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.

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A new, unified theoretical description of coupled-bunch instabilities in unevenly filled storage rings is presented. Uneven-fill longitudinal dynamics are explained in terms of two physical phenomena: fill-induced tune-spread damping and modulation coupling of strong even-fill eigenmodes. The latter is also present in the transverse plane. The analysis yields simple criteria for optimizing fill shapes to reduce the growth rates of the most unstable modes. Experimental results from the ALS and PEP-II are shown to be in good agreement with the theory.