Diego Escobar

Low frequency azimuthal stability of the ionization region of the Hall thruster discharge. II. Global analysis

The linear stability of the Hall thruster discharge is analysed against axial-azimuthal perturbations in the low frequency range using a time-dependent 2D code of the discharge. This azimuthal stability analysis is spatially global, as opposed to the more common local stability analyses, already afforded previously (D. Escobar and E. Ahedo, Phys. Plasmas 21(4), 043505 (2014)). The study covers both axial and axial-azimuthal oscillations, known as breathing mode and spoke, respectively. The influence on the spoke instability of different operation parameters such as discharge voltage, mass flow, and thruster size is assessed by means of different parametric variations and compared against experimental results. Additionally, simplified models are used to unveil and characterize the mechanisms driving the spoke. The results indicate that the spoke is linked to azimuthal oscillations of the ionization process and to the Bohm condition in the transition to the anode sheath. Finally, results obtained from local and global stability analyses are compared in order to explain the discrepancies between both methods.

Two-region model for positive and negative plasma sheaths and its application to Hall thruster metallic anodes

An asymptotic presheath/sheath model for positive and negative sheaths in front of a conducting electrode, with a continuous parametric transition at the no-sheath case, is presented. Key aspects of the model are as follows: full hydrodynamics of both species in the presheath; a kinetic formulation with a truncated distribution function for the repelled species within the sheath; and the fulfillment of the marginal Bohm condition at the sheath edge, in order to match the two formulations of the repelled species. The sheath regime depends on the ratios of particle fluxes and sound speeds between the two species. The presheath model includes the effect of a magnetic field parallel to the wall on electrons. An asymptotic, parametric study of the anode presheath is carried out in terms of the local ion-to-electron flux ratio and Hall parameter. The drift-diffusive model of magnetized electrons fails in a parametric region that includes parts of the negative sheath regime. In the case of the Hall parameter vanishing near the electrode and a weakly collisional plasma, a quasisonic, quasineutral plateau forms next to the sheath edge.

Two-Dimensional Electron Model for a Hybrid Code of a Two-Stage Hall Thruster

An axisymmetric model for magnetized electrons in a Hall thruster, to be used in combination with a particle-in-cell model for heavy species, is presented. The main innovation is the admission of exchanges of electric current at the chamber walls, thus making the model applicable to a larger variety of Hall thrusters. The model is fully 2-D for regular magnetic topologies. It combines an equilibrium law for collisionless dynamics along the direction parallel to the magnetic field with drift-fluid equations for perpendicular transport. These are coupled to sheath models for the interaction with different types of walls. The derivation of a parabolic differential equation for the temperature and the full computation of the electric field work improves clarity and accuracy over previous models. Simulations of a Hall thruster with an intermediate current-driving electrode, operating in emission, floating, and collection modes are presented. Enhancement of thrust efficiency is found for the electrode working in the high-emission mode if the magnetic field strength is adjusted appropriately. The two-stage floating mode presents lower wall losses, lower plume divergence, and higher efficiency than the equivalent one-stage configuration.

Global Stability Analysis of Azimuthal Oscillations in Hall Thrusters

A linearized time-dependent 2-D (axial and azimuthal) fluid model of the Hall thruster discharge is presented. This model is used to carry out a global stability analysis of the plasma response, as opposed to the more common local stability analyses. Experimental results indicate the existence of low-frequency long-wave-length azimuthal oscillations in the direction of the E × B drift, usually referred to as spokes. The present model predicts the presence of such oscillations for typical Hall thruster conditions with a frequency and a growth rate similar to those found in experiments. Moreover, the comparison between the simulated spoke and the simulated breathing mode, a purely axial low-frequency oscillation typical in Hall thrusters, shows similar features in them. Additionally, the contribution of this azimuthal oscillation to electron conductivity is evaluated tentatively by computing the equivalent anomalous diffusion coefficient from the linear oscillations. The results show a possible contribution to anomalous diffusion in the rear part of the thruster.

Improved electron formulation for a Hall thruster hybrid model

An advanced two-dimensional hybrid code for Hall e ect thrusters is under development. A central part of that work is an improved numerical formulation of electron dynamics. Numerical accuracy is increased by using di erential equations for conservation equations across the magnetic eld streamlines, instead of discrete, nite-volume equations, and by including the parallel Joule heating. In addition, the charge conservation equation is generalized in order to deal with non-dielectric elements at the lateral walls. This increases the code capabilities by allowing to simulate multi-electrode thrusters.

Low-frequency azimuthal stability analysis of Hall thrusters

This paper presents a linearized two-dimensional (axial and azimuthal) uid model of the Hall thruster discharge with the goal of understanding the mechanism responsible for the azimuthal oscillations in the ionization region. After a short review of the linear stability analyses carried out within the Hall Thruster research community, our model is presented. It is is based on the one dimensional model of Ahedo et al., 1 which has been extensively used in the past to characterize the plasma inside the thruster and the physics behind the ionization and acceleration regions of the thruster. Out of the myriad of oscillations in a Hall thruster, that of interest in this paper is the so-called spoke oscillation. Recent experiments 2{7 have shown the presence of the spoke in a rather large variety of Hall thrusters ranging from cylindrical to more conventional annular ones. However, there is not yet a clear understanding of the mechanism promoting and sustaining the spoke. Ultimately, the model presented here shall allow identifying the physics behind the spoke. The model can as well capture axial oscillations such as the breathing mode. Preliminary results from the model are shown for the more widely known and understood breathing mode.