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

Abstract

Presently, there are two most frequently used parameterizations 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 described 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. 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:
;
Publication Date:
Research Org.:
Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
990843
Report Number(s):
FERMILAB-PUB-10-383-AD
TRN: US1007402
DOE Contract Number:  
AC02-07CH11359
Resource Type:
Journal Article
Journal Name:
JINST 5:P10010,2010
Additional Journal Information:
Journal Name: JINST 5:P10010,2010
Country of Publication:
United States
Language:
English
Subject:
43 PARTICLE ACCELERATORS; ACCELERATORS; BETATRONS; DEGREES OF FREEDOM; ELECTRONS; HEAT EXCHANGERS; PHASE SPACE; PHYSICS; Accelerators

Citation Formats

Lebedev, V A, /Fermilab, Bogacz, S A, and /Jefferson Lab. 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, /Fermilab, Bogacz, S A, & /Jefferson Lab. Betatron motion with coupling of horizontal and vertical degrees of freedom. United States. doi:10.1088/1748-0221/5/10/P10010.
Lebedev, V A, /Fermilab, Bogacz, S A, and /Jefferson Lab. Wed . "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/990843.
@article{osti_990843,
title = {Betatron motion with coupling of horizontal and vertical degrees of freedom},
author = {Lebedev, V A and /Fermilab and Bogacz, S A and /Jefferson Lab},
abstractNote = {Presently, there are two most frequently used parameterizations 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 described 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. 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 = {JINST 5:P10010,2010},
number = ,
volume = ,
place = {United States},
year = {2010},
month = {9}
}

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    Works referencing / citing this record: