Single-particle theory of the free-electron laser in a moving frame

A summary is presented of the theory of a single electron involved in free-electron laser (FEL) operation. The method of transformation to a predetermined moving frame where the wiggler-laser scattering process is elastic is used. The classical and quantum dynamics of such an electron is discussed and the lowest order FEL behavior is evaluated from the classical pendulum equation. The presentation is tutorial throughout and stresses analytic results and physically significant dimensionless parameters. No results are included for the dynamic evolution of the light during the laser action.