Beams Document 9020-v1

DocDB Home ]  [ Search ] [ Last 20 Days ] [ List Authors ] [ List Topics ] [ List Events ]

Longitudinal Modes of Bunched Beams with Weak Space Charge

Document #:
Document type:
Submitted by:
Rob Ainsworth
Updated by:
Rob Ainsworth
Document Created:
13 Apr 2021, 16:27
Contents Revised:
13 Apr 2021, 16:27
Metadata Revised:
13 Apr 2021, 16:27
Viewable by:
  • Public document
Modifiable by:

Quick Links:
Latest Version

Longitudinal collective modes of a bunched beam with a repulsive inductive impedance (the space charge below transition or the chamber inductance above it) are analytically described by means of reduction of the linearized Vlasov equation to a parameter-less integral equation. For any multipolarity, the discrete part of the spectrum is found to consist of infinite number of modes with real tunes, which limit point is the incoherent zero-amplitude frequency. In other words, notwithstanding the RF bucket nonlinearity and potential well distortion, the Landau damping is lost. Hence, even a tiny coupled-bunch interaction makes the beam unstable; such growth rates for all the modes are analytically obtained for arbitrary multipolarity. In practice, however, the finite threshold of this loss of Landau damping is set either by the high-frequency impedance roll-off or intrabeam scattering. Above the threshold, growth of the leading collective mode should result in persistent nonlinear oscillations.
Files in Document:
DocDB Home ]  [ Search ] [ Last 20 Days ] [ List Authors ] [ List Topics ] [ List Events ]

DocDB Version 8.8.10, contact Beams Document Database Administrators