An unstable 0D model of ionization oscillations in Hall thruster plasmas

The breathing mode is an instability typical of Hall thrusters, which is characterized by oscillations of the discharge current with amplitude of the order of its mean value and frequency in the 5–30 kHz range. The strong link between this instability and the ionization processes is generally recognized. If, on one hand, 1D simulations have shown to be able to reproduce the breathing mode, on the other hand 0D models fell short in recovering self sustained oscillations, making it hard to identify the core physical mechanism governing their formation. In this work an original 0D model is presented and characterized by means of linear stability analysis and direct numerical integration. The electric field is allowed to vary in response to variations of the neutral density, acting on the ionization rate via the electron temperature and the ion dynamics. It is shown that the model is able to reproduce self-sustained oscillations with the typical characteristics of the breathing mode, even when fluctuations of the electron temperature are neglected. The stability of the model is strictly determined by the rigidity with which variations of neutral density reflect into variations of electron mobility.