Investigation of the Hall Thruster Breathing Mode

Abstract

Hall thrusters can support a wide range of instabilities, many of which remain poorly understood yet are known to play a critical role in the fundamental operation of these devices. In this work, the dominant low-frequency oscillation known as the "breathing mode" is investigated. The goal of this study is to use experimental data to inform a simple model of the breathing mode that could yield an intuitive physical and analytical description of the criteria for the onset and growth of the instability. These criteria could serve as invaluable tools in improving the reliability of Hall thrusters. Foremost, an intuitive physical description of the breathing mode can provide insight into the ramifications of operating with the breathing mode. Such a model can reveal where this instability derives energy and thus which part of the thruster's efficiency is suffering as a result of these oscillations. Additionally, growth criteria can potentially provide insight into the operating conditions and thruster design choices that can minimize these oscillations. That is, if a model can definitively relate the growth rate of the breathing mode to high-level operating parameters, thruster designs can be targeted toward quieter operating conditions. Collectively, this knowledge can be used to intelligently optimize new Hall thrusters. Existing theories of the breathing mode are compared to the collected time-averaged and time-resolved laser data. In examining the scaling of the predicted breathing frequency, positive correlation between the experimental values and those predicted by theory is found, albeit with poor sensitivity. However, a comparison of the dynamic properties of the discharge to those assumed/predicted by theory reveal numerous discrepancies. Ultimately two leading theories for the breathing mode, the classical predator-prey model and a resistive instability, are determined to be incompatible with the measured oscillatory behavior. On the other hand, the data suggests a third possibility: a plasma-driven neutral gas instability. This is substantiated by the observation of neutral drift waves in the thruster channel. The classical zero-dimensional predator-prey model is expanded by the inclusion of more fluctuation terms to increase its fidelity in an attempt to reconcile discrepancies with experiment. Of the models considered, none predict linear instability at self-consistent operating conditions. Two alternative models are proposed that either assume the existence of fluctuations in the ionization region length out of phase with fluctuations in ion density, or assume modulation of the upstream neutral gas flow. Both models are shown to be unstable -- an improvement over the traditional predator-prey model of the breathing mode. Using this theoretical and experimental data, a modified theory of the breathing mode is derived in which coupled ionization instabilities lead to modulation of the neutral gas flow upstream of the traditional ionization region in the thruster. This physical description agrees qualitatively with experimental data. The model retains much of the same properties as the predator-prey model, which is widely accepted to be qualitatively correct. Numerical studies of this model are performed and the existence of unstable roots with reasonable real frequencies is verified. A simplified version of this model is derived to produce straightforward analytical expressions for the real frequency and growth rate of the breathing mode. The high-level trends implied by this simplified model are examined and found to be consistent with empirical scaling relationships.