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旋转辐条作为一种低频、长波长不稳定性,广泛存在于磁控管、霍尔推力器等E×B放电装置中。霍尔推力器中旋转辐条表现为位于放电通道中的明亮发光区域沿着角向旋转。旋转辐条不稳定性引起的空间电势扭曲,提高了在E×B作用下沿电势等势线漂移运动的电子到达阳极的概率,增加了电子的轴向输运。本文利用轴向-角向的二维粒子-流体混合模型研究了霍尔推力器放电通道中的轴向磁场梯度对旋转辐条不稳定性的影响。采用包含等离子体密度梯度和磁场梯度效应的色散关系,结合模拟得到的离子密度分布、电势分布、电场分布对模拟结果进行了分析。模拟结果表明,随着放电通道内磁场梯度的减小,模数m=1的旋转辐条不稳定性的频率和传播速度会轻微的增加,但不会对旋转辐条的传播方向和本质特征产生影响。结合色散关系的分析结果表明,密度梯度和磁场梯度共同驱动的角向漂移不稳定性是旋转辐条的诱发因素。磁场改变引起的离子密度分布的变化对诱发旋转辐条的角向漂移不稳定性出现的轴向位置有轻微的影响,但始终位于推力器出口下游附近。本文的研究结果表明旋转辐条不稳定性不属于电离不稳定性,且改变放电通道内的磁场分布不会对旋转辐条的传播方向和模数产生影响。本文的研究结果对明确旋转辐条的激发机制及其影响因素提供了理论支撑。As one of the low-frequency, long-wavelength instabilities, rotating spokes are commonly observed in the E×B plasma discharge devices, such as the magnetrons and Hall thrusters. In Hall thrusters, the characteristic of rotating spokes are the bright luminous regions located in the discharge channel and rotating in the azimuthal direction. The space potential will be distorted by the rotating spokes, and the axially electrons transport increase as the possibility of electrons to reach the anode which drift alone the equipotential lines is enhanced. However, the excitation mechanism of the rotating spoke and its influencing factors remain ambiguous. To address this, numerical simulations and linear stability analysis are employed in this study to investigate the effect of the magnetic field gradient on the driving mechanisms and mode characteristics of the rotating spoke instability. In this paper, aparticle-fluid two-dimensional hybrid model in the axial-azimuthal plane is employed to numerical study the effect of axial magnetic field gradient in the discharge channel on the rotating spoke. The numerical simulation results are analyzed using a dispersion relation derived from fluid theory, which incorporates the effects of plasma density and magnetic field gradient. The output profiles of ions density, potential, and electric field from the numerical simulation serve as input parameters for the dispersion relation used in the linear stability analysis. The simulation results show that the frequency and propagation velocity of the m = 1 rotating spoke slightly increasing as the magnetic field gradient in the discharge channel decreases. However, varying the magnetic field gradient in the discharge channel does not affect the propagation direction and intrinsic characteristics of the rotating spoke. More specifically, when the value of α1 increases from 1.1 to 1.7 (indicating a decrease the magnetic field gradient in the discharge channel), the mode frequency rises from 6.2kHz to 7.5kHz, remaining within the frequency range of the rotating spoke instability. At the same time, the phase velocity also increases form 1013m/s to 1225m/s, which is consistent with the propagation velocity of the rotating spoke instability, and is still propagation along the E×B direction. Dispersion relation analysis indicates that the rotating spoke arises from an azimuthal drift instability which located near downstream region of the thruster exit, and it is excited by the plasma density and magnetic field gradient effects. The axial position of the azimuthal drift instability, responsible for the rotating spoke formation, is slightly modulated by density profile variations caused by the magnetic field alterations in the discharge channel. However, it remains near the downstream region of the thruster exit. The results indicate that the rotating spoke does not originate from ionization instabilities, and altering the magnetic field distribution in the discharge channel does not affect its propagation direction and mode number. The results provide theoretical support for clarifying the excitation mechanism of the rotating spoke and key influencing factors.
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Keywords:
- Hall thruster /
- rotating spokes /
- density gradient /
- magnetic gradient /
- dispersion relation
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