• electric propulsion
• Langmuir probe
• experimental method
• plasma oscillations
• plasma simulation
• Hall thruster

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 (5-30 kHz), longitudinal oscillation of the discharge current and plasma parameters playing a critical role in the thruster operation and performance. Despite strong research efforts, several aspects of this unsteady phenomenon are still poorly understood. This is due to the difficulties in performing high frequency measurements in the plasma region, the fact that the main characteristics of the discharge oscillations vary greatly with the thruster geometry and operating condition, and the complexities in modeling the non-linear plasma dynamics at play in the thruster.

The main objective of the present research is to provide a numerical and experimental framework for the assessment of the impact of longitudinal oscillations on Hall thruster operation, considering its effect on both the plasma fields and on the integral properties of total discharge current and performance.

In pursuit of this objective, we developed a novel measurement apparatus and data processing technique that allow for the quantitative reconstruction of the effects of breathing mode oscillations on the main properties of the plasma in Hall thrusters. The approach is based on the use of a triple Langmuir probe mounted on a rapidly moving arm to scan the channel centreline and was validated in an experimental campaign on a 5 kW-class Hall thruster, Sitael's HT5k. The probe data was sampled at high frequency during its motion, and a Bayesian methodology was used to reliably infer the plasma properties from the instantaneous voltage and current measurements. To model the interaction of the electrodes with the plasma, a parametrization of the Laframboise sheath solution was used. Data were collected continuously during the probe motion from the plume up to the near-anode region of the thruster, allowing for the reconstruction of the salient features of the plasma oscillations as a function of axial location. A time-frequency analysis of the measured plasma properties based on wavelets was then performed to gain insight into the evolution and phase shift of the oscillations over the investigated plasma domain. The developed diagnostic method can provide quantitative information on the instantaneous value of plasma density, electron temperature, and plasma potential along the thruster centreline with good spatial resolution and has proved to be a valid approach to investigate breathing mode oscillations in Hall thruster plasmas.

On the numerical side, we propose the use of an informed 1D fully-fluid model to provide augmented data with respect to available experimental measurements. 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. With the calibrated code, we describe how the augmented data obtained through the combination of experiments and model can provide insight on the breathing mode oscillations and the evolution of plasma properties. Specifically, the near anode and ionization dynamics are investigated in greater depth and the direct impact of the breathing mode on the thruster performance with respect to an equivalent “quiescent” condition is estimated.

As a final step, we present the results of an experimental campaign carried out on a 20 kW-class thruster prototype, Sitael's HT20k, with an exchangeable discharge channel and magnetic circuit. Three different channel sizes were tested over a wide range of operating conditions and magnetic fields. For each operating point, a high frequency measurement of the discharge current was performed, recording the main characteristics of the oscillations. The data collected were then processed to derive the influence coefficients of each thruster parameter on the discharge current characteristics, as well as their dispersion. This allowed formulating general, data-driven scaling laws for the discharge current salient features, such as oscillation amplitude and dominant frequency. The gathered insight sheds light on the physical processes involved in the thruster discharge. At the same time, the possibility to model with simple functional laws the main oscillatory mode of Hall thrusters offers a unique aid to the optimization of thruster design and operation.