Statistical analysis of RHIC beam position monitors performance

A detailed statistical analysis of beam position monitors (BPM) performance at RHIC is a critical factor in improving regular operations and future runs. Robust identification of malfunctioning BPMs plays an important role in any orbit or turn-by-turn analysis. Singular value decomposition and Fourier transform methods, which have evolved as powerful numerical techniques in signal processing, will aid in such identification from BPM data. This is the first attempt at RHIC to use a large set of data to statistically enhance the capability of these two techniques and determine BPM performance. A comparison from run 2003 data shows striking agreement between the two methods and hence can be used to improve BPM functioning at RHIC and possibly other accelerators.

Figure 1

Fourier spectrum of a good RHIC BPM signal. The spectral lines within the windows are used to determine the rms noise observable.

Figure 2

Spatial vectors and FFT of temporal vectors of the four dominant modes from simulation data. Note that singular vectors are normalized.

Figure 3

Spatial and temporal vectors of modes corresponding to two noisy BPMs with correlation.

Figure 4

Percentage of occurrences of system failure per BPM versus longitudinal location. A representation of the lattice (dipoles in black and quadrupoles in red) is shown in the bottom graph.

Figure 5

Peak-to-peak values for all BPMs in all data files.

Figure 6

Histograms of the rms observable for the two rings and the two planes. The total number of signals used in the histograms are shown.

Figure 7

Comparison between two different rms cuts showing qualitatively similar results.

Figure 8

Average rms observable versus longitudinal position of the BPM.

Figure 9

Histogram of the largest peak amplitudes of all spatial modes for both planes in both rings. The Gaussian-like distributions represent a coherent signal from good BPMs and peaks at 1 represent faulty BPMs.

Figure 10

Histograms of the norm of $n$ largest peak values in each mode in the horizontal plane. Gaussian-like distributions represent coherent signal from good BPMs and peaks at 1 represent faulty BPMs.

Figure 11

Comparison between two SVD thresholds (0.85 and 0.95) for the blue ring-horizontal plane.

Figure 12

Comparison of the FFT and SVD techniques for 678 files from the yellow ring showing a good agreement. The number of times a BPM provides a faulty signal is plotted versus its location.

Figure 13

Percentage of occurrences of system failure per BPM versus longitudinal location for run 2004. A representation of the lattice (dipoles in black and quadrupoles in red) is shown in the bottom graph.

Figure 14

Average rms observable versus longitudinal position of the BPM for run 2004.

Figure 15

Comparison between two different rms and SVD cuts for run 2004.