# Analysis of radiation focusing and guiding in the free-electron laser by use of a source-dependent expansion. Interim report

## Abstract

In the free-electron laser (FEL) the resonant interaction between the radiation field and electron beam can result in radiation focusing (optical guiding). If the centroid of the electron beam is transversely displaced off-axis, the radiation field, under certain conditions, will follow and be steered by the electron beam. The effect of a spatial modulation on the electron-beam envelope can also modify the propagation characteristics of the radiation. These and other phenomena are analytically and numerically studied using a novel source-dependent Laguerre-Gaussian modal representation of the fully three-dimensional radiation field. Unlike the vacuum Laguerre-Gaussian modal expansion, the longitudinal spatial dependence of the radiation waist and curvature are determined and characterized by the source term in the wave equation. Among the advantages of this general source-dependent-expansion (SDE) approach is that few modes are needed to accurately describe the radiation. Hence, fast and accurate numerical solutions of the fully three-dimensional FEL problem can be obtained over distances of many Rayleigh lengths. Furthermore, this expansion allows development of an envelope equation for the radiation beams as well as an expression for the centroid of the beam.

- Authors:

- Publication Date:

- Research Org.:
- Berkeley Scholars, Inc., CA (USA)

- OSTI Identifier:
- 6288653

- Report Number(s):
- AD-A-180923/5/XAB

- Resource Type:
- Technical Report

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 42 ENGINEERING; FREE ELECTRON LASERS; FOCUSING; CONTROL; ELECTRON BEAMS; EXPANSION; INTERACTIONS; MODULATION; NUMERICAL ANALYSIS; RESONANCE; SPATIAL DISTRIBUTION; WAVE EQUATIONS; BEAMS; DIFFERENTIAL EQUATIONS; DISTRIBUTION; EQUATIONS; LASERS; LEPTON BEAMS; MATHEMATICS; PARTIAL DIFFERENTIAL EQUATIONS; PARTICLE BEAMS; 420300* - Engineering- Lasers- (-1989)

### Citation Formats

```
Sprangle, P, Ting, A, and Tang, C M.
```*Analysis of radiation focusing and guiding in the free-electron laser by use of a source-dependent expansion. Interim report*. United States: N. p., 1987.
Web.

```
Sprangle, P, Ting, A, & Tang, C M.
```*Analysis of radiation focusing and guiding in the free-electron laser by use of a source-dependent expansion. Interim report*. United States.

```
Sprangle, P, Ting, A, and Tang, C M. Mon .
"Analysis of radiation focusing and guiding in the free-electron laser by use of a source-dependent expansion. Interim report". United States.
```

```
@article{osti_6288653,
```

title = {Analysis of radiation focusing and guiding in the free-electron laser by use of a source-dependent expansion. Interim report},

author = {Sprangle, P and Ting, A and Tang, C M},

abstractNote = {In the free-electron laser (FEL) the resonant interaction between the radiation field and electron beam can result in radiation focusing (optical guiding). If the centroid of the electron beam is transversely displaced off-axis, the radiation field, under certain conditions, will follow and be steered by the electron beam. The effect of a spatial modulation on the electron-beam envelope can also modify the propagation characteristics of the radiation. These and other phenomena are analytically and numerically studied using a novel source-dependent Laguerre-Gaussian modal representation of the fully three-dimensional radiation field. Unlike the vacuum Laguerre-Gaussian modal expansion, the longitudinal spatial dependence of the radiation waist and curvature are determined and characterized by the source term in the wave equation. Among the advantages of this general source-dependent-expansion (SDE) approach is that few modes are needed to accurately describe the radiation. Hence, fast and accurate numerical solutions of the fully three-dimensional FEL problem can be obtained over distances of many Rayleigh lengths. Furthermore, this expansion allows development of an envelope equation for the radiation beams as well as an expression for the centroid of the beam.},

doi = {},

journal = {},

number = ,

volume = ,

place = {United States},

year = {1987},

month = {4}

}