FOKKERPLANCK ANALYSIS OF TRANSVERSE COLLECTIVE INSTABILITIES IN ELECTRON STORAGE RINGS
Abstract
We analyze single bunch transverse instabilities due to wakefields using a FokkerPlanck model. We expand on the work of Suzuki [1], writing out the linear matrix equation including chromaticity, both dipolar and quadrupolar transverse wakefields, and the effects of damping and diffusion due to the synchrotron radiation. The eigenvalues and eigenvectors determine the collective stability of the beam, and we show that the predicted threshold current for transverse instability and the profile of the unstable agree well with tracking simulations. In particular, we find that predicting collective stability for high energy electron beams at moderate to large values of chromaticity requires the full FokkerPlanck 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) (SC22)
 OSTI Identifier:
 1389079
 DOE Contract Number:
 AC0206CH11357
 Resource Type:
 Conference
 Resource Relation:
 Conference: 2016 North American Particle Accelerator Conference, 10/09/16  10/14/16, Chicago, IL, US
 Country of Publication:
 United States
 Language:
 English
 Subject:
 FOKKERPLANCK ANALYSIS; INSTABILITIES IN ELECTRON STORAGE RINGS; STORAGE RINGS
Citation Formats
Lindberg, R. R.. FOKKERPLANCK ANALYSIS OF TRANSVERSE COLLECTIVE INSTABILITIES IN ELECTRON STORAGE RINGS. United States: N. p., 2017.
Web. doi:10.18429.
Lindberg, R. R.. FOKKERPLANCK ANALYSIS OF TRANSVERSE COLLECTIVE INSTABILITIES IN ELECTRON STORAGE RINGS. United States. doi:10.18429.
Lindberg, R. R.. 2017.
"FOKKERPLANCK ANALYSIS OF TRANSVERSE COLLECTIVE INSTABILITIES IN ELECTRON STORAGE RINGS". United States.
doi:10.18429. https://www.osti.gov/servlets/purl/1389079.
@article{osti_1389079,
title = {FOKKERPLANCK ANALYSIS OF TRANSVERSE COLLECTIVE INSTABILITIES IN ELECTRON STORAGE RINGS},
author = {Lindberg, R. R.},
abstractNote = {We analyze single bunch transverse instabilities due to wakefields using a FokkerPlanck model. We expand on the work of Suzuki [1], writing out the linear matrix equation including chromaticity, both dipolar and quadrupolar transverse wakefields, and the effects of damping and diffusion due to the synchrotron radiation. The eigenvalues and eigenvectors determine the collective stability of the beam, and we show that the predicted threshold current for transverse instability and the profile of the unstable agree well with tracking simulations. In particular, we find that predicting collective stability for high energy electron beams at moderate to large values of chromaticity requires the full FokkerPlanck analysis to properly account for the effects of damping and diffusion due to synchrotron radiation.},
doi = {10.18429},
journal = {},
number = ,
volume = ,
place = {United States},
year = 2017,
month = 6
}

We analyze single bunch transverse instabilities due to wakefields using a FokkerPlanck 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 profilemore »

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It is shown that the beambeam interaction in electron storage rings is equivalent to an additional source of noise for the particle betatron osicllations. A weak white noise acting upon a nonlinear oscillator causes a fast loss of coherence in its phase. This loss of coherence induces a broadening of the resonances, thus avoiding the problem of the divergent perturbative series which arises in the study of nonintegrable Hamiltonian systems. A ''renormalized'' FokkerPlanck equation is established which contains new diffusive terms corresponding to the presence of resonances. The solution of this equation is exhibited explicitly in a simplified case. Thismore » 
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