# Design of a One-Dimensional Sextupole Using Semi-Analytic Methods

## Abstract

Sextupole magnets provide position-dependent momentum kicks and are tuned to provide the correct kicks to parti- cles within a small acceptance region in phase space. Sextupoles are useful and even necessary in circular accelerators for chromaticity corrections. They are routinely used in most rings, i.e. CESR. Although sextupole magnets are necessary for particle energy corrections, they also have undesirable effects on dynamic aperture, especially because of their non- linear coupling term in the momentum kick. Studies of integrable systems suggest that there is an analytic way to create transport lattices with specific transfer matrices that limit the momentum kick to one dimension. A one-dimension sex- tupole is needed for chromaticity corrections: a horizontal sextupole for horizontal bending magnets. We know how to make a “composite” horizontal sextupole using regular 2D sextupoles and linear transfer matrices in an ideal thin-lens approximation. Thus, one could create an accelerator lattice using linear elements, in series with sextupole magnets to create a “1D sextupole”. This paper describes progress to- wards realizing a realistic focusing lattice resulting in a 1D sextupole.

- Authors:

- Chicago U.

- Publication Date:

- Research Org.:
- Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)

- OSTI Identifier:
- 1452795

- Report Number(s):
- FERMILAB-CONF-18-170-AD

1677469

- DOE Contract Number:
- AC02-07CH11359

- Resource Type:
- Conference

- Resource Relation:
- Conference: 9th International Particle Accelerator Conference, Vancouver, BC Canada, 04/29-05/04/2018

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 43 PARTICLE ACCELERATORS

### Citation Formats

```
Gupta, L., Nagaitsev, S., Baturin, S. S., and Kim, Y.-K..
```*Design of a One-Dimensional Sextupole Using Semi-Analytic Methods*. United States: N. p., 2018.
Web.

```
Gupta, L., Nagaitsev, S., Baturin, S. S., & Kim, Y.-K..
```*Design of a One-Dimensional Sextupole Using Semi-Analytic Methods*. United States.

```
Gupta, L., Nagaitsev, S., Baturin, S. S., and Kim, Y.-K.. Sun .
"Design of a One-Dimensional Sextupole Using Semi-Analytic Methods". United States.
doi:. https://www.osti.gov/servlets/purl/1452795.
```

```
@article{osti_1452795,
```

title = {Design of a One-Dimensional Sextupole Using Semi-Analytic Methods},

author = {Gupta, L. and Nagaitsev, S. and Baturin, S. S. and Kim, Y.-K.},

abstractNote = {Sextupole magnets provide position-dependent momentum kicks and are tuned to provide the correct kicks to parti- cles within a small acceptance region in phase space. Sextupoles are useful and even necessary in circular accelerators for chromaticity corrections. They are routinely used in most rings, i.e. CESR. Although sextupole magnets are necessary for particle energy corrections, they also have undesirable effects on dynamic aperture, especially because of their non- linear coupling term in the momentum kick. Studies of integrable systems suggest that there is an analytic way to create transport lattices with specific transfer matrices that limit the momentum kick to one dimension. A one-dimension sex- tupole is needed for chromaticity corrections: a horizontal sextupole for horizontal bending magnets. We know how to make a “composite” horizontal sextupole using regular 2D sextupoles and linear transfer matrices in an ideal thin-lens approximation. Thus, one could create an accelerator lattice using linear elements, in series with sextupole magnets to create a “1D sextupole”. This paper describes progress to- wards realizing a realistic focusing lattice resulting in a 1D sextupole.},

doi = {},

journal = {},

number = ,

volume = ,

place = {United States},

year = {Sun Apr 01 00:00:00 EDT 2018},

month = {Sun Apr 01 00:00:00 EDT 2018}

}