Introduction to the theory of free electron lasers
Abstract
Presented is 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 lowgain regime is discussed using Colson's pendulum equations and Madey's theorems. The highgain regime is treated by an extension of the work of Bonifacio, Pellegrini, and Narducci. Dynamical variables to describe the radiation field is introduced, 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 selfamplified spontaneous radiation is considered, and the relationship between this approach and the use of coupled VlasovMaxwell equations is discussed.
 Publication:

Presented at the SLAC Summer School on the Physics of High Energy Particle Accelerators
 Pub Date:
 1985
 Bibcode:
 1985slac.conf.....K
 Keywords:

 Amplification;
 Electron Radiation;
 Free Electron Lasers;
 Stimulated Emission;
 Hamiltonian Functions;
 Maxwell Equation;
 Time Dependence;
 Wiggler Magnets;
 Lasers and Masers