# 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 electrons 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 extention 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.:
- Brookhaven National Lab., Upton, NY (USA)

- OSTI Identifier:
- 6994769

- Report Number(s):
- BNL-38824; CONF-850771-8

ON: DE87002392

- DOE Contract Number:
- AC02-76CH00016

- Resource Type:
- Conference

- Resource Relation:
- Conference: SLAC summer school on the physics of high energy particle accelerators, Stanford, CA, USA, 15 Jul 1985; Other Information: Portions of this document are illegible in microfiche products

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 43 PARTICLE ACCELERATORS; 42 ENGINEERING; FREE ELECTRON LASERS; CANONICAL TRANSFORMATIONS; GAIN; MAXWELL EQUATIONS; STIMULATED EMISSION; SYNCHROTRON RADIATION; WIGGLER MAGNETS; AMPLIFICATION; BREMSSTRAHLUNG; DIFFERENTIAL EQUATIONS; ELECTRICAL EQUIPMENT; ELECTROMAGNETIC RADIATION; ELECTROMAGNETS; EMISSION; ENERGY-LEVEL TRANSITIONS; EQUATIONS; EQUIPMENT; LASERS; MAGNETS; PARTIAL DIFFERENTIAL EQUATIONS; RADIATIONS; TRANSFORMATIONS; 430303* - Particle Accelerators- Experimental Facilities & Equipment; 420300 - Engineering- Lasers- (-1989)

### Citation Formats

```
Krinsky, S.
```*Introduction to the theory of free electron lasers*. United States: N. p., 1985.
Web.

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

```
Krinsky, S. 1985.
"Introduction to the theory of free electron lasers". United States. https://www.osti.gov/servlets/purl/6994769.
```

```
@article{osti_6994769,
```

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 electrons 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 extention 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/6994769},
journal = {},

number = ,

volume = ,

place = {United States},

year = {1985},

month = {1}

}