Results based on a local linear stability analysis of the Hall thruster discharge are presented. A one-dimensional azimuthal framework is used including three species: neutrals, singly charged ions, and electrons. A simplified linear model is developed with the aim of deriving analytical expressions to characterize the stability of the ionization region. The results from the local analysis presented here indicate the existence of an instability that gives rise to an azimuthal oscillation in the +E × B direction with a long wavelength. According to the model, the instability seems to appear only in regions where the ionization and the electric field make it possible to have positive gradients of plasma density and ion velocity at the same time. A more complex model is also solved numerically to validate the analytical results. Additionally, parametric variations are carried out with respect to the main parameters of the model to identify the trends of the instability. As the temperature increases and the neutral-to-plasma density ratio decreases, the growth rate of the instability decreases down to a limit where azimuthal perturbations are no longer unstable.
REFERENCES
1.
G.
Cann
and G.
Marlotte
, AIAA J.
2
, 1234
(1964
).2.
3.
A.
Morozov
, A.
Kislov
, and I.
Zubkov
, ZhETF Pis ma Redaktsiiu
7
, 224
(1968
) [7, 172 (1968)]; available at http://www.jetpletters.ac.ru/ps/1683/article_25624.pdf.4.
M.
Martinez-Sanchez
and J.
Pollard
, J. Propul. Power
14
, 688
(1998
).5.
A.
Morozov
, Y.
Esipchuk
, G.
Tilinin
, A.
Trofimov
, and Y.
Sharov
, Sov. Phys.: Tech. Phys.
17
, 38
(1972
).6.
N.
Meezan
and M.
Cappelli
, “Electron density measurements for determining the anomalous electron mobility in a coaxial Hall discharge plasma
,” in Proceedings of the 36th Joint Propulsion Conference
(American Institute of Aeronautics and Astronautics, 2000), A1AA-2000–3420.7.
N.
Meezan
, W.
Hargus
, Jr., and M.
Cappelli
, Phys. Rev. E
63
, 26410
(2001
).8.
M.
Cappelli
, N.
Meezan
, and N.
Gascon
, “Transport physics in Hall plasma thrusters
,” in Proceedings of the 40th AIAA Aerospace and Sciences Meeting and Exhibit
(American Institute of Aeronautics and Astronautics, 2002
), AIAA-2002–0485.9.
J. A.
Linnell
and A. D.
Gallimore
, “Hall thruster electron motion characterization based on internal probe measurements
,” in Proceedings of the 31st International Electric Propulsion Conference
(Electric Rocket Propulsion Society, 2009
), IEPC-2009–105.10.
C.
Boniface
, L.
Garrigues
, G.
Hagelaar
, J.
Boeuf
, D.
Gawron
, and S.
Mazouffre
, Appl. Phys. Lett.
89
, 161503
(2006
).11.
D.
Gawron
, S.
Mazouffre
, and C.
Boniface
, Plasma Sources Sci. Technol.
15
, 757
(2006
).12.
A.
Morozov
, Y.
Esipchuk
, A.
Kapulkin
, V.
Nevrovskii
, and V.
Smirnov
, Sov. Phys.: Tech. Phys.
17
, 482
(1972
).13.
S.
Yoshikawa
and D.
Rose
, Phys. Fluids
5
, 334
(1962
).14.
G.
Janes
and R.
Lowder
, Phys. Fluids
9
, 1115
(1966
).15.
16.
E.
Ahedo
, J.
Gallardo
, and M.
Martinez-Sanchez
, Phys. Plasmas
10
, 3397
(2003
).17.
L.
Garrigues
, G.
Hagelaar
, C.
Boniface
, and J.
Boeuf
, J. Appl. Phys.
100
, 123301
(2006
).18.
F.
Parra
, E.
Ahedo
, J.
Fife
, and M.
Martinez-Sanchez
, J. Appl. Phys.
100
, 023304
(2006
).19.
P.
Lomas
and J.
Kilkenny
, Plasma Phys.
19
, 329
(1977
).20.
E.
Chesta
, C.
Lam
, N.
Meezan
, D.
Schmidt
, and M.
Cappelli
, IEEE Trans. Plasma Sci.
29
, 582
(2001
).21.
J.
Parker
, Y.
Raitses
, and N.
Fisch
, Appl. Phys. Lett.
97
, 091501
(2010
).22.
Y.
Esipchuk
, A.
Morozov
, G.
Tilinin
, and A.
Trofimov
, Sov. Phys.: Tech. Phys.
18
, 928
(1974
).23.
W. A.
Hargus
, N. B.
Meezan
, and M. A.
Cappelli
, “A study of a low power hall thruster transient behavior
,” in Proceedings of the 25th International Electric Propulsion Conference
(Electric Rocket Propulsion Society, 1997
), IEPC-1997-058.24.
A.
Dinklage
, T.
Klinger
, G.
Marx
, and L.
Schweikhard
, Plasma Physics: Confinement, Transport and Collective Effects
(Springer-Verlag
, Berlin
, 2005
).25.
N.
Gascon
, N.
Meezan
, and M.
Cappelli
, “Low frequency plasma wave dispersion and propagation in Hall thrusters
,” in Proceedings of the 27th International Electric Propulsion Conference
(Electric Rocket Propulsion Society, 2001
), IEPC-2001-056.26.
N.
Gascon
and M.
Cappelli
, “Wall effects on the excitation and propagation of instabilities in Hall thrusters
,” in Proceedings of the 28th International Electric Propulsion Conference
(Electric Rocket Propulsion Society, 2003
), IEPC-2003-328.27.
N.
Gascon
and M.
Cappelli
, “Plasma instabilities in the ionization regime of a Hall thruster
,” in Proceedings of the 39th Joint Propulsion Conference
(American Institute of Aeronautics and Astronautics, 2003), AIAA-2003-4857.28.
A.
Smith
and M.
Cappelli
, “Time and space-correlated plasma property measurements in the near-field of a coaxial hall discharge
,” in Proceedings of the 31st International Electric Propulsion Conference
(Electric Rocket Propulsion Society, 2009
), IEPC-2009-135.29.
Y.
Raitses
, A.
Smirnov
, and N.
Fisch
, Phys. Plasmas
16
, 057106
(2009
).30.
C. L.
Ellison
, Y.
Raitses
, and N. J.
Fisch
, “Direct measurement of spoke-induced, cross-field electron current in a cylindrical Hall thruster
,” in Proceedings of the 32nd International Electric Propulsion Conference
(Electric Rocket Propulsion Society, 2011
), IEPC-2011-173.31.
C.
Ellison
, Y.
Raitses
, and N.
Fisch
, IEEE Trans. Plasma Sci.
39
, 2950
(2011
).32.
C.
Ellison
, Y.
Raitses
, and N.
Fisch
, Phys. Plasmas
19
, 013503
(2012
).33.
Y.
Raitses
, M.
Griswold
, L.
Ellison
, J.
Parker
, and N.
Fisch
, in Proceedings of the 48th Joint Propulsion Conference
(American Institute of Aeronautics and Astronautics, 2012
), AIAA-2012-4179.34.
M.
Griswold
, C.
Ellison
, Y.
Raitses
, and N.
Fisch
, Phys. Plasmas
19
, 053506
(2012
).35.
Y.
Shi
, Y.
Raitses
, and A.
Diallo
, “Driving azimuthal modes in magnetized discharge with segmented anode
,” in Proceedings of the 4th Annual Meeting
, DOE Center for Predictive Control of Plasma Kinetics, 2013
.36.
M.
McDonald
, C.
Bellant
, B.
Pierre
, and A.
Gallimore
, “Measurement of cross-field electron current in a Hall thruster due to rotating spoke instabilities
,” in Proceedings of the 47th Joint Propulsion Conference
(American Institute of Aeronautics and Astronautics, 2011
), AIAA-2011-5810.37.
M. S.
McDonald
and A. D.
Gallimore
, “Parametric investigation of the rotating spoke instability in Hall thrusters
,” in Proceedings of the 32nd International Electric Propulsion Conference
(Electric Rocket Propulsion Society, 2011
), IEPC-2011-242.38.
M. S.
McDonald
and A. D.
Gallimore
, IEEE Trans. Plasma Sci.
39
, 2952
(2011
).39.
M.
Sekerak
, M.
McDonald
, R.
Hofer
, and A.
Gallimore
, “Hall thruster plume measurements from high-speed dual langmuir probes with ion saturation reference
,” in 2013 IEEE Aerospace Conference
(IEEE
, 2013
), pp. 1
–16
.40.
D.
Liu
, “Two-dimensional time-dependent plasma structures of a Hall-effect thruster
,” Ph.D. dissertation (Standford University
, 2011
).41.
D.
Liu
, R.
Huffman
, R.
Branam
, and W.
Hargus
, IEEE Trans. Plasma Sci.
39
, 2926
(2011
).42.
C. M.
Lam
, A. K.
Knoll
, M. A.
Cappelli
, and E.
Fernandez
, “Two-dimensional (z-θ) simulations of Hall thruster anomalous transport
,” in Proceedings of the 31st International Electric Propulsion Conference
(Electric Rocket Propulsion Society, 2009
), IEPC-2009-102.43.
J.
Fife
, “Hybrid-PIC modelling and electrostatic probe survey of Hall thrusters
,” Ph.D. dissertation (Massachusetts Institute of Technology
, 1998
).44.
A.
Litvak
and N.
Fisch
, Phys. Plasmas
11
, 1379
(2004
).45.
A.
Kapulkin
and V.
Prisnyakov
, “Dissipative method of suppression of electron drift instability in SPT
,” in Proceedings of the 24th International Electric Propulsion Conference
(Electric Rocket Propulsion Society, 1995
), IEPC-1995-037.46.
A.
Kapulkin
, J.
Ashkenazy
, A.
Kogan
, G.
Appelbaum
, D.
Alkalay
, and M.
Guelman
, “Electron instabilities in Hall thrusters: modelling and application to electric field diagnostics
,” in Proceedings of the 28th International Electric Propulsion Conference
(Electric Rocket Propulsion Society, 2003
), IEPC-2003-100.47.
A.
Kapulkin
and M.
Guelman
, “Lower-hybrid instability in Hall thruster
,” in Proceedings of the 29th International Electric Propulsion Conference
(Electric Rocket Propulsion Society, 2005
), IEPC-2005-088.48.
H. K.
Malik
and S.
Singh
, Phys. Rev. E
83
, 036406
(2011
).49.
A.
Nelson
and M.
Haines
, Plasma Phys.
11
, 811
(1969
).50.
A.
Simon
, Phys. Fluids
6
, 382
(1963
).51.
52.
A.
Kapulkin
and M.
Guelman
, “Low frequency instability and enhanced transfer of electrons in near-anode region of Hall thruster
,” in Proceedings of the 30th International Electric Propulsion Conference
(Electric Rocket Propulsion Society, 2007
), IEPC-2007-079.53.
A.
Kapulkin
and M. M.
Guelman
, IEEE Trans. Plasma Sci.
36
, 2082
(2008
).54.
W.
Frias
, A. I.
Smolyakov
, I. D.
Kaganovich
, and Y.
Raitses
, Phys. Plasmas
19
, 072112
(2012
).55.
A.
Smolyakov
, W.
Frias
, Y.
Raitses
, and N. J.
Fisch
, “Gradient instabilities in Hall thruster plasmas
,” in Proceedings of the 32nd International Electric Propulsion Conference
(Electric Rocket Propulsion Society, 2011
), IEPC-2011-271.56.
W.
Frias
, A. I.
Smolyakov
, I. D.
Kaganovich
, and Y.
Raitses
, Phys. Plasmas
20
, 052108
(2013
).57.
E.
Chesta
, N.
Meezan
, and M.
Cappelli
, J. Appl. Phys.
89
, 3099
(2001
).58.
J.
Gallardo
and E.
Ahedo
, “On the anomalous diffusion mechanism in Hall-effect thrusters
,” in Proceedings of 29th International Electric Propulsion Conference
(Electric Rocket Propulsion Society, 2005
), IEPC-2005-117.59.
H. K.
Malik
and S.
Singh
, Phys. Plasmas
20
, 052115
(2013
).60.
S.
Barral
, K.
Makowski
, Z.
Peradzyński
, and M.
Dudeck
, Phys. Plasmas
12
, 073504
(2005
).61.
E.
Choueiri
, Phys. Plasmas
8
, 1411
(2001
).62.
63.
D.
Escobar
and E.
Ahedo
, “Global stability analysis of azimuthal oscillations in Hall thrusters
,” in Proceedings of the 33rd International Electric Propulsion Conference
(Electric Rocket Propulsion Society, 2013
), IEPC-2013-304.© 2014 AIP Publishing LLC.
2014
AIP Publishing LLC
You do not currently have access to this content.
