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:
- 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.
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.
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.
@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}
}
DOI: 10.1103/PhysRevAccelBeams.21.124402
Figures / Tables:

Works referenced in this record:
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Figures / Tables found in this record: