• breathing mode
• electric propulsion
• hall thrusters
• hollow cathodes
• ion acoustic turbulence
• ionization instability
• low-temperature plasma

Hall thrusters are plasma-based devices that are currently considered one of the most attractive and mature electric propulsion technologies for space applications. To operate, they require to be coupled with an electron source, usually in the form of a hollow cathode, which provides the electrons necessary for the ionization of the propellant and the neutralization of the ion beam. Due to the lack of understanding of a variety of complex physical phenomena that are known to occur in Hall thrusters and hollow cathodes, significant uncertainty is still present in the prediction of their performance, lifetime, and stability envelope, which mainly relies on expensive and time-consuming experiments. In this work, we investigate the plasma physics in Hall thrusters and hollow cathodes through reduced-order fluid models. On the thruster side, we focus on the investigation of the breathing mode, an instability observed ubiquitously in these and other similar devices. This operating regime is characterized by low-frequency (5−30kHz) fluctuations of the discharge current, which are generated by corresponding plasma oscillations that originate inside the thruster and propagate longitudinally. It is generally recognized that the breathing mode is an ionization instability, related to a periodic depletion and refilling of the propellant in the chamber. However, there are several aspects related to this instability that are still poorly understood. In particular, the physical mechanisms governing the growth of the oscillations are uncertain, as well as their scaling with the thruster’s geometry and operating parameters. On the cathode side, we investigate the behavior of the plasma in the plume, which is the region that combines and dynamically interacts with the thruster plasma. This region is particularly challenging to characterize due to the presence of small-scale plasma turbulence that affects the macroscopic dynamics in a non-classical way and couples with large-scale, longitudinal ionization oscillations.
In pursuit of improving the collective understanding of these topics, different numerical
tools are developed through a series of gradual steps, each building on the results of the previous one. The starting point is a one-dimensional, time-dependent, fluid model of the thruster discharge. First, the model is calibrated against an experimental discharge current trace showing strong breathing oscillations, and the results are validated by comparing the theoretical predictions with spatiotemporal measurements of the plasma properties along the channel and near-plume. The calibrated model is shown to be effective in reproducing both the time-averaged axial distribution of the plasma and the characteristics of the dynamical response typical of the breathing mode, giving us confidence in using it to investigate the physical origin of the instability. The subsequent analysis is based on the identification of the base state, i.e., the unstable equilibrium state around which breathing mode develops. Through the synergistic use of linear stability analysis and ad-hoc non-linear simulations, the feedback mechanism behind the growth of the oscillations is revealed. In particular, a linear dependence between oscillations of neutral density and electron mobility is shown to be necessary for triggering the instability in the proposed model, by inducing fluctuations in phase opposition of the electric field and, in turn, of the ion velocity.
In light of these results, an original 0D formulation is developed and characterized by linear stability analysis and nonlinear simulations. The model is aimed at isolating the identified feedback mechanism, and at further demonstrating the capability of such mechanism of triggering and sustaining low-frequency ionization oscillations in Hall thrusters. The results well agree with the previous analysis: the proposed 0D formulation is capable of reproducing unstable oscillations with the typical characteristics of the breathing mode, even when the electron temperature is kept constant. In particular, the stability of the system strictly depends on the magnitude of the proportionality coefficient which links variations in electron mobility and neutral density. This analysis represents a step forward compared to previous literature, being the first time that a pure 0D formulation of a Hall thruster produces unstable and realistic results. Once the stability properties of the model are characterized in a general sense, the equations are expanded to relate the stability of the system to the intensity of the radial magnetic field inside the channel, which is known to be a key operating parameter in regulating the onset of the oscillations. The model, when appropriately tuned, manages to recover trends in line with several experimental observations reported in the literature, showing a stability transition at low magnetic fields, as for the real cases. Finally, the model is employed to investigate the effect of different propellants and of the anode temperature on the thruster’s stability.
Building upon the experience acquired during the investigation of the breathing mode, in the last part we develop a one-dimensional numerical model for the investigation of the hollow cathode plume plasma. The model is thoroughly characterized and validated against two different sets of experimental data available from the literature, providing new insight into the cathode plume dynamics.
Overall, this work provides new perspectives on different fundamental processes governing plasmas in Hall thrusters and hollow cathodes, along with an established numerical and theoretical framework that could be replicated and adapted to investigate similar low-temperature plasma configurations.