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Phys. Rev. ST Accel. Beams 2, 084401 (1999) [8 pages]

Phase space tracking of coupled-bunch instabilities

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S. Prabhakar, J. D. Fox, D. Teytelman, and A. Young
Stanford Linear Accelerator Center, Stanford University, Stanford, California 94309

Received 9 June 1999; published 9 August 1999

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 low-threshold 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.


©1999 The American Physical Society

URL: http://link.aps.org/doi/10.1103/PhysRevSTAB.2.084401
DOI: 10.1103/PhysRevSTAB.2.084401
PACS: 29.27.Bd, 29.20.Dh

Supplemental Material

Video 1 [ QuickTime (3937 kB) | RealMedia (68 kB) | MPEG (877 kB) | AVI (696 kB) ]
Thumbnail of Video 1 A video representing the evolution of the vertical instability transient shown in the last four figures. Each frame shows the oscillation magnitudes ak and relative phase space angles (φk  -  φ150) of the 150 bunches on a single turn. Successive frames are separated by 20 turns. Only the last 7 ms of data are animated. The relative phase pattern is largely fixed, with a small upward trend in the section from bunch 60 to bunch 140.
Video 2 [ MPEG (1036 kB) | RealMedia (89 kB) | AVI (1252 kB) | QuickTime (6945 kB) ]
Thumbnail of Video 2The distinction between projections of a single eigenmode and superpositions of two or more eigenmodes is quite clear in this animation. The data are the same as in Fig. 9. As before, we plot Um(t)  exp(-jωreft) in the complex plane rather than Um(t).Successive frames, separated by 60 turns, show snapshots of the modal phase space coordinates of the two sets of "modes." Subframe (a) shows "modes" 805-815. These "modes" rotate at identical speeds as they grow, since they are merely projections of a single uneven-fill eigenmode. Subframe (b) shows the phasors corresponding to "modes" 780-786. The variation in amplitude and relative phase is due to the fact that each of these phasors is a superposition of two or more uneven-fill eigenmodes, with two or more coherent frequencies and growth rates. The paths that the tips of these phasors trace are the trajectories in Fig. 9.

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