A simple rate theory is presented that satisfactorily describes several aspects of the collinear optically pumped far-infrared (FIR) amplifier. The use of the rate model is justified, and its limitations discussed. The theory, when fitted to the experimental results of other workers, yields an FIR emission cross section of

cm
2. The dependence of optimum amplifier pressure on column length emerges from the equations. The influence of pump and FIR intensities and of amplifier pressure on efficiency and gain are discussed. Some guidelines are enunciated for designing a multistage high power FIR amplifier.