Betatron coupling: Merging Hamiltonian and matrix approaches

Betatron coupling: Merging Hamiltonian and matrix approaches

Betatron coupling is usually analyzed using either matrix formalism or Hamiltonian perturbation theory. The latter is less exact but provides a better physical insight. In this paper direct relations are derived between the two formalisms. This makes it possible to interpret the matrix approach in t...

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Main Authors: R. Calaga, R. Tomás, A. Franchi
Format: Article
Language:English
Published: American Physical Society 2005-03-01
Series:Physical Review Special Topics. Accelerators and Beams
Online Access:http://doi.org/10.1103/PhysRevSTAB.8.034001
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spelling doaj-0b2a5917e6944b51af2274b0256ac09f2020-11-25T00:59:44ZengAmerican Physical SocietyPhysical Review Special Topics. Accelerators and Beams1098-44022005-03-018303400110.1103/PhysRevSTAB.8.034001Betatron coupling: Merging Hamiltonian and matrix approachesR. CalagaR. TomásA. FranchiBetatron coupling is usually analyzed using either matrix formalism or Hamiltonian perturbation theory. The latter is less exact but provides a better physical insight. In this paper direct relations are derived between the two formalisms. This makes it possible to interpret the matrix approach in terms of resonances, as well as use results of both formalisms indistinctly. An approach to measure the complete coupling matrix and its determinant from turn-by-turn data is presented. Simulations using methodical accelerator design MAD-X, an accelerator design and tracking program, were performed to validate the relations and understand the scope of their application to real accelerators such as the Relativistic Heavy Ion Collider.http://doi.org/10.1103/PhysRevSTAB.8.034001
collection DOAJ
language English
format Article
sources DOAJ
author R. Calaga
R. Tomás
A. Franchi
spellingShingle R. Calaga
R. Tomás
A. Franchi
Betatron coupling: Merging Hamiltonian and matrix approaches
Physical Review Special Topics. Accelerators and Beams
author_facet R. Calaga
R. Tomás
A. Franchi
author_sort R. Calaga
title Betatron coupling: Merging Hamiltonian and matrix approaches
title_short Betatron coupling: Merging Hamiltonian and matrix approaches
title_full Betatron coupling: Merging Hamiltonian and matrix approaches
title_fullStr Betatron coupling: Merging Hamiltonian and matrix approaches
title_full_unstemmed Betatron coupling: Merging Hamiltonian and matrix approaches
title_sort betatron coupling: merging hamiltonian and matrix approaches
publisher American Physical Society
series Physical Review Special Topics. Accelerators and Beams
issn 1098-4402
publishDate 2005-03-01
description Betatron coupling is usually analyzed using either matrix formalism or Hamiltonian perturbation theory. The latter is less exact but provides a better physical insight. In this paper direct relations are derived between the two formalisms. This makes it possible to interpret the matrix approach in terms of resonances, as well as use results of both formalisms indistinctly. An approach to measure the complete coupling matrix and its determinant from turn-by-turn data is presented. Simulations using methodical accelerator design MAD-X, an accelerator design and tracking program, were performed to validate the relations and understand the scope of their application to real accelerators such as the Relativistic Heavy Ion Collider.
url http://doi.org/10.1103/PhysRevSTAB.8.034001
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AT rtomas betatroncouplingmerginghamiltonianandmatrixapproaches
AT afranchi betatroncouplingmerginghamiltonianandmatrixapproaches
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