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 1–5MHz 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.

使用流体模型和线性全局稳定性方法研究了霍尔推进器等离子体放电的轴向-方位角不稳定性，适用于平衡解的大轴向不均匀性。在平衡解和扰动解中都考虑了电子压力和电子惯性。进行时间和方位角的傅里叶变换，并通过数值获得色散关系，用于控制模式轴向行为的合成 Sturm-Liouville 问题。该分析侧重于中高频和大波数，确定了两种主要的不稳定性类型。主要模式在 1-5MHz 和方位模式数 ~10-50 的近羽流中发展，具有弱离子响应并且似乎由磁场的负梯度触发。次主导模式在阳极附近以 100-300 kHz 的频率和方位模式数~1-10 发展，并且似乎是旋转辐条型。通过研究它们的倾斜传播、设计和操作参数的影响以及阳极-阴极电连接、电子惯性和温度扰动的影响，这两种不稳定性都得到了很好的表征。这些不稳定性对电子交叉场传输的可能影响是通过准线性方法估计的，这会产生空间波纹湍流力。