The stability of sidebands in a free-electron laser is determined in the regime in which the three-dimensional structure of the modes is important. It is found that the growth rate of the sidebands in the presence of a fundamental mode that is weakly guided by the beam is reduced. The indications are that for some parameters the spatial growth rate of the sidebands can be made less than that of the fundamental.
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Antonsen et al. (1989) studied this question.
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