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A Matrix Formalism for Landau Damping


Existing methods of analysing the effect of bunch-to-bunch tune shifts on coupled bunch instabilities are applicable to beams with a single unstable mode, or a few non-interacting unstable modes. We present a more general approach that involves computing the eigenvalues of a reduced state matrix. The method is applied to the analysis of PEP-II longitudinal coupled bunch modes, a large number of which are unstable in the absence of feedback.

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