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The propagation of a cold relativistic electron beam in a free electron laser with an axial guide magnetic field is considered. The possibility of several steady-state helical trajectories for the electrons is shown, and the stability against perturbations and accessibility of such steady states is considered. Necessary and sufficient conditions for the stability are derived and indicate the importance of the transition region at the entrance of the laser. Possible modes of operation of the laser in different steady-state regimes are suggested and illustrated by numerical examples.
L. Frièdland (1980) studied this question.