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Title: Betatron motion with coupling of horizontal and vertical degrees of freedom

Abstract

Presently, there are two most frequently used parameterezations of linear x-y coupled motion used in the accelerator physics. They are the Edwards-Teng and Mais-Ripken parameterizations. The article is devoted to an analysis of close relationship between the two representations, thus adding a clarity to their physical meaning. It also discusses the relationship between the eigen-vectors, the beta-functions, second order moments and the bilinear form representing the particle ellipsoid in the 4D phase space. Then, it consideres a further development of Mais-Ripken parameteresation where the particle motion is descrabed by 10 parameters: four beta-functions, four alpha-functions and two betatron phase advances. In comparison with Edwards-Teng parameterization the chosen parametrization has an advantage that it works equally well for analysis of coupled betatron motion in circular accelerators and in transfer lines. In addition, considered relationship between second order moments, eigen-vectors and beta-functions can be useful in interpreting tracking results and experimental data. As an example, the developed formalizm is applied to the FNAL electron cooler and Derbenev’s vertex-to-plane adapter.

Authors:
 [1];  [2]
  1. Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
  2. Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
Publication Date:
Research Org.:
Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
991635
Report Number(s):
JLAB-ACP-10-1251; DOE/OR/23177-1353
Journal ID: ISSN 1748-0221; TRN: US1007522
Grant/Contract Number:  
AC05-06OR23177
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Journal of Instrumentation
Additional Journal Information:
Journal Volume: 5; Journal Issue: 10; Journal ID: ISSN 1748-0221
Publisher:
Institute of Physics (IOP)
Country of Publication:
United States
Language:
English
Subject:
43 PARTICLE ACCELERATORS; ACCELERATORS; BETATRONS; DEGREES OF FREEDOM; DESIGN; ELECTRONS; EQUATIONS OF MOTION; HEAT EXCHANGERS; MAGNETIC FIELDS; MONITORS; PHASE SPACE; PHYSICS; accelerator modelling and simulations (multi-particle dynamics; single-particle dynamics); beam-line instrumentation (beam position and profile monitors; beam-intensity monitors; bunch length monitors)

Citation Formats

Lebedev, V. A., and Bogacz, S. A. Betatron motion with coupling of horizontal and vertical degrees of freedom. United States: N. p., 2010. Web. doi:10.1088/1748-0221/5/10/P10010.
Lebedev, V. A., & Bogacz, S. A. Betatron motion with coupling of horizontal and vertical degrees of freedom. United States. doi:10.1088/1748-0221/5/10/P10010.
Lebedev, V. A., and Bogacz, S. A. Thu . "Betatron motion with coupling of horizontal and vertical degrees of freedom". United States. doi:10.1088/1748-0221/5/10/P10010. https://www.osti.gov/servlets/purl/991635.
@article{osti_991635,
title = {Betatron motion with coupling of horizontal and vertical degrees of freedom},
author = {Lebedev, V. A. and Bogacz, S. A.},
abstractNote = {Presently, there are two most frequently used parameterezations of linear x-y coupled motion used in the accelerator physics. They are the Edwards-Teng and Mais-Ripken parameterizations. The article is devoted to an analysis of close relationship between the two representations, thus adding a clarity to their physical meaning. It also discusses the relationship between the eigen-vectors, the beta-functions, second order moments and the bilinear form representing the particle ellipsoid in the 4D phase space. Then, it consideres a further development of Mais-Ripken parameteresation where the particle motion is descrabed by 10 parameters: four beta-functions, four alpha-functions and two betatron phase advances. In comparison with Edwards-Teng parameterization the chosen parametrization has an advantage that it works equally well for analysis of coupled betatron motion in circular accelerators and in transfer lines. In addition, considered relationship between second order moments, eigen-vectors and beta-functions can be useful in interpreting tracking results and experimental data. As an example, the developed formalizm is applied to the FNAL electron cooler and Derbenev’s vertex-to-plane adapter.},
doi = {10.1088/1748-0221/5/10/P10010},
journal = {Journal of Instrumentation},
issn = {1748-0221},
number = 10,
volume = 5,
place = {United States},
year = {2010},
month = {10}
}

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Cited by: 12 works
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