In the present work, we make use of simplified nonlinear models based on the compressibility factor (Peter et al., Phys. Plasmas, vol. 20 (12), 2013, 123104) to predict the gain of one-dimensional (1-D) free-electron lasers (FELs), considering space-charge and thermal effects. These models proved to be reasonable to estimate some aspects of 1-D FEL theory, such as the position
of the onset of mixing, in the case of a initially cold electron beam, and the position
of the breakdown of the laminar regime, in the case of an initially warm beam (Peter et al., Phys. Plasmas, vol. 21 (11), 2014, 113104). The results given by the models are compared to wave–particle simulations showing a reasonable agreement.