A relativistic theory for Raman backscattering, in the beam frame of electrons, is presented and is used to find the growth rate of a free-electron laser in Raman regime. The effects of the self-electric and self-magnetic fields, on the equilibrium trajectories of electrons, are taken into account. The wiggler effects, on the linear dispersion relations of the space-charge wave and radiation, are included in the analysis. A numerical computation is conducted to investigate the wiggler and self-field effects on the growth rate. The results of the relativistic and nonrelativistic treatments are compared.
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