Thermal properties of a plasma-loaded free-electron laser are studied with the aid of a dispersion relation obtained from the kinetic theory. The electron beam and the background plasma are assumed to have, respectively, small and finite momentum spread in the axial direction, using water-bag distribution functions. Thermal effects of the beam electrons are found to be stronger than those of the plasma. The maximum growth rate rises and falls as the momentum spread of the plasma is increased over a wide interval. In the Compton regime, with the high-energy and low-density electron beam, the plasma and its momentum spread have almost no effects on the growth rate.
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