Stability of a magnetized Hall plasma discharge

Abstract

Using recent experimental data on the time-averaged, spatially varying plasma properties within a Hall discharge plasma, we present in this article, a theoretical study of the response of this plasma to small (linear) perturbations in its properties. As a starting point for this analysis, we assume a two-dimensional fluid description that includes a simplified equation for the electron energy, and constrain the azimuthal wave vector such that we excite only the dominant (m=1) azimuthal modes. The growth rate and frequencies of predominantly axial and azimuthally propagating plasma disturbances are obtained by numerical solution of the resulting eigenvalue problem under a quasiuniform plasma condition, along the entire discharge channel. The results identify the persistence of a low frequency instability that is associated with the ionization process, concentrated largely in the vicinity of the exit plane, where the magnetic field is at its maximum value, consistent with experimental observations for the relatively low operating voltages (∼100 V) considered in this study.

Conditions and growth rate of Rayleigh instability in a Hall thruster under the effect of ion temperature

“…Figure 1 shows the variation of growth rate γ [≡ (ω 3 /ω pi )] of the instability with magnetic field when T e = 10 eV, T i = 1 eV, Y e = 2, Y i = 2, n 0 = 10 18 /m 3 , u 0 = 10 6 m/s, k y = 25/m, and d = 5.5 cm. These parameters are within the prescribed range as used in the literature [12,[20][21][22] and realized in the experiment [22]. It is seen from the figure that the instability grows faster in the presence of stronger magnetic field.…”

“…Also, a 1 and a 2 are the coefficients of ω 2 and ω terms in Eq. (20) and a 3 is the constant term, that is,…”

Measurement of Cross-Field ElectronCurrent in a Hall Thruster Due to Rotating Spoke Instabilities

“…27 Chesta's efforts are noteworthy as the first since the work of Lomas to attempt a model of the Hall thruster discharge channel in a 2-D axial-azimuthal (z-θ) formulation, using numerical techniques to solve the complicated dispersion relations and carry out stability analyses on the resulting modes. 28 Like the earlier work of Janes and Lomas, Chesta ultimately attributed the spoke formation to electrothermal processes such as ionization, though the detailed mechanisms of this formation were left and still remain unclear. Later work at Stanford by Meezan would experimentally characterize an anomalously high electron mobility near the thruster acceleration region and, by association with large plasma fluctuations also measured in that region, make a correlative argument that the plasma fluctuations were linked to the transport.…”

Global Stability Analysis of Azimuthal Oscillations in Hall Thrusters

“…The latter are based on the analysis of the fluid equations at a fixed axial location of the channel and this requires freezing the macroscopic plasma variables and their derivatives, whereas the former method does account consistently for the axial variation of those variables and their linear perturbations. Most of the stability analyses of the Hall discharge in the azimuthal direction carried out so far are local and can be grouped in those that do not account for the ionization process [8], [27]- [31] and those that take it into consideration in the model through particle source terms and fluid equations for the neutral species [17], [32]- [35]. However, all these local stability studies suffer from the problems mentioned above.…”