Abstract
Hall plasma devices with electron E × B drift are subject to a class of long wavelength instabilities driven by the electron current, gradients of plasma density, temperature, and magnetic field. In the first companion paper [Frias et al., Phys. Plasmas 19, 072112 (2012)], the theory of these modes was revisited. In this paper, we apply analytical theory to show that modern Hall thrusters exhibit azimuthal and axial oscillations in the frequency spectrum from tens KHz to few MHz, often observed in experiments. The azimuthal phase velocity of these modes is typically one order of magnitude lower than the E × B drift velocity. The growth rate of these modes scales inversely with the square root of the ion mass, . It is shown that several different thruster configurations share the same common feature: the gradient drift instabilities are localized in two separate regions, near the anode and in the plume region, and absent in the acceleration region. Our analytical results show complex interaction of plasma and magnetic field gradients and the E × B drift flow as the sources of the instability. The special role of plasma density gradient is revealed and it is shown that the previous theory is not applicable in the region where the ion flux density is not uniform. This is particularly important for near anode region due to ionization and in the plume region due to diverging ion flux.
The authors thank Dr. Nathaniel J. Fisch for helpful discussions, Dr. Richard Hofer for allowing the use of the data from the HPHall2 simulations and Dr. Igal Kronhaus and Dr. Alexander Kapulkin for providing the data for the CAMILA Hall thruster. This work was sponsored by the Natural Sciences and Engineering Research Council of Canada and partially supported by the Air Force Office of Scientific Research and the US Department of Energy.
I. INTRODUCTION
II. GRADIENT DRIFT INSTABILITIES
III. STABILITY ANALYSIS
A. PPPL HTX
B. Nearanode region HTX thruster
C. SPT100 thruster simulations
D. CAMILA thruster simulations
IV. SUMMARY
Key Topics
 Magnetic fields
 65.0
 Anodes
 32.0
 Plasma instabilities
 24.0
 Electric fields
 22.0
 Plasma density
 19.0
Figures
Experimental profiles of the plasma density, magnetic field, electron equilibrium drift velocity, u 0, and electron temperature for the HTX thruster. 13 The exit plane is at x = 0.
Experimental profiles of the plasma density, magnetic field, electron equilibrium drift velocity, u 0, and electron temperature for the HTX thruster. 13 The exit plane is at x = 0.
Characteristic gradient lengths for the plume region of the HTX thruster. 13 The exit plane is at x = 0.
Characteristic gradient lengths for the plume region of the HTX thruster. 13 The exit plane is at x = 0.
Growth rate and frequency of the instabilities in the HTX thruster 13 as a function of axial distance as predicted by the twofield model ((a) and (b)) and the threefield model ((c) and (d)). The exit plane is at x = 0.
Growth rate and frequency of the instabilities in the HTX thruster 13 as a function of axial distance as predicted by the twofield model ((a) and (b)) and the threefield model ((c) and (d)). The exit plane is at x = 0.
Floating plasma potential for the HTX thruster. 13 The well of the plasma potential coincides with the regions where the gradient drift instabilities are strongest. The exit plane is at x = 0.
Floating plasma potential for the HTX thruster. 13 The well of the plasma potential coincides with the regions where the gradient drift instabilities are strongest. The exit plane is at x = 0.
Magnetic field lines in the 12.3 cm Hall thruster for three magnetic field configurations: B 0, Bpos , and Bneg . All diagrams are drawn to scale. Reprinted with permission from Phys. Plasmas 13, 057104 (2006). Copyright 2006 American Institute of Physics. 14
Magnetic field lines in the 12.3 cm Hall thruster for three magnetic field configurations: B 0, Bpos , and Bneg . All diagrams are drawn to scale. Reprinted with permission from Phys. Plasmas 13, 057104 (2006). Copyright 2006 American Institute of Physics. 14
Three different profiles for magnetic field configuration and electron density and temperature measured at the midpoint between the channel walls as reported in Ref. 14 .
Three different profiles for magnetic field configuration and electron density and temperature measured at the midpoint between the channel walls as reported in Ref. 14 .
Growth rate and frequency of the instabilities as a function of axial distance as predicted by the twofield model for the profiles in Fig. 6 .
Growth rate and frequency of the instabilities as a function of axial distance as predicted by the twofield model for the profiles in Fig. 6 .
Plasma density, magnetic field, electron equilibrium drift velocity, u 0, and electron temperature profiles in SPT100 Hall thruster obtained from HPHall2 simulations as shown in Fig. 10 from Ref. 15 . The exit plane is at x = 2.5 cm.
Plasma density, magnetic field, electron equilibrium drift velocity, u 0, and electron temperature profiles in SPT100 Hall thruster obtained from HPHall2 simulations as shown in Fig. 10 from Ref. 15 . The exit plane is at x = 2.5 cm.
Gradient lengths for the channel region of SPT100 Hall thruster. The exit plane is at x = 2.5 cm.
Gradient lengths for the channel region of SPT100 Hall thruster. The exit plane is at x = 2.5 cm.
Growth rate and frequency of the instabilities in a SPT100 thruster 15 as a function of axial distance to the anode as predicted by the twofield model ((a) and (b)) and the threefield model ((c) and (d)). The exit plane is at x = 2.5 cm.
Growth rate and frequency of the instabilities in a SPT100 thruster 15 as a function of axial distance to the anode as predicted by the twofield model ((a) and (b)) and the threefield model ((c) and (d)). The exit plane is at x = 2.5 cm.
Plasma density, magnetic field, electron equilibrium drift velocity, u 0, and electron temperature profiles in CAMILA Hall thruster from Ref. 16 . The exit plane is at x = 0.
Plasma density, magnetic field, electron equilibrium drift velocity, u 0, and electron temperature profiles in CAMILA Hall thruster from Ref. 16 . The exit plane is at x = 0.
Gradient lengths for the channel region of CAMILA Hall thruster. The exit plane is at x = 0.
Gradient lengths for the channel region of CAMILA Hall thruster. The exit plane is at x = 0.
Growth rate and frequency of the instabilities in the CAMILA thruster 16 as a function of axial distance to the anode as predicted by the twofield model ((a) and (b)) and the threefield model ((c) and (d)). The exit plane is at x = 0.
Growth rate and frequency of the instabilities in the CAMILA thruster 16 as a function of axial distance to the anode as predicted by the twofield model ((a) and (b)) and the threefield model ((c) and (d)). The exit plane is at x = 0.
Growth rate of the instabilities for the (a) HTX thruster, (b) SPT100, and (c) CAMILA, as predicted by the twofield model, Eq. (19) from Ref. 8 and antidrift instability. 6,12
Growth rate of the instability as predicted by the two field model and by Eq. (16) for (a) HTX thruster, (b) SPT100, and (c) CAMILA.
Growth rate of the instability as predicted by the two field model and by Eq. (16) for (a) HTX thruster, (b) SPT100, and (c) CAMILA.
Product for the (a) HTX thruster, (b) SPT100, and (c) CAMILA.
Product for the (a) HTX thruster, (b) SPT100, and (c) CAMILA.
Tables
Conditions for instability in different regions of Hall thrusters. Condition I: . Condition II: .
Conditions for instability in different regions of Hall thrusters. Condition I: . Condition II: .
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