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| WEPLT159 |
Linear Vlasov Analysis for Stability of a Bunched Beam
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2212 |
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- R.L. Warnock, G.V. Stupakov
SLAC, Menlo Park, California
- J.A. Ellison
UNM, Albuquerque, New Mexico
- M. Venturini
LBNL, Berkeley, California
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We study the linearized Vlasov equation for a bunched beam subject to an arbitrary wake function. Following Oide and Yokoya, the equation is reduced to an integral equation expressed in angle-action coordinates of the distorted potential well. Numerical solution of the equation as a formal eigenvalue problem leads to difficulties, because of singular eigenmodes from the incoherent spectrum. We rephrase the equation so that it becomes non-singular in the sense of operator theory, and has only regular solutions for coherent modes. We report on a code that finds thresholds of instability by detecting zeros of the determinant of the system as they enter the upper-half frequency plane, upon increase of current. Results are compared with a time-domain integration of the nonlinear Vlasov equation, and with experiment, for a realistic wake function for the SLC damping rings.
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