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在霍尔推力器中，电子漂移、电子碰撞，以及等离子体密度、温度、磁场梯度所蕴含的自由能会驱动各种频率和波长的不稳定性。不稳定性的存在会破坏等离子体的稳定放电，削弱推力器与电源处理单元的匹配度，降低推力器的性能。基于此，本文利用基于流体模型推导的色散关系研究了霍尔推力器中由电子碰撞、等离子体密度和磁场梯度驱动的不稳定性。结果表明：1）在考虑电子惯性、电子与中性原子的碰撞、以及电子E×B漂移时能够在推力器近阳极区到羽流区内的任一轴向位置处激发不稳定性。随着角向波数ky的增加（k=2π/λ ，λ为波长），模式将从由碰撞激发的低杂波不稳定性转变为离子声波不稳定性。当ky=10m-1时，最大增长率γmax 对应频率 ωr随着碰撞频率νen 的增加而轻微减小；当ky=300m-1时，γmax对应的频率ωr以及最大频率ωrmax几乎不随碰撞频率变化。不依赖于ky的大小，对于碰撞激发的不稳定性，模式的增长率随着碰撞频率的增加而增加。同时考虑电子惯性、电子碰撞效应，以及密度梯度时，密度梯度对驱动不稳定性占主导作用。模式的动力学行为不会随ky的增加而变化，但模式的本征值随ky的增加而增加。在密度梯度κN=0的两侧，由于密度梯度引起的抗磁性漂移频率ωs的符号发生了变化，模式的本征值在κN=0两侧有相反的变化趋势：当ω*与ωr符号相反时，密度梯度对不稳定性的激发有削弱作用(κN＞0)；当ω*与ωr符号相同时，密度梯度对不稳定性的激发有增强作用(κN＜0)；3）在模型中同时考虑等离子体密度梯度、磁场梯度，以及电子惯性和碰撞效应时，模式本征值的变化依赖于电子的漂移频率，以及密度和磁场梯度引起的抗磁性漂移频率的相对大小。当仅包含密度梯度和磁场梯度时，推力器放电通道内将出现稳定窗，即增长率为0的区间；包含电子惯性和碰撞效应后，稳定窗消失。The free energy contained in electron drift, electron collision, and gradient of plasma density, temperature, magnetic can trigger the different frequency and wavelength instabilities in hall thrusters. The instabilities will destroy the stable discharge of plasma, affect the matching degree between the thruster and the power processing unit, and down the performance of the thruster. Based on this, the instabilities triggered by electron collision and gradient of plasma density and magnetic field in the hall thruster is studied by using dispersion relation derived from the fluid model. The results show that: 1) The instabilities can be excited at any axial position from the near anode region of the thruster to the plume region when the effect of electron inertia、electron collision with neutral atoms and electron drift are included in the model. The transition of the lower-hybrid mode excited by electron collision into the ion sound mode take place with the azimuthal wavenumber ky is increasing. Where k=2π/λ ，λ is the wave length. The real frequency ωr corresponding to the maximum growth rate γmax slightly decreases with collision frequency increasing for ky=10m-1. However, the maximum real frequency and real frequency ωr corresponding to the maximum growth rate γmax will not change with collision frequency varying for ky=300m-1. Independent on the size of ky, the growth rate of mode triggered by electron collision increases with collision frequency increasing. 2) The plasma density gradient effect plays the dominant role in driving instabilities when the electron inertia, electron-neutral collisions and plasma density gradient are simultaneously included in the model. The dynamic behavior of the model does not change with the increasing of ky, but the eigenvalue of the model increases with the ky increasing. Since the sign of anti-drift frequency induced by the plasma density gradient is changed, and the mode eigenvalue have the opposite change trend on both sides of point κN=0. When the sign of ωs and ωr are opposite, the density gradient effect has a stabilization effect on instability excitation (κN＞0). When the sign of ωs and ωr are same, the density gradient effect enhances the excitation of instability (κN＜0) .3) If the gradient of the plasma density and magnetic field, electron inertia and electron-neutral collisions are included in the dispersion, the mode eigenvalue relies on the size of electron drift frequency, and the diamagnetic drift frequency induced by the gradient of density and magnetic field. When the density gradient and magnetic gradient effect are considered, there is a stable window in the discharge channel. However，if the electron inertia and electron-neutral collisions are also included, the stable window will disappear.
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Keywords:
- Hall thruster /
- density gradient /
- magnetic gradient /
- electron collision /
- instability
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