# Single-particle dynamics in theoretical minimum emittance cell

## Abstract

Here, we have developed a parametrization of the linear optics in a theoretical minimum emittance cell with three quadrupoles. It consists of five independent parameters: two phase advances, a dimensionless horizontal beta function at the center of the dipole, and a bending angle Φ and a length L of the dipole. For the zero chromaticity cell, we again find that the dynamic aperture in the normalized phase space is scaled according to, ¯A∝Φ√L. Moreover, we study nonlinear dynamics near the third-order coupled resonances in the framework of the resonance normal form. In particular, we derive the effective Hamiltonians using the Lie algebra method and show that the periodic orbits in tracking can be interpreted as solutions of the Hamilton’s equations. Surprisingly, we discover that the scheme is not only applicable to the single resonance but also to the double resonances.

- Authors:

- Publication Date:

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

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1482768

- Alternate Identifier(s):
- OSTI ID: 1490065

- Grant/Contract Number:
- AC02-76SF00515

- Resource Type:
- Published Article

- Journal Name:
- Physical Review Accelerators and Beams

- Additional Journal Information:
- Journal Name: Physical Review Accelerators and Beams Journal Volume: 21 Journal Issue: 11; Journal ID: ISSN 2469-9888

- Publisher:
- American Physical Society

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

### Citation Formats

```
Cai, Yunhai. Single-particle dynamics in theoretical minimum emittance cell. United States: N. p., 2018.
Web. doi:10.1103/PhysRevAccelBeams.21.114002.
```

```
Cai, Yunhai. Single-particle dynamics in theoretical minimum emittance cell. United States. doi:10.1103/PhysRevAccelBeams.21.114002.
```

```
Cai, Yunhai. Mon .
"Single-particle dynamics in theoretical minimum emittance cell". United States. doi:10.1103/PhysRevAccelBeams.21.114002.
```

```
@article{osti_1482768,
```

title = {Single-particle dynamics in theoretical minimum emittance cell},

author = {Cai, Yunhai},

abstractNote = {Here, we have developed a parametrization of the linear optics in a theoretical minimum emittance cell with three quadrupoles. It consists of five independent parameters: two phase advances, a dimensionless horizontal beta function at the center of the dipole, and a bending angle Φ and a length L of the dipole. For the zero chromaticity cell, we again find that the dynamic aperture in the normalized phase space is scaled according to, ¯A∝Φ√L. Moreover, we study nonlinear dynamics near the third-order coupled resonances in the framework of the resonance normal form. In particular, we derive the effective Hamiltonians using the Lie algebra method and show that the periodic orbits in tracking can be interpreted as solutions of the Hamilton’s equations. Surprisingly, we discover that the scheme is not only applicable to the single resonance but also to the double resonances.},

doi = {10.1103/PhysRevAccelBeams.21.114002},

journal = {Physical Review Accelerators and Beams},

number = 11,

volume = 21,

place = {United States},

year = {2018},

month = {11}

}

DOI: 10.1103/PhysRevAccelBeams.21.114002

#### Figures / Tables:

_{1,2}are the focus points, PP

_{1,2}the principal planes, and

*f*the focus length of the optical system.

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Figures / Tables found in this record:

*Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.*