Description: In this paper, the eigenvalue type solution to the bunched beam instability with frequency spread is studied. The approach provides a comprehensive solution to the problem by including all necessary modes. The synchrotron frequency spread is represented by a mode decomposition, the decomposed modes have different inherent frequencies from each other and the corresponding radial functions are different from the ones without frequency spread. The environmental impedance induced feedback applied to these modes and then creates Landau damping effect. The radial modes and therefore the line densities can be solved throughout the Landau damping, thus to provide some insight into the process. Several conceptual and computational problems are discussed, and the method is compared with the conventional Landau damping treatment. Finally, the case of mode coupling is also discussed.
Date: September 1, 1994
Creator: Zhang, S. Y. & Weng, W. T.
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