Coupled equations describing the propagation of the laser field (Maxwell equation) and the evolution of the electron distribution (generalized pendulum equations) are derived classically for the case of ultrarelativistic electrons moving in a helical magnet with an arbitrary slowly varying amplitude. The equations apply to coherent transient phenomena, such as picosecond pulse propagation, as well as to continuous-wave laser operation.
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Moore et al. (1980) studied this question.
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