# Spectral and structural stability properties of charged particle dynamics in coupled lattices

## Abstract

It has been realized in recent years that coupled focusing lattices in accelerators and storage rings have significant advantages over conventional uncoupled focusing lattices, especially for high-intensity charged particle beams. A theoretical framework and associated tools for analyzing the spectral and structural stability properties of coupled lattices are formulated in this paper, based on the recently developed generalized Courant-Snyder theory for coupled lattices. It is shown that for periodic coupled lattices that are spectrally and structurally stable, the matrix envelope equation must admit matched solutions. Using the technique of normal form and pre-Iwasawa decomposition, a new method is developed to replace the (inefficient) shooting method for finding matched solutions for the matrix envelope equation. Stability properties of a continuously rotating quadrupole lattice are investigated. The Krein collision process for destabilization of the lattice is demonstrated.

- Authors:

- Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08543 (United States)
- (China)
- Department of Physics, Ulsan National Institute of Science and Technology, Ulsan 689-798 (Korea, Republic of)

- Publication Date:

- OSTI Identifier:
- 22410417

- Resource Type:
- Journal Article

- Journal Name:
- Physics of Plasmas

- Additional Journal Information:
- Journal Volume: 22; Journal Issue: 5; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1070-664X

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 43 PARTICLE ACCELERATORS; 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; ACCELERATORS; CHARGED PARTICLES; COLLISIONS; DYNAMICS; EQUATIONS; FOCUSING; MATHEMATICAL SOLUTIONS; PARTICLE BEAMS; STORAGE RINGS

### Citation Formats

```
Qin, Hong, Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, Chung, Moses, Davidson, Ronald C., and Burby, Joshua W.
```*Spectral and structural stability properties of charged particle dynamics in coupled lattices*. United States: N. p., 2015.
Web. doi:10.1063/1.4920961.

```
Qin, Hong, Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, Chung, Moses, Davidson, Ronald C., & Burby, Joshua W.
```*Spectral and structural stability properties of charged particle dynamics in coupled lattices*. United States. doi:10.1063/1.4920961.

```
Qin, Hong, Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, Chung, Moses, Davidson, Ronald C., and Burby, Joshua W. Fri .
"Spectral and structural stability properties of charged particle dynamics in coupled lattices". United States. doi:10.1063/1.4920961.
```

```
@article{osti_22410417,
```

title = {Spectral and structural stability properties of charged particle dynamics in coupled lattices},

author = {Qin, Hong and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026 and Chung, Moses and Davidson, Ronald C. and Burby, Joshua W.},

abstractNote = {It has been realized in recent years that coupled focusing lattices in accelerators and storage rings have significant advantages over conventional uncoupled focusing lattices, especially for high-intensity charged particle beams. A theoretical framework and associated tools for analyzing the spectral and structural stability properties of coupled lattices are formulated in this paper, based on the recently developed generalized Courant-Snyder theory for coupled lattices. It is shown that for periodic coupled lattices that are spectrally and structurally stable, the matrix envelope equation must admit matched solutions. Using the technique of normal form and pre-Iwasawa decomposition, a new method is developed to replace the (inefficient) shooting method for finding matched solutions for the matrix envelope equation. Stability properties of a continuously rotating quadrupole lattice are investigated. The Krein collision process for destabilization of the lattice is demonstrated.},

doi = {10.1063/1.4920961},

journal = {Physics of Plasmas},

issn = {1070-664X},

number = 5,

volume = 22,

place = {United States},

year = {2015},

month = {5}

}