A free-electron laser in a uniform magnetic field

The interaction of free electrons and free electromagnetic radiation, in the presence of a uniform magnetic field, can result in stimulated emission or absorption. We analyze the dynamics of single electrons by solving the classical, relativistic Lorentz force equations of motion in these combined fields. An electron may gain energy from, or lose energy to, the radiation field, depending crucially on the phase and oscillation frequency of the electron's helical motion within the superposed, circularly polarized light wave. To first order in the radiation field strength, electrons in a monoenergetic, uniformly distributed beam become spatially bunched, but there is no net energy change. To second order, however, the beam may experience a gain or loss of energy, corresponding to attenuation or amplification of radiation. We compare the bunching of this laser process to the bunching processes involved in 1) the Stanford free-electron laser and 2) the cyclotron maser, and find significant differences in each case. Our analytic results provide a clear, simple picture of the interaction process, and can be useful in exploring light amplification in astrophysical magnetic fields, the magnetosphere, or in laboratory devices. Supported in part by Army Contract No. DASG 60-77-C-0083 and NASA Grant NSG-7490.