A Coupled 0-D Plasma Thermal Model for Hollow Cathodes

Hollow cathodes are essential components of dc electric thrusters for space applications, such as ion and Hall thrusters. Since the late 1970's, several mathematical models have been proposed with the goal of characterizing the working principle and the plasma properties of such devices. Currently the more advanced 2-D models are used to effectively describe the onset of instabilities inside the plasma plume, but the increased complexity and the required calibrations make them not particularly suitable for cathode prototyping. Zero-dimensional models, on the other hand, can be used quickly and effectively to compute the main plasma parameters. In spite of their good qualities, reduced models usually do not perform well when used for very different cathodes with respect to the ones they were created for, especially due to the strong assumptions and free parameters which must be tuned to the specific case. By coupling a newly developed 0-D plasma model with a robust finite element analysis thermal simulation, the proposed model aims at filling this lack of flexibility, enabling the fast simulation of cathodes in a wide range of discharge currents and geometries. The model is able to compute self consistently all the physical quantities of interest, except the effective emission length, being the only free parameter. The model includes the approximate computation of the plasma sheath density on the emitter surface and the charge exchange heating (CEX) for the heavy species temperature. The thermal simulation is fully parametrized to quickly test different geometries and materials, while the prototyping tool allows great flexibility in terms of propellants and emissive insert materials.