Exact expressions are derived for the gain of a free-electron laser based on a uniform longitudinal magnetic field configuration operating in the single-particle, low-gain regime. The gain is calculated for different parameters of the system. For strong enough a field, the gain decreases with an increase of the amplitude, becoming negative when passing a threshold value, which depends on the system parameters. Implications regarding the saturation of the lasing process are discussed.
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Physics of Quantum Electronics Vol. 5, ed. by S. Jacob, M. Sargent, M.O. Scully (Addison-Wesley Reading, Mass. 1978)
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Gell, Y., Torstensson, J.R., Wilhelmsson, H. et al. On a free-electron-laser in a uniform magnetic field. A solution for arbitrarily strong electromagnetic radiation fields. Appl. Phys. B 27, 15–18 (1982). https://doi.org/10.1007/BF00697291