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Register a new userPrincipal Component Analysis of Cavity Beam Position Monitor Signals
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Model-independent analysis (MIA) methods are generally useful for analysing complex systems in which relationships between the observables are non-trivial and noise is present. Principle Component Analysis (PCA) is one of MIA methods allowing to isolate components in the input data graded to their contribution to the variability of the data. In this publication we show how the PCA can be applied to digitised signals obtained from a cavity beam position monitor (CBPM) system on the example of a 3-cavity test system installed at the Accelerator Test Facility 2 (ATF2) at KEK in Japan. We demonstrate that the PCA based method can be used to extract beam position information, and matches conventional techniques in terms of performance, while requiring considerably less settings and data for calibration.
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The Accelerator Test Facility 2 (ATF2) is a scaled demonstrator system for final focus beam lines of linear high energy colliders. This paper describes the high resolution cavity beam position monitor (BPM) system, which is a part of the ATF2 diagnostics. Two types of cavity BPMs are used, C-band operating at 6.423 GHz, and S-band at 2.888 GHz with an increased beam aperture. The cavities, electronics, and digital processing are described. The resolution of the C-band system with attenuators was determined to be approximately 250 nm and 1 m for the S-band system. Without attenuation the best recorded C-band cavity resolution was 27 nm.
This paper describes the development of a digital-based Beam Position System which was designed, developed, and adapted for the Tevatron during Collider Run II.
The readout electronics for the resonant beam position monitors (BPMs) in the Fermilab Switchyard (SY) have been upgraded, utilizing a low noise amplifier transition board and Fermilab designed digitizer boards. The stripline BPMs are estimated to have an average signal output of between -110 dBm and -80 dBm, with an estimated peak output of -70 dBm. The external resonant circuit is tuned to the SY machine frequency of 53.10348 MHz. Both the digitizer and transition boards have variable gain in order to accommodate the large dynamic range and irregularity of the resonant extraction spill. These BPMs will aid in auto-tuning of the SY beamline as well as enabling operators to monitor beam position through the spill.
The Neutrinos at the Main Injector (NuMI) project will extract 120 GeV protons from the FNAL Main Injector in 8.56usec spills of 4E13 protons every 1.9 sec. We have designed secondary emission monitor (SEM) detectors to measure beam profile and halo along the proton beam transport line. The SEM?s are Ti foils 5um in thickness segmented in either 1?mm or 0.5?mm pitch strips, resulting in beam loss ~5E-6. We discuss aspects of the mechanical design, calculations of expected beam heating, and results of a beam test at the 8 GeV transport line to MiniBoone at FNAL.
We show how to efficiently project a vector onto the top principal components of a matrix, without explicitly computing these components. Specifically, we introduce an iterative algorithm that provably computes the projection using few calls to any black-box routine for ridge regression. By avoiding explicit principal component analysis (PCA), our algorithm is the first with no runtime dependence on the number of top principal components. We show that it can be used to give a fast iterative method for the popular principal component regression problem, giving the first major runtime improvement over the naive method of combining PCA with regression. To achieve our results, we first observe that ridge regression can be used to obtain a smooth projection onto the top principal components. We then sharpen this approximation to true projection using a low-degree polynomial approximation to the matrix step function. Step function approximation is a topic of long-term interest in scientific computing. We extend prior theory by constructing polynomials with simple iterative structure and rigorously analyzing their behavior under limited precision.
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