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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:
Publication Date:
Research Org.:
Argonne National Lab. (ANL), Argonne, IL (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES)
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 Name: Physical Review Accelerators and Beams Journal Volume: 21 Journal Issue: 12; Journal ID: ISSN 2469-9888
Publisher:
American Physical Society
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. https://doi.org/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. https://doi.org/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. https://doi.org/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
https://doi.org/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:

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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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