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Title: Fokker-Planck analysis of transverse collective instabilities in electron storage rings

Abstract

We analyze single bunch transverse instabilities due to wakefields using a Fokker-Planck model. We first expand on the work of T. Suzuki, Part. Accel. 12, 237 (1982) to derive the theoretical model including chromaticity, both dipolar and quadrupolar transverse wakefields, and the effects of damping and diffusion due to the synchrotron radiation. We reduce the problem to a linear matrix equation, whose eigenvalues and eigenvectors determine the collective stability of the beam. We then show that various predictions of the theory agree quite well with results from particle tracking simulations, including the threshold current for transverse instability and the profile of the unstable mode. In particular, we find that predicting collective stability for high energy electron beams at moderate to large values of chromaticity requires the full Fokker-Planck analysis to properly account for the effects of damping and diffusion due to synchrotron radiation.

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:
1373908
DOE Contract Number:  
AC02-06CH11357
Resource Type:
Journal Article
Journal Name:
Physical Review Accelerators and Beams
Additional Journal Information:
Journal Volume: 19; Journal Issue: 12; Journal ID: ISSN 2469-9888
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English

Citation Formats

Lindberg, Ryan R. Fokker-Planck analysis of transverse collective instabilities in electron storage rings. United States: N. p., 2016. Web. doi:10.1103/PhysRevAccelBeams.19.124402.
Lindberg, Ryan R. Fokker-Planck analysis of transverse collective instabilities in electron storage rings. United States. https://doi.org/10.1103/PhysRevAccelBeams.19.124402
Lindberg, Ryan R. 2016. "Fokker-Planck analysis of transverse collective instabilities in electron storage rings". United States. https://doi.org/10.1103/PhysRevAccelBeams.19.124402.
@article{osti_1373908,
title = {Fokker-Planck analysis of transverse collective instabilities in electron storage rings},
author = {Lindberg, Ryan R.},
abstractNote = {We analyze single bunch transverse instabilities due to wakefields using a Fokker-Planck model. We first expand on the work of T. Suzuki, Part. Accel. 12, 237 (1982) to derive the theoretical model including chromaticity, both dipolar and quadrupolar transverse wakefields, and the effects of damping and diffusion due to the synchrotron radiation. We reduce the problem to a linear matrix equation, whose eigenvalues and eigenvectors determine the collective stability of the beam. We then show that various predictions of the theory agree quite well with results from particle tracking simulations, including the threshold current for transverse instability and the profile of the unstable mode. In particular, we find that predicting collective stability for high energy electron beams at moderate to large values of chromaticity requires the full Fokker-Planck analysis to properly account for the effects of damping and diffusion due to synchrotron radiation.},
doi = {10.1103/PhysRevAccelBeams.19.124402},
url = {https://www.osti.gov/biblio/1373908}, journal = {Physical Review Accelerators and Beams},
issn = {2469-9888},
number = 12,
volume = 19,
place = {United States},
year = {Thu Dec 01 00:00:00 EST 2016},
month = {Thu Dec 01 00:00:00 EST 2016}
}

Works referenced in this record:

On a new instability in electron-positron storage rings (The head-tail effect)
journal, November 1969


Single Beam Instabilities in PETRA
journal, January 1979


Suppression of Transverse Bunch Instabilities by Asymmetries in the Chamber Geometry
journal, March 1999


Pelegant: A Parallel Accelerator Simulation Code for Electron Generation and Tracking
conference, January 2006


Nested head-tail Vlasov solver
journal, February 2014


Transverse mode coupling in a bunched beam
journal, April 1983


Theory of the alternating-gradient synchrotron
journal, January 1958


Transverse Resistive Instabilities of Intense Coasting Beams in Particle Accelerators
journal, April 1965


Coupling impedance of beam pipes of general cross section
journal, January 1993