# Simple model for the nonlinear radiation field of a free electron laser

## Abstract

It is shown that Jacobi elliptic function solutions of the nonlinear Duffing equation model the radiation field in a high-gain free electron laser through early saturation. After initial start-up, the field can be expressed equivalently with a hyperbolic secant. The model is derived for arbitrary detuning from resonance, which enables study of the spectral properties in the early nonlinear regime.

- Authors:

- Publication Date:

- Research Org.:
- SLAC National Accelerator Lab., Menlo Park, CA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES)

- OSTI Identifier:
- 1731025

- Alternate Identifier(s):
- OSTI ID: 1768388

- Grant/Contract Number:
- AC02-76SF00515; 2017-SLAC-100382

- Resource Type:
- Published Article

- Journal Name:
- Physical Review Accelerators and Beams

- Additional Journal Information:
- Journal Name: Physical Review Accelerators and Beams Journal Volume: 23 Journal Issue: 12; Journal ID: ISSN 2469-9888

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 43 PARTICLE ACCELERATORS

### Citation Formats

```
Hemsing, Erik. Simple model for the nonlinear radiation field of a free electron laser. United States: N. p., 2020.
Web. https://doi.org/10.1103/PhysRevAccelBeams.23.120703.
```

```
Hemsing, Erik. Simple model for the nonlinear radiation field of a free electron laser. United States. https://doi.org/10.1103/PhysRevAccelBeams.23.120703
```

```
Hemsing, Erik. Fri .
"Simple model for the nonlinear radiation field of a free electron laser". United States. https://doi.org/10.1103/PhysRevAccelBeams.23.120703.
```

```
@article{osti_1731025,
```

title = {Simple model for the nonlinear radiation field of a free electron laser},

author = {Hemsing, Erik},

abstractNote = {It is shown that Jacobi elliptic function solutions of the nonlinear Duffing equation model the radiation field in a high-gain free electron laser through early saturation. After initial start-up, the field can be expressed equivalently with a hyperbolic secant. The model is derived for arbitrary detuning from resonance, which enables study of the spectral properties in the early nonlinear regime.},

doi = {10.1103/PhysRevAccelBeams.23.120703},

journal = {Physical Review Accelerators and Beams},

number = 12,

volume = 23,

place = {United States},

year = {2020},

month = {12}

}

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https://doi.org/10.1103/PhysRevAccelBeams.23.120703

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