# Output power in guided modes for amplified spontaneous emission in a single-pass free-electron laser

## Abstract

Treating diffraction effects within the paraxial approximation, we solve the initial-value problem determining the start-up of a single-pass free-electron laser from shot noise in the electron beam. Linearized Vlasov-Maxwell equations are used to derive an equation for the three-dimensional slowly varying envelope function of the radiated electric field. In the high-gain regime before saturation, the output power is expressed in terms of Moore's exponentially growing guided modes. For a cylindrical monoenergetic electron beam with step-function profile, explicit numerical and analytical calculations have been performed, determining the power in the guided modes. The condition for the dominance of the fundamental mode is discussed. Our solution of the initial-value problem is based upon a Green's-function technique, and our results are derived despite the lack of orthogonality and completeness of the guided modes. The Green's function is expanded in terms of an orthonormal set of eigenfunctions of a two-dimensional Schroedinger equation with non-self-adjoint Hamiltonian. In the limit of a long wiggler, the asymptotic representation of the Green's function is found to be dominated by the contribution of the guided modes. The radiated electric field, and hence the output power, is determined with use of the Green's function.

- Authors:

- Publication Date:

- Research Org.:
- National Synchrotron Light Source, Brookhaven National Laboratory, Upton, New York 11973-5000

- OSTI Identifier:
- 6039466

- Resource Type:
- Journal Article

- Journal Name:
- Phys. Rev. A; (United States)

- Additional Journal Information:
- Journal Volume: 35:8

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 42 ENGINEERING; FREE ELECTRON LASERS; GAIN; MODE CONTROL; BOUNDARY-VALUE PROBLEMS; MAXWELL EQUATIONS; PARAMETRIC ANALYSIS; POWER POTENTIAL; WIGGLER MAGNETS; AMPLIFICATION; CONTROL; DIFFERENTIAL EQUATIONS; ELECTRICAL EQUIPMENT; ELECTROMAGNETS; EQUATIONS; EQUIPMENT; LASERS; MAGNETS; PARTIAL DIFFERENTIAL EQUATIONS; 420300* - Engineering- Lasers- (-1989)

### Citation Formats

```
Krinsky, S, and Yu, L H.
```*Output power in guided modes for amplified spontaneous emission in a single-pass free-electron laser*. United States: N. p., 1987.
Web. doi:10.1103/PhysRevA.35.3406.

```
Krinsky, S, & Yu, L H.
```*Output power in guided modes for amplified spontaneous emission in a single-pass free-electron laser*. United States. https://doi.org/10.1103/PhysRevA.35.3406

```
Krinsky, S, and Yu, L H. 1987.
"Output power in guided modes for amplified spontaneous emission in a single-pass free-electron laser". United States. https://doi.org/10.1103/PhysRevA.35.3406.
```

```
@article{osti_6039466,
```

title = {Output power in guided modes for amplified spontaneous emission in a single-pass free-electron laser},

author = {Krinsky, S and Yu, L H},

abstractNote = {Treating diffraction effects within the paraxial approximation, we solve the initial-value problem determining the start-up of a single-pass free-electron laser from shot noise in the electron beam. Linearized Vlasov-Maxwell equations are used to derive an equation for the three-dimensional slowly varying envelope function of the radiated electric field. In the high-gain regime before saturation, the output power is expressed in terms of Moore's exponentially growing guided modes. For a cylindrical monoenergetic electron beam with step-function profile, explicit numerical and analytical calculations have been performed, determining the power in the guided modes. The condition for the dominance of the fundamental mode is discussed. Our solution of the initial-value problem is based upon a Green's-function technique, and our results are derived despite the lack of orthogonality and completeness of the guided modes. The Green's function is expanded in terms of an orthonormal set of eigenfunctions of a two-dimensional Schroedinger equation with non-self-adjoint Hamiltonian. In the limit of a long wiggler, the asymptotic representation of the Green's function is found to be dominated by the contribution of the guided modes. The radiated electric field, and hence the output power, is determined with use of the Green's function.},

doi = {10.1103/PhysRevA.35.3406},

url = {https://www.osti.gov/biblio/6039466},
journal = {Phys. Rev. A; (United States)},

number = ,

volume = 35:8,

place = {United States},

year = {1987},

month = {4}

}