Physical Review Special Topics. Accelerators and Beams (Mar 2007)

Collective beam instability study using a correlation-moment analysis

  • Samuel A Heifets,
  • Alexander W. Chao

DOI
https://doi.org/10.1103/PhysRevSTAB.10.034402
Journal volume & issue
Vol. 10, no. 3
p. 034402

Abstract

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A general formalism for treating simultaneously the transverse coupled-bunch and transverse coupled-mode instabilities is presented. In this approach, the equations of motion of a coupled multibunch beam are expanded to yield a system of equations involving correlation moments of the transverse and longitudinal motions. After a proper truncation, the system of equations is closed and can be solved. This approach allows us to formulate within one framework several known instability mechanisms including the single-bunch mode-coupling instability, the coupled-bunch instability, the mode-coupling instability, and the coupled-mode coupled-bunch instability as particular cases.