# Three-dimensional analysis of harmonic generation in self-amplified spontaneous emission.

## Abstract

In a high-gain free-electron laser, strong bunching at the fundamental wavelength can drive substantial harmonic bunching and sizable power levels at the harmonic frequencies. In this paper, we investigate the three-dimensional evolution of the harmonic fields based on the coupled Maxwell-Vlasov equations that take into account the nonlinear harmonic interaction. Each harmonic field is the sum of a self-amplified term and a term driven by the nonlinear harmonic interaction. In the exponential gain regime, the growth rate of the dominant nonlinear term is much faster than that of the self-amplified harmonic field. As a result, the gain length and the transverse profile of the first few harmonics are completely determined by those of the fundamental. A percentage of the fundamental power level is found at the third harmonic frequency right before saturation for the current self-amplified spontaneous emission projects.

- Authors:

- Publication Date:

- Research Org.:
- Argonne National Lab., IL (US)

- Sponsoring Org.:
- US Department of Energy (US)

- OSTI Identifier:
- 11814

- Report Number(s):
- ANL/ASD/CP-99050

TRN: US0102139

- DOE Contract Number:
- W-31109-ENG-38

- Resource Type:
- Conference

- Resource Relation:
- Conference: 21st International Free Electron Laser Conference, Hamburg (DE), 08/23/1999--08/28/1999; Other Information: PBD: 1 Sep 1999

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 43 PARTICLE ACCELERATORS; FREE ELECTRON LASERS; HARMONIC GENERATION; SATURATION; THREE-DIMENSIONAL CALCULATIONS; BEAM BUNCHING; BOLTZMANN-VLASOV EQUATION

### Citation Formats

```
Huang, Z., and Kim, K.-J.
```*Three-dimensional analysis of harmonic generation in self-amplified spontaneous emission.*. United States: N. p., 1999.
Web.

```
Huang, Z., & Kim, K.-J.
```*Three-dimensional analysis of harmonic generation in self-amplified spontaneous emission.*. United States.

```
Huang, Z., and Kim, K.-J. Wed .
"Three-dimensional analysis of harmonic generation in self-amplified spontaneous emission.". United States. https://www.osti.gov/servlets/purl/11814.
```

```
@article{osti_11814,
```

title = {Three-dimensional analysis of harmonic generation in self-amplified spontaneous emission.},

author = {Huang, Z. and Kim, K.-J.},

abstractNote = {In a high-gain free-electron laser, strong bunching at the fundamental wavelength can drive substantial harmonic bunching and sizable power levels at the harmonic frequencies. In this paper, we investigate the three-dimensional evolution of the harmonic fields based on the coupled Maxwell-Vlasov equations that take into account the nonlinear harmonic interaction. Each harmonic field is the sum of a self-amplified term and a term driven by the nonlinear harmonic interaction. In the exponential gain regime, the growth rate of the dominant nonlinear term is much faster than that of the self-amplified harmonic field. As a result, the gain length and the transverse profile of the first few harmonics are completely determined by those of the fundamental. A percentage of the fundamental power level is found at the third harmonic frequency right before saturation for the current self-amplified spontaneous emission projects.},

doi = {},

journal = {},

number = ,

volume = ,

place = {United States},

year = {1999},

month = {9}

}