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Hollow cathodes are used as thermionic emitters in a variety of electric propulsion devices, such as the Hall thruster. This work studies the derivation and discusses the results of a phenomenological (zero-dimensional) plasma model for a hollow cathode with open-end emitter and orificed keeper. This represents the first attempt at modeling the plasma in the three regions of hollow cathodes with open-end emitter geometry, namely, the keeper orifice, the cathode-keeper gap, and the insert. The current continuity, ion balance, and plasma power balance equations are solved to compute the main plasma property in each of the aforementioned regions. One novelty of this work is the definition of ready-to-use expressions for the dynamic viscosity and ionization and excitation rates for krypton. Moreover, the resistive losses in the cathode–anode region are computed to model the cathode standalone diode testing with an external anode. The model delivers cathode operational parameters, such as the discharge power and potential, which are compared to experimental data for both xenon- and krypton-fed cathodes. Furthermore, the influence of the geometry of the three regions as well as the propellant flow rate and the discharge current on plasma property and cathode power budget of sample cathodes is discussed at length. |
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