Abstract
The lasing by stimulated bremsstrahlung of a relativistic dilute electron beam passing through a spatially periodic longitudinal electrostatic field is investigated by means of the quantum-kinetic method. It is shown that the energy transfer from the electrons to the radiation field by the Lorentz force of the radiation field can be neglected compared with that by the force due to net stimulated bremsstrahlung (the emission by stimulated bremsstrahlung minus the absorption by inverse bremsstrahlung). The gain per unit length in the intensity of the laser light and the force acting on the electron due to free electron lasing are explicitly expressed as a function of the relevant parameters of the laser light and the electron beam.
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