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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Bibliographic Details
Published in:Physical review special topics. PRST-AB. Accelerators and beams 2006-02, Vol.9 (2), p.024001, Article 024001
Main Author: Wolski, Andrzej
Format: Article
Language:English
Subjects:
First principles
Parameters
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Summary: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.
ISSN:1098-4402
1098-4402
2469-9888
DOI:10.1103/PhysRevSTAB.9.024001