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Title: Theory of coupled-bunch longitudinal instabilities in a storage ring for arbitrary rf potentials

Abstract

Here, we present a theory of coupled-bunch longitudinal instabilities that is based on the coupled set of Vlasov equations governing the particle distribution function, and can be applied to arbitrary longitudinal potentials. We find that the coupled-bunch growth rate is given by a dispersion relation that is parametrized by the eigenvalues of the linear (harmonic) coupled-bunch matrix problem. Our theory therefore treats the wakefield-driven source of the instability and the effect of Landau damping together and on equal footing, and also indicates that the stabilizing effects of Landau damping can approximately be compared to the instability growth rates in a harmonic potential that has the same bunch length. We then apply the theory to a weakly nonlinear oscillator and to a quartic potential that is relevant for ultra-low emittance storage rings that employ bunch-lengthening systems. In the latter case we find that the theory compares quite favorably with particle tracking simulations for the parameters of the planned upgrade of the Advanced Photon Source.

Authors:
 [1]
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  1. Argonne National Lab. (ANL), Argonne, IL (United States)
Publication Date:
Research Org.:
Argonne National Lab. (ANL), Argonne, IL (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
OSTI Identifier:
1485742
Alternate Identifier(s):
OSTI ID: 1491846
Grant/Contract Number:  
AC02-06CH11357
Resource Type:
Published Article
Journal Name:
Physical Review Accelerators and Beams
Additional Journal Information:
Journal Volume: 21; Journal Issue: 12; Journal ID: ISSN 2469-9888
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
43 PARTICLE ACCELERATORS

Citation Formats

Lindberg, Ryan R. Theory of coupled-bunch longitudinal instabilities in a storage ring for arbitrary rf potentials. United States: N. p., 2018. Web. doi:10.1103/PhysRevAccelBeams.21.124402.
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Lindberg, Ryan R. Theory of coupled-bunch longitudinal instabilities in a storage ring for arbitrary rf potentials. United States. doi:10.1103/PhysRevAccelBeams.21.124402.
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Lindberg, Ryan R. Thu . "Theory of coupled-bunch longitudinal instabilities in a storage ring for arbitrary rf potentials". United States. doi:10.1103/PhysRevAccelBeams.21.124402.
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@article{osti_1485742,
title = {Theory of coupled-bunch longitudinal instabilities in a storage ring for arbitrary rf potentials},
author = {Lindberg, Ryan R.},
abstractNote = {Here, we present a theory of coupled-bunch longitudinal instabilities that is based on the coupled set of Vlasov equations governing the particle distribution function, and can be applied to arbitrary longitudinal potentials. We find that the coupled-bunch growth rate is given by a dispersion relation that is parametrized by the eigenvalues of the linear (harmonic) coupled-bunch matrix problem. Our theory therefore treats the wakefield-driven source of the instability and the effect of Landau damping together and on equal footing, and also indicates that the stabilizing effects of Landau damping can approximately be compared to the instability growth rates in a harmonic potential that has the same bunch length. We then apply the theory to a weakly nonlinear oscillator and to a quartic potential that is relevant for ultra-low emittance storage rings that employ bunch-lengthening systems. In the latter case we find that the theory compares quite favorably with particle tracking simulations for the parameters of the planned upgrade of the Advanced Photon Source.},
doi = {10.1103/PhysRevAccelBeams.21.124402},
journal = {Physical Review Accelerators and Beams},
number = 12,
volume = 21,
place = {United States},
year = {2018},
month = {12}
}
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Journal Article:
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Publisher's Version of Record
DOI: 10.1103/PhysRevAccelBeams.21.124402
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Figures / Tables:

FIG. 1 FIG. 1: Theoretical coupled-bunch growth rate as a function of the HOM frequency difference from a revolution harmonic. (a) plots the theoretical growth rate as we increase the matrix growth rate λ from being equal to the nonlinearity to four times that. (b) shows the effect of Landau damping bymore » comparing two cases from panel (a) to those os a simple harmonic oscillator.« less
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Works referenced in this record:

Interplay of Touschek scattering, intrabeam scattering, and rf cavities in ultralow-emittance storage rings
journal, May 2014

Longitudinal stability limit for electron bunches in a double RF system
journal, October 1983

The anti-bend cell for ultralow emittance storage ring lattices
journal, February 2014

  • Streun, A.
  • Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, Vol. 737
  • DOI: 10.1016/j.nima.2013.11.064

Self-consistent simulations and analysis of the coupled-bunch instability for arbitrary multibunch configurations
journal, February 2016

Commissioning of a higher harmonic RF system for the Advanced Light Source
journal, December 2000

  • Byrd, J. M.; Santis, S. De; Georgsson, M.
  • Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, Vol. 455, Issue 2
  • DOI: 10.1016/S0168-9002(00)00504-0

Robinson instabilities with a higher-harmonic cavity
journal, July 2001

  • Bosch, R. A.; Kleman, K. J.; Bisognano, J. J.
  • Physical Review Special Topics - Accelerators and Beams, Vol. 4, Issue 7
  • DOI: 10.1103/PhysRevSTAB.4.074401

Vertical Fast Blow-Up in a Single Bunch
journal, January 1981

Equilibrium phase instability in the double RF system for Landau damping
journal, October 1987

  • Miyahara, Y.; Asaoka, S.; Mikuni, A.
  • Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, Vol. 260, Issue 2-3
  • DOI: 10.1016/0168-9002(87)90125-2

The MAX IV storage ring project
journal, August 2014

  • Tavares, Pedro F.; Leemann, Simon C.; Sjöström, Magnus
  • Journal of Synchrotron Radiation, Vol. 21, Issue 5
  • DOI: 10.1107/S1600577514011503

Instability Studies and Double RF-System Operation at BESSY
journal, October 1985

  • Weihreter, E.; Gaupp, A.; Hoberg, H. G.
  • IEEE Transactions on Nuclear Science, Vol. 32, Issue 5
  • DOI: 10.1109/TNS.1985.4333898

Landau cavities at MAX II
journal, November 1998

  • Georgsson, M.; Andersson, Å.; Eriksson, M.
  • Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, Vol. 416, Issue 2-3
  • DOI: 10.1016/S0168-9002(98)00667-6

Bunch length control in DAΦNE by a higher harmonic cavity
journal, January 1995

  • Migliorati, M.; Palumbo, L.; Zobov, M.
  • Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, Vol. 354, Issue 2-3
  • DOI: 10.1016/0168-9002(94)01005-6
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    Figures / Tables found in this record:

    FIG. 1(p. 7)figure
    TABLE I(p. 9)table
    TABLE II(p. 9)table
    FIG. 2(p. 10)figure
    FIG. 3(p. 11)figure
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