# Introduction to the theory of free electron lasers

## Abstract

We present an introduction to some fundamental aspects of the theory of free electron lasers. Spontaneous radiation emitted by electron traversing a wiggler magnet is briefly reviewed, and stimulated emission in the low-gain regime is discussed using Colson's pendulum equations and Madey's theorems. The high-gain regime is treated by an extension of the work of Bonifacio, Pellegrini, and Narducci. We introduce dynamical variables to describe the radiation field, and a Hamiltonian formulation of Maxwell's equations is employed. A canonical transformation to the interaction representation factors out the fast time variation of the radiation field, and the slow time dependence is determined by linearized equations for the appropriate collective variables. As an application of this technique we consider self-amplified spontaneous radiation, and we comment upon the relationship between our approach and the use of coupled Vlasov--Maxwell equations.

- Authors:

- Publication Date:

- Research Org.:
- National Synchrotron Light Source, Brookhaven National Laboratory, Upton, NY 11973

- OSTI Identifier:
- 5525135

- Report Number(s):
- CONF-850771-

Journal ID: CODEN: APCPC

- Resource Type:
- Conference

- Journal Name:
- AIP Conf. Proc.; (United States)

- Additional Journal Information:
- Journal Volume: 153:1; Conference: SLAC summer school on the physics of high energy particle accelerators, Stanford, CA, USA, 15 Jul 1985

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 42 ENGINEERING; FREE ELECTRON LASERS; MATHEMATICAL MODELS; WIGGLER MAGNETS; MAGNETIC FIELDS; ELECTRON BEAMS; HAMILTONIANS; MAXWELL EQUATIONS; SYNCHROTRON RADIATION; BEAMS; BREMSSTRAHLUNG; DIFFERENTIAL EQUATIONS; ELECTRICAL EQUIPMENT; ELECTROMAGNETIC RADIATION; ELECTROMAGNETS; EQUATIONS; EQUIPMENT; LASERS; LEPTON BEAMS; MAGNETS; MATHEMATICAL OPERATORS; PARTIAL DIFFERENTIAL EQUATIONS; PARTICLE BEAMS; QUANTUM OPERATORS; RADIATIONS; 420300* - Engineering- Lasers- (-1989)

### Citation Formats

```
Krinsky, S.
```*Introduction to the theory of free electron lasers*. United States: N. p., 1987.
Web.

```
Krinsky, S.
```*Introduction to the theory of free electron lasers*. United States.

```
Krinsky, S. 1987.
"Introduction to the theory of free electron lasers". United States.
```

```
@article{osti_5525135,
```

title = {Introduction to the theory of free electron lasers},

author = {Krinsky, S},

abstractNote = {We present an introduction to some fundamental aspects of the theory of free electron lasers. Spontaneous radiation emitted by electron traversing a wiggler magnet is briefly reviewed, and stimulated emission in the low-gain regime is discussed using Colson's pendulum equations and Madey's theorems. The high-gain regime is treated by an extension of the work of Bonifacio, Pellegrini, and Narducci. We introduce dynamical variables to describe the radiation field, and a Hamiltonian formulation of Maxwell's equations is employed. A canonical transformation to the interaction representation factors out the fast time variation of the radiation field, and the slow time dependence is determined by linearized equations for the appropriate collective variables. As an application of this technique we consider self-amplified spontaneous radiation, and we comment upon the relationship between our approach and the use of coupled Vlasov--Maxwell equations.},

doi = {},

url = {https://www.osti.gov/biblio/5525135},
journal = {AIP Conf. Proc.; (United States)},

number = ,

volume = 153:1,

place = {United States},

year = {1987},

month = {2}

}