• breathingmode
• Hallthrusters
• LotkaVolterra
• plasmaphysics

Hall thrusters are electrical propulsion engines mainly mounted on satellites and spacecraft and achieve thrust by accelerating the ions of which the plasma is composed with an electric field and ejecting them outside the engine.

During normal operation of the thruster numerous plasma oscillations occur and in particular those with the lowest frequencies, $\mathcal{O}(10)\;kHz$, are usually called "breathing mode". The main hypothesis to explain this phenomenon has been proposed in \cite{boeuf:lowfrequencyoscillationsinastationaryplasmathruster} by Boeuf and Garrigues and modeled in a very simple way by Fife et al. in \cite{fife:anumericalstudyoflow-frequencydischargeoscillationsinhallthrusters}: it's a "predator-prey" model (or Lotka-Volterra equations) applied to the considered situation, establishing an analogy between predator-electron and prey-neutral atoms.

The breathing mode oscillations can be well described through 1D models but it is not clear what is the physical mechanism that generates them. This evidence is taken into account in the present work but the hypothesis is that the breathing mode mechanism can still be captured with a 0D model.

Currently all the proposed 0D models are able to predict oscillation frequencies very close to those measured but always have damped amplitudes: experimentally we measure different behavior, that is a positive growth rate in the initial tansient and the achievement of a stable mode with constant oscillation amplitudes. Net of this, the hypothesis that the 0D models are able to describe the breathing mode it has not yet been discarded but indeed there is much research in this direction. This thesis fits exactly in this context.

In the present work the most important traits of the main predator-prey models of the breathing mode are highlighted and a new model based on both theoretical and experimental considerations is proposed. The hypothesis advanced from Dale and Jorns in \cite{jorns:two-zonehallthrusterbreathingmodemechanismpartI:theory} is that the breathing mode can be captured dividing the thruster in two communicating zones in each of which a process of the predator-prey type happens.

Taking inspiraton from their work, in this thesis is proposed a new 0D model in which neutral atoms and ions are considered "cold" while the electronic species is described by the transport equations of the warm plasma model. The thruster channel is divided into two communicating zones and in both preys are the neutral atoms and the predators the ions. The basic hypothesis is that the physical mechanism of breathing mode also has a spatial origin and that the plasma oscillations are also fed by temperature variations: for these reasons the proposed 0D model consists respectively of two adjacent zones and equations for the evolution of internal energy. In this thesis the proposed model will be analyzed numerically and, where possible, analytically.

The proposed model presents damped oscillations therefore it cannot solve the main problem of the investigation but at the same time reveals some important characteristics that 1D models are also able to bring out. After having commented the results of the simulations, we proceed with an extensive discussion with the aim of understanding the critical behaviors of the model. In this sense, a new simplified model is exposed and analyzed; the comparison between the two proposed models allows to have a clearer vision of the dynamics that is established in the Hall thruster. Furthermore, the dependence of the models on the anomalous transport of electrons is investigated, a physical process that seems to have great importance in the dynamics of the breathing mode.

Finally we draw the conclusions of the thesis and present a new way forward which will be relevant for future work.