# Beam envelope calculations in general linear coupled lattices

## Abstract

The envelope equations and Twiss parameters (β and α) provide important bases for uncoupled linear beam dynamics. For sophisticated beam manipulations, however, coupling elements between two transverse planes are intentionally introduced. The recently developed generalized Courant-Snyder theory offers an effective way of describing the linear beam dynamics in such coupled systems with a remarkably similar mathematical structure to the original Courant-Snyder theory. In this work, we present numerical solutions to the symmetrized matrix envelope equation for β which removes the gauge freedom in the matrix envelope equation for w. Furthermore, we construct the transfer and beam matrices in terms of the generalized Twiss parameters, which enables calculation of the beam envelopes in arbitrary linear coupled systems.

- Authors:

- Department of Physics, Ulsan National Institute of Science and Technology, Ulsan 689-798 (Korea, Republic of)
- Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08543 (United States)
- (China)
- GSI Helmholtzzentrum für Schwerionenforschung GmbH, Planckstrasse 1, D-64291 Darmstadt (Germany)

- Publication Date:

- OSTI Identifier:
- 22408021

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physics of Plasmas; Journal Volume: 22; Journal Issue: 1; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BEAM DYNAMICS; COUPLING; EQUATIONS; MATRICES; NUMERICAL SOLUTION

### Citation Formats

```
Chung, Moses, E-mail: mchung@unist.ac.kr, Qin, Hong, Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, Groening, Lars, Xiao, Chen, and Davidson, Ronald C..
```*Beam envelope calculations in general linear coupled lattices*. United States: N. p., 2015.
Web. doi:10.1063/1.4903457.

```
Chung, Moses, E-mail: mchung@unist.ac.kr, Qin, Hong, Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, Groening, Lars, Xiao, Chen, & Davidson, Ronald C..
```*Beam envelope calculations in general linear coupled lattices*. United States. doi:10.1063/1.4903457.

```
Chung, Moses, E-mail: mchung@unist.ac.kr, Qin, Hong, Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, Groening, Lars, Xiao, Chen, and Davidson, Ronald C.. Thu .
"Beam envelope calculations in general linear coupled lattices". United States.
doi:10.1063/1.4903457.
```

```
@article{osti_22408021,
```

title = {Beam envelope calculations in general linear coupled lattices},

author = {Chung, Moses, E-mail: mchung@unist.ac.kr and Qin, Hong and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026 and Groening, Lars and Xiao, Chen and Davidson, Ronald C.},

abstractNote = {The envelope equations and Twiss parameters (β and α) provide important bases for uncoupled linear beam dynamics. For sophisticated beam manipulations, however, coupling elements between two transverse planes are intentionally introduced. The recently developed generalized Courant-Snyder theory offers an effective way of describing the linear beam dynamics in such coupled systems with a remarkably similar mathematical structure to the original Courant-Snyder theory. In this work, we present numerical solutions to the symmetrized matrix envelope equation for β which removes the gauge freedom in the matrix envelope equation for w. Furthermore, we construct the transfer and beam matrices in terms of the generalized Twiss parameters, which enables calculation of the beam envelopes in arbitrary linear coupled systems.},

doi = {10.1063/1.4903457},

journal = {Physics of Plasmas},

number = 1,

volume = 22,

place = {United States},

year = {Thu Jan 15 00:00:00 EST 2015},

month = {Thu Jan 15 00:00:00 EST 2015}

}