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Multiple resonance compensation for betatron coupling and its equivalence with matrix method

Analyses of betatron coupling can be broadly divided into two categories: the matrix approach that decouples the single-turn matrix to reveal the normal modes and the hamiltonian approach that evaluates the coupling in terms of the action of resonances in perturbation theory. The latter is often reg...

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Detalles Bibliográficos
Autores principales: De Ninno, G, Fanelli, D
Lenguaje:eng
Publicado: 1999
Materias:
Acceso en línea:http://cds.cern.ch/record/394445
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author De Ninno, G
Fanelli, D
author_facet De Ninno, G
Fanelli, D
author_sort De Ninno, G
collection CERN
description Analyses of betatron coupling can be broadly divided into two categories: the matrix approach that decouples the single-turn matrix to reveal the normal modes and the hamiltonian approach that evaluates the coupling in terms of the action of resonances in perturbation theory. The latter is often regarded as being less exact but good for physical insight. The common opinion is that the correction of the two closest sum and difference resonances to the working point is sufficient to reduce the off-axis terms in the 4X4 single-turn matrix, but this is only partially true. The reason for this is explained, and a method is developed that sums to infinity all coupling resonances and, in this way, obtains results equivalent to the matrix approach. The two approaches is discussed with reference to the dynamic aperture. Finally, the extension of the summation method to resonances of all orders is outlined and the relative importance of a single resonance compared to all resonances of a given order is analytically described as a function of the working point.
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institution Organización Europea para la Investigación Nuclear
language eng
publishDate 1999
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spelling cern-3944452019-09-30T06:29:59Zhttp://cds.cern.ch/record/394445engDe Ninno, GFanelli, DMultiple resonance compensation for betatron coupling and its equivalence with matrix methodAccelerators and Storage RingsAnalyses of betatron coupling can be broadly divided into two categories: the matrix approach that decouples the single-turn matrix to reveal the normal modes and the hamiltonian approach that evaluates the coupling in terms of the action of resonances in perturbation theory. The latter is often regarded as being less exact but good for physical insight. The common opinion is that the correction of the two closest sum and difference resonances to the working point is sufficient to reduce the off-axis terms in the 4X4 single-turn matrix, but this is only partially true. The reason for this is explained, and a method is developed that sums to infinity all coupling resonances and, in this way, obtains results equivalent to the matrix approach. The two approaches is discussed with reference to the dynamic aperture. Finally, the extension of the summation method to resonances of all orders is outlined and the relative importance of a single resonance compared to all resonances of a given order is analytically described as a function of the working point.physics/9907040oai:cds.cern.ch:3944451999-07-26
spellingShingle Accelerators and Storage Rings
De Ninno, G
Fanelli, D
Multiple resonance compensation for betatron coupling and its equivalence with matrix method
title Multiple resonance compensation for betatron coupling and its equivalence with matrix method
title_full Multiple resonance compensation for betatron coupling and its equivalence with matrix method
title_fullStr Multiple resonance compensation for betatron coupling and its equivalence with matrix method
title_full_unstemmed Multiple resonance compensation for betatron coupling and its equivalence with matrix method
title_short Multiple resonance compensation for betatron coupling and its equivalence with matrix method
title_sort multiple resonance compensation for betatron coupling and its equivalence with matrix method
topic Accelerators and Storage Rings
url http://cds.cern.ch/record/394445
work_keys_str_mv AT deninnog multipleresonancecompensationforbetatroncouplinganditsequivalencewithmatrixmethod
AT fanellid multipleresonancecompensationforbetatroncouplinganditsequivalencewithmatrixmethod