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

We give a summary of the theory of a single electron involved in free-electron laser (FEL) operation. We use the method of transformation to a predetermined moving frame where the wiggler-laser scattering process is elastic. In this paper, we discuss the classical and quantum dynamics of such an electron and evaluate perturbatively the lowest order FEL behavior 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.