Stimulated emission from relativistic electrons passing through a spatially periodic transverse magnetic field

Stimulated emission from a relativistic beam of electrons passing through a spatially periodic right-hand circularly polarized magnetic field is considered. The amplification is found to be due to a ponderomotive bunching of the electrons. The effect is completely classical and for an infinite interaction distance a dispersion relation, which takes into account space-charge effects, describing the scattered field is derived. Conditions on the pump field amplitude, beam density, and momentum spread of the beam for emission from individual electrons to occur or for emission from plasma oscillations to occur are examined. Also, emission from individual electrons over a finite interaction distance is considered and gain is determined for distances less than an $e$-folding length.