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A reduced-order numerical model describing the plasma in an orificed hollow cathode is presented as a quick tool for the design of thermionic cathodes. A time-independent, volume-averaged model is developed to determine plasma properties, wall temperatures, and cathode lifetime without requiring experimental data as input. A system of particle and energy balance equations is numerically solved without invoking a Saha-type equilibrium under the hypothesis of a direct-impact ionization process. Further, a lumped-parameter thermal model is coupled with the plasma model to estimate the temperature profile along the cathode axis and the emitter lifetime. The obtained results capture most of the characteristic features of this class of hollow cathodes as compared with the available experimental data. In addition, the model gives insight into the most important power deposition processes affecting the emitter and orifice regions. The effect of the geometry on both plasma parameters and cathode performance is discussed to suggest design guidelines for the development of state-of-the-art hollow cathodes.