# Three-dimensional theory of the Cerenkov free-electron laser

## Abstract

We describe an analytical theory for the gain of a Cerenkov free-electron laser including diffraction of the optical beam in the direction transverse to the electron beam, parallel to the surface of the dielectric. Since the width of the optical beam depends on the gain, the usual cubic dispersion relation of two-dimensional slow-wave structures is replaced by a 5/2-power dispersion relation, but three of the five roots are extraneous. The results show that for a narrow electron beam, the optical beam is much wider than the electron beam. This reduces the gain by an order of magnitude. Moreover, in the three-dimensional theory the allowed roots of the dispersion relation have positive real parts, so they correspond to slow waves; when transverse diffraction is included, fast waves are forbidden.

- Authors:

- Department of Physics, Vanderbilt University, Nashville, Tennessee 37235 (United States)

- Publication Date:

- OSTI Identifier:
- 20982902

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Applied Physics; Journal Volume: 101; Journal Issue: 10; Other Information: DOI: 10.1063/1.2734540; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; DIELECTRIC MATERIALS; DIFFRACTION; DISPERSION RELATIONS; ELECTRON BEAMS; FREE ELECTRON LASERS; THREE-DIMENSIONAL CALCULATIONS; TWO-DIMENSIONAL CALCULATIONS

### Citation Formats

```
Andrews, H. L., and Brau, C. A.
```*Three-dimensional theory of the Cerenkov free-electron laser*. United States: N. p., 2007.
Web. doi:10.1063/1.2734540.

```
Andrews, H. L., & Brau, C. A.
```*Three-dimensional theory of the Cerenkov free-electron laser*. United States. doi:10.1063/1.2734540.

```
Andrews, H. L., and Brau, C. A. Tue .
"Three-dimensional theory of the Cerenkov free-electron laser". United States.
doi:10.1063/1.2734540.
```

```
@article{osti_20982902,
```

title = {Three-dimensional theory of the Cerenkov free-electron laser},

author = {Andrews, H. L. and Brau, C. A.},

abstractNote = {We describe an analytical theory for the gain of a Cerenkov free-electron laser including diffraction of the optical beam in the direction transverse to the electron beam, parallel to the surface of the dielectric. Since the width of the optical beam depends on the gain, the usual cubic dispersion relation of two-dimensional slow-wave structures is replaced by a 5/2-power dispersion relation, but three of the five roots are extraneous. The results show that for a narrow electron beam, the optical beam is much wider than the electron beam. This reduces the gain by an order of magnitude. Moreover, in the three-dimensional theory the allowed roots of the dispersion relation have positive real parts, so they correspond to slow waves; when transverse diffraction is included, fast waves are forbidden.},

doi = {10.1063/1.2734540},

journal = {Journal of Applied Physics},

number = 10,

volume = 101,

place = {United States},

year = {Tue May 15 00:00:00 EDT 2007},

month = {Tue May 15 00:00:00 EDT 2007}

}