Linear Vlasov analysis for stability of a bunched beam

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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 ... continued below

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4 pages

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Warnock, Robert; Stupakov, Gennady; Venturini, Marco & Ellison, James A. June 30, 2004.

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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 with a realistic wake function for the SLC damping rings. There is close agreement between the two calculations.

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4 pages

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INIS; OSTI as DE00827098

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  • European Particle Accelerator Conference, Lucerne (CH), 07/05/2004--07/09/2004

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  • Report No.: LBNL--55806
  • Grant Number: AC03-76SF00098
  • Office of Scientific & Technical Information Report Number: 827098
  • Archival Resource Key: ark:/67531/metadc781407

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  • June 30, 2004

Added to The UNT Digital Library

  • Dec. 3, 2015, 9:30 a.m.

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  • April 4, 2016, 4:18 p.m.

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Warnock, Robert; Stupakov, Gennady; Venturini, Marco & Ellison, James A. Linear Vlasov analysis for stability of a bunched beam, article, June 30, 2004; Berkeley, California. (digital.library.unt.edu/ark:/67531/metadc781407/: accessed September 26, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.