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

Lindberg, Ryan R.

doi:10.1103/PhysRevAccelBeams.21.124402

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

Journal Article · Thu Dec 13 00:00:00 EST 2018 · Physical Review Accelerators and Beams

DOI:https://doi.org/10.1103/PhysRevAccelBeams.21.124402· OSTI ID:1485742

Lindberg, Ryan R.

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.

View Journal Article

Cite

Export

Save

Research Organization:: Argonne National Lab. (ANL), Argonne, IL (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: AC02-06CH11357

OSTI ID:: 1485742

Alternate ID(s):: OSTI ID: 1491846

Journal Information:: Physical Review Accelerators and Beams, Journal Name: Physical Review Accelerators and Beams Vol. 21 Journal Issue: 12; ISSN 2469-9888

Publisher:: American Physical SocietyCopyright Statement

Country of Publication:: United States

Language:: English

Citation Metrics:

Cited by: 8 works

Citation information provided by
Web of Science

References (13)

Suppression of longitudinal coupled-bunch instabilities by a passive higher harmonic cavity Bosch, R. A.; Hsue, C. S. Proceedings of International Conference on Particle Accelerators https://doi.org/10.1109/PAC.1993.309653	conference	January 1993
Interplay of Touschek scattering, intrabeam scattering, and rf cavities in ultralow-emittance storage rings Leemann, S. C. Physical Review Special Topics - Accelerators and Beams, Vol. 17, Issue 5 https://doi.org/10.1103/PhysRevSTAB.17.050705	journal	May 2014
Longitudinal stability limit for electron bunches in a double RF system Chin, Yongho Nuclear Instruments and Methods in Physics Research, Vol. 215, Issue 3 https://doi.org/10.1016/0167-5087(83)90485-4	journal	October 1983
The anti-bend cell for ultralow emittance storage ring lattices Streun, A. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, Vol. 737 https://doi.org/10.1016/j.nima.2013.11.064	journal	February 2014
Self-consistent simulations and analysis of the coupled-bunch instability for arbitrary multibunch configurations Bassi, Gabriele; Blednykh, Alexei; Smaluk, Victor Physical Review Accelerators and Beams, Vol. 19, Issue 2 https://doi.org/10.1103/PhysRevAccelBeams.19.024401	journal	February 2016
Commissioning of a higher harmonic RF system for the Advanced Light Source 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 https://doi.org/10.1016/S0168-9002(00)00504-0	journal	December 2000
Robinson instabilities with a higher-harmonic cavity Bosch, R. A.; Kleman, K. J.; Bisognano, J. J. Physical Review Special Topics - Accelerators and Beams, Vol. 4, Issue 7 https://doi.org/10.1103/PhysRevSTAB.4.074401	journal	July 2001
Vertical Fast Blow-Up in a Single Bunch Ruth, R. D.; Wang, J. M. IEEE Transactions on Nuclear Science, Vol. 28, Issue 3 https://doi.org/10.1109/TNS.1981.4331707	journal	January 1981
Equilibrium phase instability in the double RF system for Landau damping 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 https://doi.org/10.1016/0168-9002(87)90125-2	journal	October 1987
The MAX IV storage ring project Tavares, Pedro F.; Leemann, Simon C.; Sjöström, Magnus Journal of Synchrotron Radiation, Vol. 21, Issue 5 https://doi.org/10.1107/S1600577514011503	journal	August 2014
Instability Studies and Double RF-System Operation at BESSY Weihreter, E.; Gaupp, A.; Hoberg, H. G. IEEE Transactions on Nuclear Science, Vol. 32, Issue 5 https://doi.org/10.1109/TNS.1985.4333898	journal	October 1985
Landau cavities at MAX II 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 https://doi.org/10.1016/S0168-9002(98)00667-6	journal	November 1998
Bunch length control in DAΦNE by a higher harmonic cavity 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 https://doi.org/10.1016/0168-9002(94)01005-6	journal	January 1995