# Singularity and stability in a periodic system of particle accelerators

## Abstract

We study the single-particle dynamics in a general and parametrized alternating-gradient cell with zero chromaticity using the Lie algebra method. To our surprise, the first-order perturbation of the sextupoles largely determines the dynamics away from the major resonances. The dynamic aperture can be estimated from the topology and geometry of the phase space. In the linearly normalized phase space, it is scaled according to $$\bar{A}$$∝ Φ √L, where Φ is the bending angle and L the length of the cell. Finally, for the 2 degrees of freedom with equal betatron tunes, the analytical perturbation theory leads us to the invariant or quasi-invariant tori, which play an important role in determining the stable volume in the four-dimensional phase space.

- Authors:

- SLAC National Accelerator Lab., Menlo Park, CA (United States)

- Publication Date:

- Research Org.:
- SLAC National Accelerator Lab., Menlo Park, CA (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1438520

- Alternate Identifier(s):
- OSTI ID: 1458460

- Grant/Contract Number:
- AC02-76SF00515

- Resource Type:
- Published Article

- Journal Name:
- Physical Review Accelerators and Beams

- Additional Journal Information:
- Journal Volume: 21; Journal Issue: 5; Journal ID: ISSN 2469-9888

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 43 PARTICLE ACCELERATORS

### Citation Formats

```
Cai, Yunhai. Singularity and stability in a periodic system of particle accelerators. United States: N. p., 2018.
Web. doi:10.1103/physrevaccelbeams.21.054002.
```

```
Cai, Yunhai. Singularity and stability in a periodic system of particle accelerators. United States. doi:10.1103/physrevaccelbeams.21.054002.
```

```
Cai, Yunhai. Wed .
"Singularity and stability in a periodic system of particle accelerators". United States. doi:10.1103/physrevaccelbeams.21.054002.
```

```
@article{osti_1438520,
```

title = {Singularity and stability in a periodic system of particle accelerators},

author = {Cai, Yunhai},

abstractNote = {We study the single-particle dynamics in a general and parametrized alternating-gradient cell with zero chromaticity using the Lie algebra method. To our surprise, the first-order perturbation of the sextupoles largely determines the dynamics away from the major resonances. The dynamic aperture can be estimated from the topology and geometry of the phase space. In the linearly normalized phase space, it is scaled according to $\bar{A}$∝ Φ √L, where Φ is the bending angle and L the length of the cell. Finally, for the 2 degrees of freedom with equal betatron tunes, the analytical perturbation theory leads us to the invariant or quasi-invariant tori, which play an important role in determining the stable volume in the four-dimensional phase space.},

doi = {10.1103/physrevaccelbeams.21.054002},

journal = {Physical Review Accelerators and Beams},

number = 5,

volume = 21,

place = {United States},

year = {2018},

month = {5}

}

DOI: 10.1103/physrevaccelbeams.21.054002

*Citation information provided by*

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