Results based on a local linear stability analysis of the Hall thruster discharge are presented. A one-dimensional azimuthal framework is used including three species: neutrals, singly charged ions, and electrons. A simplified linear model is developed with the aim of deriving analytical expressions to characterize the stability of the ionization region. The results from the local analysis presented here indicate the existence of an instability that gives rise to an azimuthal oscillation in the +E × B direction with a long wavelength. According to the model, the instability seems to appear only in regions where the ionization and the electric field make it possible to have positive gradients of plasma density and ion velocity at the same time. A more complex model is also solved numerically to validate the analytical results. Additionally, parametric variations are carried out with respect to the main parameters of the model to identify the trends of the instability. As the temperature increases and the neutral-to-plasma density ratio decreases, the growth rate of the instability decreases down to a limit where azimuthal perturbations are no longer unstable.
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