# Application of the Green's function method to some nonlinear problems of an electron storage ring. Part III. Beam-size enhancement due to the presence of nonlinear magnets in a ring

## Abstract

A perturbation method which allows one to find the distribution function and the beam size for a broad class of storage ring nonlinear problems is described in Part I of this work. In present note I apply this method to a particular problem. Namely, I want to evaluate an enhancement of the vertical beam size of a bunch due to the presence of the ring of nonlinear magnetic fields. The main part of the work deals with sextupole magnets. Formula for the beam size in the presence of octupole fields are also developed to the first order in the octupole strength, although octupole magnets are not widely used in present storage ring designs. This calculation is done mainly because the octupole field has the same symmetry as the beam-beam force for the head-on collision. This will give us the opportunity to compare the conduct of the bunch due to this two types of nonlinear kicks. The general terms of the applicability of the Green's function method is discussed in the first part of this work.

- Authors:

- Publication Date:

- Research Org.:
- Stanford Linear Accelerator Center, CA (USA)

- OSTI Identifier:
- 5858296

- Report Number(s):
- SLAC/AP-2

ON: DE83015081; TRN: 83-019301

- DOE Contract Number:
- AC03-76SF00515

- Resource Type:
- Technical Report

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 43 PARTICLE ACCELERATORS; STORAGE RINGS; BEAM DYNAMICS; BEAM BUNCHING; BEAM EMITTANCE; ELECTRON BEAMS; GREEN FUNCTION; HEXAPOLES; MAGNETIC FIELDS; NONLINEAR PROBLEMS; OCTUPOLES; PERTURBATION THEORY; BEAMS; FUNCTIONS; LEPTON BEAMS; MULTIPOLES; PARTICLE BEAMS; 430200* - Particle Accelerators- Beam Dynamics, Field Calculations, & Ion Optics; 430400 - Particle Accelerators- Storage Rings

### Citation Formats

```
Kheifets, S.
```*Application of the Green's function method to some nonlinear problems of an electron storage ring. Part III. Beam-size enhancement due to the presence of nonlinear magnets in a ring*. United States: N. p., 1983.
Web. doi:10.2172/5858296.

```
Kheifets, S.
```*Application of the Green's function method to some nonlinear problems of an electron storage ring. Part III. Beam-size enhancement due to the presence of nonlinear magnets in a ring*. United States. doi:10.2172/5858296.

```
Kheifets, S. Sat .
"Application of the Green's function method to some nonlinear problems of an electron storage ring. Part III. Beam-size enhancement due to the presence of nonlinear magnets in a ring". United States. doi:10.2172/5858296. https://www.osti.gov/servlets/purl/5858296.
```

```
@article{osti_5858296,
```

title = {Application of the Green's function method to some nonlinear problems of an electron storage ring. Part III. Beam-size enhancement due to the presence of nonlinear magnets in a ring},

author = {Kheifets, S},

abstractNote = {A perturbation method which allows one to find the distribution function and the beam size for a broad class of storage ring nonlinear problems is described in Part I of this work. In present note I apply this method to a particular problem. Namely, I want to evaluate an enhancement of the vertical beam size of a bunch due to the presence of the ring of nonlinear magnetic fields. The main part of the work deals with sextupole magnets. Formula for the beam size in the presence of octupole fields are also developed to the first order in the octupole strength, although octupole magnets are not widely used in present storage ring designs. This calculation is done mainly because the octupole field has the same symmetry as the beam-beam force for the head-on collision. This will give us the opportunity to compare the conduct of the bunch due to this two types of nonlinear kicks. The general terms of the applicability of the Green's function method is discussed in the first part of this work.},

doi = {10.2172/5858296},

journal = {},

number = ,

volume = ,

place = {United States},

year = {1983},

month = {1}

}