Phase space tracking of coupled-bunch instabilities

Abstract

We describe an instability diagnostic that exploits the information contained in the angular evolution of coupled-bunch oscillations in phase space. In addition to enabling measurement of coherent tunes and bunch tunes with accuracy of a few hertz, phase space tracking allows new kinds of comparisons between instability theory and experiment. Phase space evolution of bunches participating in a lowthreshold vertical instability in the high energy ring of the Stanford Linear Accelerator Center B factory (PEP-II) is used to distinguish between the fast beam-ion instability and conventional instabilities. Tracking of longitudinal instabilities at the LBNL Advanced Light Source and PEP-II is used to measure coherent tunes and gain new insights into uneven-fill instabilities.

Architectures and Algorithms for Control and Diagnostics of Coupled-Bunch Instabilities in Circular Accelerators

“…The main new contribution presented here is the estimation of the complex eigenvalue from the exponentially growing or decaying oscillatory motion. Before this work there existed methods developed by S. Prabhakar for estimating the exponential growth or damping rates by considering the envelope of the motion [2] and for estimating the oscillation frequency from phase-space trajectories [3]. Since these extract the real (growth or damping rate) and the imaginary (oscillation frequency) parts of the eigenvalue separately information is lost in the process.…”

“…In addition we bandpass filter the bunch signals around the synchrotron frequency and convert the measured real trajectories to complex signals. The conversion is accomplished using the Hilbert transform and provides estimates of the phase-space motion trajectories [3].…”

“…3.6. It shows excellent agreement with the scaled Gaussian probability density function with variance computed from the residuals.Joint estimation of growth rate and oscillation frequency has several advantages over techniques presented in[2,3] that separately estimate each quantity. Exponential fitting to the envelope of motion has large errors when noise levels are high.…”

Development of a high-speed digital signal process system for bunch-by-bunch feedback systems

“…This powerful method of analyzing instabilities is known as transientdomain analysis [5,9]. Six large-scale memory boards for all planes of both rings with a capacity of 20 MB have been prepared for analysis as bunch oscillation recorders.…”

Development and diagnostic tools in the feedback system of SRRC

“…The batch data capture is support to all bunches information access by network. These data will be saved in a file and analyzed by Prabhakar's MATLAB code [4,5]. The operation graphical interface can be operated in WindowNT/98 and UNIX workstation as shown in figure 3.…”