Axial–azimuthal instabilities of a Hall-thruster plasma discharge are investigated using fluid model and a linear global stability approach, appropriate to the large axial inhomogeneity of the equilibrium solution. Electron pressure and electron inertia are considered in both the equilibrium and perturbed solutions. Fourier transform in time and azimuth are taken and the dispersion relation, for the resultant Sturm–Liouville problem governing the axial behavior of the modes, is numerically obtained. The analysis, focused in mid-to-high frequencies and large wavenumbers identifies two main instability types. The dominant mode develops in the near plume at 1–5 MHz and azimuthal mode numbers ∼10–50, has a weak ion response and seems to be triggered by negative gradients of the magnetic field. The subdominant mode develops near the anode at 100–300 kHz and azimuthal mode numbers ∼1–10, and seems of the rotating-spoke type. Both instabilities are well characterized by investigating their oblique propagation, the influence of design and operation parameters, and the effects of anode–cathode electric connection, electron inertia, and temperature perturbations. The possible impact of these instabilities on electron cross-field transport is estimated through a quasilinear approach, which yields a spatially-rippled turbulent force.

The standard time-dependent three-fluid model found in the literature is here enhanced by extending the physical
domain beyond the cathodic surface into the far plume, and improving the modelling of some physical phenomena.
The neutral momentum equation, azimuthal electron inertia, the neutral energy equation, and the ion energy equation
are progressively included to conform a suite of five models.
Fully stationary solutions are benchmarked against those of a purely stationary model, this one using a different
integration scheme, and the effects of the added physics are assessed. A limited parametric study on the presence of
breathing-mode type of solutions is presented, showing that they are affected by both the parameters and the physics of
the model. A weak plasma attachment to the anode seems to be related to the presence of the breathing mode and can
end in the failure of the present model if the normal anode sheath collapses.

A local study of linear electrostatic modes, applicable to the dynamics perpendicular to the magnetic field in a plasma with crossed electric and magnetic fields, is presented. The analysis is based on a two-fluid model that takes into account the finite-electron-gyroradius effects through a rigorous gyroviscosity tensor and includes a dissipative friction force in the electron momentum equation. A comprehensive dispersion relation, valid for arbitrary electron temperature, is derived, which describes properly all the relevant waves for wavelengths longer than the electron Larmor radius. For a homogeneous and dissipationless plasma, such a fluid dispersion relation agrees with the longwavelength limit of the kinetic electron-cyclotron-drift instability dispersion relation that extends the results to arbitrary short wavelengths. The general fluid dispersion relation covers different parametric regimes that depend on the relative ion-to-electron drift velocity and on the presence of equilibrium inhomogeneities and/or dissipation. Depending on such conditions, its roots yield as follows: two-stream instabilities, driven solely by the relative drift between species; drift-gradient instabilities, driven by the combination of the relative drift and equilibrium gradients; and drift-dissipative instabilities, driven by the combination of the relative drift and friction. Instability thresholds are determined and some distinctive unstable modes are described analytically.

Nonlinear and low-frequency solitary waves are investigated in the framework of the onedimensional Hall-magnetohydrodynamic model with finite Larmor effects and a double adiabatic model for plasma pressures. The organization of these localized structures in terms of the propagation angle with respect to the ambient magnetic field θ and the propagation velocity C is discussed. There are three types of regions in the θ −C plane that correspond to domains where either solitary waves cannot exist, are organized in branches, or have a continuous spectrum. A numerical method valid for the two latter cases, that rigorously proves the existence of the waves, is presented and used to locate many waves, including bright and dark structures. Some of them belong to parametric domains where solitary waves were not found in previous works. The stability of the structures has been investigated by first performing a linear analysis of the background plasma state and second by means of numerical simulations. They show that the cores of some waves can be robust but, for the parameters considered in the analysis, the tails are unstable. The substitution of the double adiabatic model by evolution equations for the plasma pressures appears to suppress the instability in some cases and to allow the propagation of the solitary waves during long times.Exact solitary waves solutions in the Hall-MHD model for cold [21] and warm plasmas with scalar [22] and double-adiabatic pressure models [12] have been also found.In the case of the Hall-MHD model with a double adiabatic pressure tensor, the traveling wave ansatz leads to a pair of coupled ordinary differential equations that governs the normalized components of the magnetic field normal to the propagation direction, named b y and b z . Such a system has a hamiltonian structure and is reversible, i.e. solutions are invariant under the transformation (ζ, b y , b z → −ζ, −b y , b z ), with ζ the independent variable. Adding FLR effects does not change the reversible character of the dynamical system but it increases the effective dimension from two to four [23]. Numerical evidence about the existence of solitary waves in the parametric domain where the upstream state is a saddle-center was also given [23]. The hamiltonian character of the dynamical system with FLR effects is an open and interesting topic, especially because an energy conservation theorem is not known for the Hall-MHD model with double adiabatic pressure and without FLR effects.This work investigates the existence and stability of solitary waves in the FLR-Hall-MHD model with double adiabatic pressure tensor. Section II follows Ref.[23] closely, and presents in a concise way the procedure to find the dynamical system that governs the solitary waves. The details of the method are given in Appendix A, where few discrepancies with the results of Ref.[23] are highlighted. Section II also discusses the main properties of the dynamical system and takes advantage of some geometrical arguments related with the dimension, reversible ...