contaminating signals of bad BPMs. The spatial pattern and temporal pattern of each resulting component (mode) can be used to identify and analyze the associated physical cause. Beam optics can be studied on the basis of the betatron modes. The method has been successfully applied to the Booster Synchrotron at Fermilab.