Location of Repository

LINEAR VLASOV ANALYSIS FOR STABILITY OF A BUNCHED BEAM ∗

By R. Warnock and G. Stupakov

Abstract

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

Year: 2011
OAI identifier: oai:CiteSeerX.psu:10.1.1.196.898
Provided by: CiteSeerX
Download PDF:
Sorry, we are unable to provide the full text but you may find it at the following location(s):
  • http://citeseerx.ist.psu.edu/v... (external link)
  • http://www-library.lbl.gov/doc... (external link)
  • Suggested articles


    To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.