Alternative approach to general coupled linear optics

The Twiss parameters provide a convenient description of beam optics in uncoupled linear beam lines. For coupled beam lines, a variety of approaches are possible for describing the linear optics; here, we propose an approach and notation that naturally generalizes the familiar Twiss parameters to th...

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Main Author: Andrzej Wolski
Format: Article
Language:English
Published: American Physical Society 2006-02-01
Series:Physical Review Special Topics. Accelerators and Beams
Online Access:http://doi.org/10.1103/PhysRevSTAB.9.024001
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spelling doaj-dfd9a560c1f4432b92f5d434f5619e182020-11-25T02:01:06ZengAmerican Physical SocietyPhysical Review Special Topics. Accelerators and Beams1098-44022006-02-019202400110.1103/PhysRevSTAB.9.024001Alternative approach to general coupled linear opticsAndrzej WolskiThe Twiss parameters provide a convenient description of beam optics in uncoupled linear beam lines. For coupled beam lines, a variety of approaches are possible for describing the linear optics; here, we propose an approach and notation that naturally generalizes the familiar Twiss parameters to the coupled case in 3 degrees of freedom. Our approach is based on an eigensystem analysis of the matrix of second-order beam moments, or alternatively (in the case of a storage ring) on an eigensystem analysis of the linear single-turn map. The lattice functions that emerge from this approach have an interpretation that is conceptually very simple: in particular, the lattice functions directly relate the beam distribution in phase-space to the invariant emittances. To emphasize the physical significance of the coupled lattice functions, we develop the theory from first principles, using only the assumption of linear symplectic transport. We also give some examples of the application of this approach, demonstrating its advantages of conceptual and notational simplicity.http://doi.org/10.1103/PhysRevSTAB.9.024001
collection DOAJ
language English
format Article
sources DOAJ
author Andrzej Wolski
spellingShingle Andrzej Wolski
Alternative approach to general coupled linear optics
Physical Review Special Topics. Accelerators and Beams
author_facet Andrzej Wolski
author_sort Andrzej Wolski
title Alternative approach to general coupled linear optics
title_short Alternative approach to general coupled linear optics
title_full Alternative approach to general coupled linear optics
title_fullStr Alternative approach to general coupled linear optics
title_full_unstemmed Alternative approach to general coupled linear optics
title_sort alternative approach to general coupled linear optics
publisher American Physical Society
series Physical Review Special Topics. Accelerators and Beams
issn 1098-4402
publishDate 2006-02-01
description The Twiss parameters provide a convenient description of beam optics in uncoupled linear beam lines. For coupled beam lines, a variety of approaches are possible for describing the linear optics; here, we propose an approach and notation that naturally generalizes the familiar Twiss parameters to the coupled case in 3 degrees of freedom. Our approach is based on an eigensystem analysis of the matrix of second-order beam moments, or alternatively (in the case of a storage ring) on an eigensystem analysis of the linear single-turn map. The lattice functions that emerge from this approach have an interpretation that is conceptually very simple: in particular, the lattice functions directly relate the beam distribution in phase-space to the invariant emittances. To emphasize the physical significance of the coupled lattice functions, we develop the theory from first principles, using only the assumption of linear symplectic transport. We also give some examples of the application of this approach, demonstrating its advantages of conceptual and notational simplicity.
url http://doi.org/10.1103/PhysRevSTAB.9.024001
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