# Effect of a large Oth harmonic octupole on stable betatron oscillations

## Abstract

S>The effect of a 0th harmonic octupole (that is, constant in dependence on azimuth) on stable betatron oscillations is treated in smooth approximation. In this approximation, an exact invariant is obtained. Bounded motion results, except when the octupole component is very large. A condition for stability- is obtained and, in the case of bounded motion, an expression for the amplitude variation is given. Some comments are made regarding the method of phase averaging. (auth)

- Authors:

- Publication Date:

- Research Org.:
- Brookhaven National Lab., Upton, N.Y. (USA)

- OSTI Identifier:
- 4417589

- Report Number(s):
- BNL-18259

- NSA Number:
- NSA-29-001071

- Resource Type:
- Technical Report

- Resource Relation:
- Other Information: Orig. Receipt Date: 30-JUN-74

- Country of Publication:
- United States

- Language:
- English

- Subject:
- N54400* -Particle Accelerators-Ion Optics & Field Calculations; *BETATRON OSCILLATIONS; OCTUPOLES; STABILITY

### Citation Formats

```
Month, M.
```*Effect of a large Oth harmonic octupole on stable betatron oscillations*. United States: N. p., 1973.
Web. doi:10.2172/4417589.

```
Month, M.
```*Effect of a large Oth harmonic octupole on stable betatron oscillations*. United States. doi:10.2172/4417589.

```
Month, M. Thu .
"Effect of a large Oth harmonic octupole on stable betatron oscillations". United States.
doi:10.2172/4417589. https://www.osti.gov/servlets/purl/4417589.
```

```
@article{osti_4417589,
```

title = {Effect of a large Oth harmonic octupole on stable betatron oscillations},

author = {Month, M.},

abstractNote = {S>The effect of a 0th harmonic octupole (that is, constant in dependence on azimuth) on stable betatron oscillations is treated in smooth approximation. In this approximation, an exact invariant is obtained. Bounded motion results, except when the octupole component is very large. A condition for stability- is obtained and, in the case of bounded motion, an expression for the amplitude variation is given. Some comments are made regarding the method of phase averaging. (auth)},

doi = {10.2172/4417589},

journal = {},

number = ,

volume = ,

place = {United States},

year = {Thu Sep 20 00:00:00 EDT 1973},

month = {Thu Sep 20 00:00:00 EDT 1973}

}

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