One of the main oscillatory modes found ubiquitously in Hall thrusters is the so-called breathing mode. This is recognized as a relatively low-frequency (10–30 kHz), longitudinal oscillation of the discharge current and plasma parameters. In this paper, we present a synergic experimental and numerical investigation of the breathing mode in a 5 kW-class Hall thruster. To this aim, we propose the use of an informed 1D fully-fluid model to provide augmented data with respect to available experimental measurements. The experimental data consists of two datasets, i.e., the discharge current signal and the local near-plume plasma properties measured at high-frequency with a fast-diving triple Langmuir probe. The model is calibrated on the discharge current signal and its accuracy is assessed by comparing predictions against the available measurements of the near-plume plasma properties. It is shown that the model can be calibrated using the discharge current signal, which is easy to measure, and that, once calibrated, it can predict with reasonable accuracy the spatio-temporal distributions of the plasma properties, which would be difficult to measure or estimate otherwise. Finally, we describe how the augmented data obtained through the combination of experiments and calibrated model can provide insight into the breathing mode oscillations and the evolution of plasma properties.

Breathing mode is an ionization instability which is observed ubiquitously in the operation of Hall thrusters. It is recognized as a relatively low frequency (10–30 kHz) longitudinal oscillation of the discharge current and the plasma parameters. Although breathing instability is widely studied in the literature, the conditions for its origin are not fully understood. In this work we investigate the mechanisms responsible for the origin of the breathing mode in Hall thrusters by using a numerical model, allowing us to highlight the importance of electron mobility fluctuations for the onset and self-sustenance of the instability. Our one-dimensional, fully fluid model of the thruster channel is calibrated against the measured discharge current signal for a 5 kW-class Hall thruster operating in a condition where breathing mode is fully developed. The corresponding steady, unstable configuration (base state) is numerically computed by applying the Selective Frequency Damping (SFD) method. Then, a series of numerical tests is performed to show the existence of a feedback loop involving fluctuations around the base state of the neutral density, electron mobility, and electric field. We show that oscillations of the electron mobility are mainly caused by variations of the neutral density and are in phase with them; this, in turn, induces oscillations of the electric field, which are in phase opposition. The electric field acts simultaneously on the electron temperature and on the ion dynamics, promoting the depletion and replenishment of neutrals in the chamber.

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.