Betatron motion with coupling of horizontal and vertical degrees of freedom

Lebedev, V. A.; Bogacz, S. A.

doi:10.1088/1748-0221/5/10/P10010

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

Journal Article · Thu Oct 21 00:00:00 EDT 2010 · Journal of Instrumentation

DOI:https://doi.org/10.1088/1748-0221/5/10/P10010· OSTI ID:991635

Lebedev, V. A. ^[1]; Bogacz, S. A. ^[2]

Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)

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.

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Research Organization:: Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: AC05-06OR23177

OSTI ID:: 991635

Report Number(s):: JLAB-ACP-10-1251; DOE/OR/23177-1353; TRN: US1007522

Journal Information:: Journal of Instrumentation, Vol. 5, Issue 10; ISSN 1748-0221

Publisher:: Institute of Physics (IOP)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 27 works

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References (8)

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Cited By (1)

The Story of the Tevatron Accelerators: Accelerator Science and Technology Breakthroughs, Achievements and Lessons Shiltsev, V. Modern Physics Letters A, Vol. 27, Issue 01 https://doi.org/10.1142/s0217732312300017	journal	January 2012

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43 PARTICLE ACCELERATORS
ACCELERATORS
BETATRONS
DEGREES OF FREEDOM
DESIGN
ELECTRONS
EQUATIONS OF MOTION
HEAT EXCHANGERS
MAGNETIC FIELDS
MONITORS
PHASE SPACE
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Title: Betatron motion with coupling of horizontal and vertical degrees of freedom

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