On the onset of breathing mode in Hall thrusters and the role of electron mobility fluctuations

Abstract

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.

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

“…The proposed 0D model is built on the basis of the 1D model detailed in [13]. The magnetic field is assumed to have a dominant radial component, which is representative of the magnetic field topology in conventional Hall thrusters.…”

“…A second mechanism (E2) is also proposed, based on the observation that the oscillations of the electric field establish a positive feedback on the ionization rate also via the subsequent ion dynamics, through variations of the plasma density and regardless of the electron temperature. Indeed, the results of [13] show that fluctuations are observed also when the electron temperature is assumed to be stationary, indicating that the electron energy dynamics can influence the instability but is not necessary for its onset, at least in the investigated case.…”

“…In [13] a novel mechanism for the generation of breathing mode is identified by means of a three-species (neutrals, ions, electrons) 1D model of the plasma discharge in Hall thrusters. The model employs well established simulation techniques and is calibrated against a reference experimental configuration, as detailed in [12].…”

“…The model employs well established simulation techniques and is calibrated against a reference experimental configuration, as detailed in [12]. The analysis proposed in [13] focuses on both the linearized dynamics around the steady solution and on the non-linear behavior of the model. It is shown that the instability can be observed even if the electron mobility is linearized with respect to the neutral density, which implies fluctuations of the electric field in phase opposition with the oscillations of the neutral density.…”

“…In this work, a 0D model is proposed to further support the identification of the original feedback mechanism E2 highlighted above. The proposed 0D formulation is based on the 1D model and on the related results detailed in [13]. Unlike the onedimensional case, in the 0D model the spatial gradients of the plasma properties are not resolved, and the focus is on the global behavior of the plasma in a control volume delimited by the anode and channel exit sections, and the lateral walls.…”