Classical Theory of the Scattering of Intense Laser Radiation by Free Electrons

A complete discussion of the classical theory of high-intensity Thomson scattering by free electrons is presented. Neglecting the radiation reaction, the equations of motion for an electron in an arbitrarily intense, elliptically polarized, plane electromagnetic wave can be solved exactly. From the solutions for the electron motion, the radiated power, momentum, and harmonics are calculated in two special Lorentz frames: the laboratory frame and the frame in which the electron is on the average at rest. The difference between the radiated power measured by an observer and that emitted by the electron is discussed for each frame. A sum rule for the radiated harmonics is derived. The limitation due to the neglect of radiation reaction is considered. Finally, the high- and low-intensity behavior of the spectrum and angular distribution of the radiation is analyzed in both frames.