A kinetic theory for the description of a coupled system between relativistic electrons and radiation fields is developed on the basis of the Klimontovich formalism. Considering a system in which a relativistic beam of electrons passes through a transverse helical magnetic field, we specifically calculate the rates of the spontaneous and induced emission of electromagnetic radiation, and the collision term for the electrons resulting from the radiative processes. The results are applied to the free-electron laser experiments performed recently at Stanford.
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Ichimaru et al. (1978) studied this question.