# Normal form analysis of linear beam dynamics in a coupled storagering

## Abstract

The techniques of normal form analysis, well known in the literature, can be used to provide a straightforward characterization of linear betatron dynamics in a coupled lattice. Here, we consider both the beam distribution and the betatron oscillations in a storage ring. We find that the beta functions for uncoupled motion generalize in a simple way to the coupled case. Defined in the way that we propose, the beta functions remain well behaved (positive and finite) under all circumstances, and have essentially the same physical significance for the beam size and betatron oscillation amplitude as in the uncoupled case. Application of this analysis to the online modeling of the PEP-II rings is also discussed.

- Authors:

- Publication Date:

- Research Org.:
- Ernest Orlando Lawrence Berkeley NationalLaboratory, Berkeley, CA (US)

- Sponsoring Org.:
- USDOE Director. Office of Science. Office of High EnergyPhysics

- OSTI Identifier:
- 861579

- Report Number(s):
- LBNL-55727

R&D Project: 459663; BnR: KA1502020; TRN: US0600369

- DOE Contract Number:
- DE-AC02-05CH11231

- Resource Type:
- Conference

- Resource Relation:
- Conference: European Particle Accelerator Conference 2004,Lucerne, Switzerland, July 5-9, 2004

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 43 PARTICLE ACCELERATORS; ACCELERATORS; AMPLITUDES; BEAM DYNAMICS; BETATRON OSCILLATIONS; BETATRONS; DISTRIBUTION; SIMULATION; STORAGE RINGS

### Citation Formats

```
Wolski, Andrzej, and Woodley, Mark D.
```*Normal form analysis of linear beam dynamics in a coupled storagering*. United States: N. p., 2004.
Web.

```
Wolski, Andrzej, & Woodley, Mark D.
```*Normal form analysis of linear beam dynamics in a coupled storagering*. United States.

```
Wolski, Andrzej, and Woodley, Mark D. Wed .
"Normal form analysis of linear beam dynamics in a coupled storagering". United States. https://www.osti.gov/servlets/purl/861579.
```

```
@article{osti_861579,
```

title = {Normal form analysis of linear beam dynamics in a coupled storagering},

author = {Wolski, Andrzej and Woodley, Mark D.},

abstractNote = {The techniques of normal form analysis, well known in the literature, can be used to provide a straightforward characterization of linear betatron dynamics in a coupled lattice. Here, we consider both the beam distribution and the betatron oscillations in a storage ring. We find that the beta functions for uncoupled motion generalize in a simple way to the coupled case. Defined in the way that we propose, the beta functions remain well behaved (positive and finite) under all circumstances, and have essentially the same physical significance for the beam size and betatron oscillation amplitude as in the uncoupled case. Application of this analysis to the online modeling of the PEP-II rings is also discussed.},

doi = {},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2004},

month = {6}

}

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