A statistical analysis is conducted to identify which physically relevant non-dimensional parameters influence the total (neutral, ion, and electron) static pressure inside thermionic orificed hollow cathodes. It is critical to uncover and order the importance of the physical mechanisms that affect the pressure inside hollow cathodes because it influences the plasma attachment length, the electron temperature, and the sheath potential. These plasma parameters, in turn, affect the emitter lifetime. A principal component analysis of total pressure data obtained from the literature reveals that four non-dimensional variables can account for most of the variation in the total-to-magnetic pressure ratio over five orders of magnitude. The relevant variables are identified with a backward stepwise selection process and an exhaustive grid search and include, by order of importance: the gasdynamic-to-magnetic pressure ratio, the ratio of the mass flow rate to the discharge current, the orifice-to-insert diameter ratio, and the orifice Reynolds number. It is also shown, using various models and regression analyses, that empirical, Poiseuille, or isentropic flow models should not be used for predictive cathode design work. The data-driven study suggests that, while viscous effects may be important, the variation in those effects between cathodes is negligible compared to the effects of the modification of the gas constant due to the plasma, the transitional flow, the flux of heavy species on the orifice plate, and the Lorentz force.
REFERENCES
1.
A. T.
Forrester
, D. M.
Goebel
, and J. T.
Crow
, “IBIS: A hollow-cathode multipole boundary ion source
,” Appl. Phys. Lett.
33
, 11
–13
(1978
). 2.
S.
Tanaka
, H.
Morita
, and J.
Sakuraba
, “Use of a hollow cathode in a duopigatron hydrogen ion source
,” Jpn. J. Appl. Phys.
19
, 1703
(1980
). 3.
P. P.
Deichuli
, G. F.
Abdrashitov
, A. A.
Ivanov
, V. V.
Kolmogorov
, V. V.
Mishagin
, G. I.
Shul’zhenko
, N. V.
Stupishin
, D.
Beals
, and R.
Granetz
, “Ion source with LaB hollow cathode for a diagnostic neutral beam injector
,” Rev. Sci. Instrum.
77
, 03B514
(2006
). 4.
Y. S.
Kuo
, R. F.
Bunshah
, and D.
Okrent
, “Hot hollow cathode and its applications in vacuum coating: A concise review
,” J. Vac. Sci. Technol. A
4
, 397
–402
(1986
). 5.
A.
Lunk
, “Plasma activated physical vapour deposition (PAPVD) by hollow cathode arc (HCA)
,” Vacuum
41
, 1965
–1967
(1990
). 6.
H.
Morgner
, M.
Neumann
, S.
Straach
, and M.
Krug
, “The hollow cathode: A high-performance tool for plasma-activated deposition
,” Surf. Coat. Technol.
108–109
, 513
–519
(1998
). 7.
J. J.
Szabo
, B.
Pote
, R.
Tedrake
, S.
Paintal
, L.
Byrne
, V. J.
Hruby
, H.
Kamhawi
, and T.
Smith
, “High throughput 600 Watt Hall effect thruster for space exploration,” in 52nd AIAA/SAE/ASEE Joint Propulsion Conference & Exhibit (AIAA, 2016), AIAA Paper No. 2016-4830.8.
J. R.
Brophy
, “NASA’s deep space 1 ion engine
,” Rev. Sci. Instrum.
73
, 1071
–1078
(2002
). 9.
D. M.
Goebel
and E.
Chu
, “High current lanthanum hexaboride hollow cathodes for high power Hall thrusters,” in 32nd International Electric Propulsion Conference (Electric Rocket Propulsion Society, 2011), IEPC-2011-053.10.
R.
Hofer
, T.
Randolph
, D.
Oh
, J.
Snyder
, and K.
de Grys
, “Evaluation of a 4.5 kW commercial Hall thruster system for NASA science missions,” in 42nd AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit (AIAA, 2006), AIAA Paper No. 2006-4469.11.
D. L.
Brown
, B. E.
Beal
, and J. M.
Haas
, “Air Force Research Laboratory high power electric propulsion technology development,” in IEEE Aerospace Conference (IEEE, 2010).12.
P.-Y. C. R.
Taunay
, C. J.
Wordingham
, and E. Y.
Choueiri
, “Physics of thermionic orificed hollow cathodes. Part 1: Theory and experimental validation
,” Plasma Sources Sci. Technol.
(submitted) (2022
).13.
S. J.
Hall
, B. J.
Jorns
, A. D.
Gallimore
, H.
Kamhawi
, T. W.
Haag
, J. A.
Mackey
, J. H.
Gilland
, P. Y.
Peterson
, and M.
Baird
, “High-power performance of a 100-kw class nested Hall thruster,” in 35th International Electric Propulsion Conference (Electric Rocket Propulsion Society, 2017), IEPC-2017-228.14.
B.
Jorns
, A. D.
Gallimore
, S. J.
Hall
, P. Y.
Peterson
, J. E.
Gilland
, D. M.
Goebel
, R.
Hofer
, and I.
Mikellides
, “Update on the nested Hall thruster subsystem for the NextSTEP XR-100 program,” in AIAA Propulsion and Energy Forum (AIAA, 2018), AIAA Paper No. 2018-4418.15.
S. W.
Shark
, S. J.
Hall
, B.
Jorns
, R. R.
Hofer
, and D. M.
Goebel
, “High power demonstration of a 100 kW nested Hall thruster system,” in AIAA Propulsion and Energy Forum (AIAA, 2019), AIAA Paper No. 2019-3809.16.
C. J.
Wordingham
, P.-Y. C. R.
Taunay
, and E. Y.
Choueiri
, “The attachment length in orificed hollow cathodes
,” Plasma Sources Sci. Technol.
(in press) (2021
). 17.
D. E.
Siegfried
and P. J.
Wilbur
, “Studies on an experimental quartz tube hollow cathode,” in 14th International Electric Propulsion Conference (AIAA, 1979), AIAA Paper No. 1979-2056.18.
D. E.
Siegfried
, “A phenomenological model for orificed hollow cathodes,” Ph.D. thesis (Colorado State University, 1982).19.
D. E.
Siegfried
and P. J.
Wilbur
, “Phenomenological model describing orificed, hollow cathode operation
,” AIAA J.
21
, 5
–6
(1983
). 20.
D. E.
Siegfried
and P. J.
Wilbur
, “A model for mercury orificed hollow cathodes—Theory and experiment
,” AIAA J.
22
, 1405
–1412
(1984
). 21.
P. J.
Wilbur
, “Advanced ion thruster research,” Technical Report CR-168340, NASA, 1984.22.
D. E.
Siegfried
and P. J.
Wilbur
, “An investigation of mercury hollow cathode phenomena,” in 13th International Electric Propulsion Conference (AIAA, 1978), AIAA Paper No. 1978-0705.23.
A.
Salhi
and P. J.
Turchi
, “Theoretical modeling of orificed hollow cathode discharges,” in 23rd International Electric Propulsion Conference (Electric Rocket Propulsion Society, 1993), IEPC-1993-024.24.
A.
Salhi
, “Theoretical and experimental studies of orificed, hollow cathode operation,” Ph.D. thesis (The Ohio State University, 1993).25.
D.
Goebel
and I.
Katz
, Fundamentals of Electric Propulsion: Ion and Hall Thrusters
(John Wiley & Sons, Inc.
, 2008
).26.
J. P.
Mizrahi
, V.
Vekselman
, Y.
Krasik
, and V.
Gurovich
, “0-D plasma model for orificed hollow cathodes,” in 32nd International Electric Propulsion Conference (Electric Rocket Propulsion Society, 2011), IEPC-2011-334.27.
J.
Mizrahi
, V.
Vekselman
, V.
Gurovich
, and Y. E.
Krasik
, “Simulation of plasma parameters during hollow cathodes operation
,” J. Propul. Power
28
, 1134
–1137
(2012
). 28.
M. T.
Domonkos
, “Evaluation of low-current orificed hollow cathodes,” Ph.D. thesis (University of Michigan, 1999).29.
M. T.
Domonkos
, “A particle and energy balance model of the orificed hollow cathode,” in 38th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit (AIAA, 2002), AIAA Paper No. 2002-4240.30.
R.
Albertoni
, “Cathode processes in MPD thrusters,” Ph.D. thesis (Universita Degli Studi di Pisa, 2012).31.
R.
Albertoni
, D.
Pedrini
, F.
Paganucci
, and M.
Andrenucci
, “A reduced-order model for thermionic hollow cathodes
,” IEEE Trans. Plasma Sci.
41
, 1731
–1745
(2013
). 32.
V. J.
Friedly
, “Hollow cathode operation at high discharge currents,” M.Sc. thesis (Colorado State University, 1990).33.
S. W.
Patterson
and D. G.
Fearn
, “The generation of high energy ions in hollow cathode discharges,” in 26th International Electric Propulsion Conference (Electric Rocket Propulsion Society, 1999), pp. 695–702, IEPC-1999-125.34.
P. J.
Wilbur
, “Ion and advanced electric thruster research,” Technical Report CR-165253, NASA, 1980.35.
D. G.
Fearn
and S. W.
Patterson
, “Characterisation of the high current hollow cathode for the t6 thruster,” in 34th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit (AIAA, 1998), AIAA Paper No. 1998-3346.36.
D. M.
Goebel
, K. K.
Jameson
, and I.
Katz
, “Hollow cathode and keeper-region plasma measurements using ultra-fast miniature scanning probes,” in 40th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit (AIAA, 2004), AIAA Paper No. 2004-3430.37.
K. K.
Jameson
, D. M.
Goebel
, and R. M.
Watkins
, “Hollow cathode and keeper-region plasma measurements,” in 41st AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit (AIAA, 2005), AIAA Paper No. 2005-3667.38.
K. K.
Jameson
, D. M.
Goebel
, and R. M.
Watkins
, “Hollow cathode and thruster discharge chamber plasma measurements using high-speed scanning probes,” in 29th International Electric Propulsion Conference (Electric Rocket Propulsion Society, 2005), IEPC-2005-269.39.
I. G.
Mikellides
, “Effects of viscosity in a partially ionized channel flow with thermionic emission
,” Phys. Plasmas
16
, 013501
(2009
). 40.
J.
Polk
, A.
Grubisic
, N.
Taheri
, D. M.
Goebel
, and S. E.
Hornbeck
, “Emitter temperature distributions in the nstar discharge hollow cathode,” in 41st AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit (AIAA, 2005), AIAA Paper No. 2005-4398.41.
G.
Becatti
, D. M.
Goebel
, J. E.
Polk
, and P.
Guerrero
, “Life evaluation of a lanthanum hexaboride hollow cathode for high-power Hall thruster
,” J. Propul. Power
34
, 893
–900
(2017
). 42.
E.
Chu
and D. M.
Goebel
, “High-current lanthanum hexaboride hollow cathode for 10-to-50-kW Hall thrusters
,” IEEE Trans. Plasma Sci.
40
, 2133
–2144
(2012
). 43.
This expression can be derived from kinetic theory by assuming a hard-sphere potential for the gas. The mean free path and dynamic viscosity are then given by (see, e.g., Ref. 66, pp. 359, 430) and , respectively, where is the gas atomic mass, is the gas mass density, is the interatomic distance, is the Boltzmann constant, and is the gas temperature.
44.
L. I.
Stiel
and G.
Thodos
, “The viscosity of nonpolar gases at normal
,” AIChE J.
7
, 611
–615
(1961
). 45.
L. F.
Epstein
and M. D.
Powers
, “Liquid metals. I. The viscosity of mercury vapor and the potential function for mercury
,” J. Phys. Chem.
57
, 336
–341
(1953
). 46.
N. B.
Vargaftik
, Tables on the Thermophysical Properties of Liquids and Gases
, 2nd ed. (Hemisphere Publishing Corp.
, Washington, DC
, 1975
), p. 152
.47.
H. V.
Tippelskirch
, E. U.
Franck
, F.
Hensel
, and J.
Kestin
, “The viscosity of fluid mercury to 1520 k and 1000 bar
,” Ber. Bunsen. Phys. Chem.
79
, 889
–897
(1975
). 48.
A. I.
Ivanov
, V. E.
Lyusternik
, and L. R.
Fokin
, “Analysis and correlation of new data on the thermophysical properties of mercury vapor
,” J. Eng. Phys.
39
, 1360
–1365
(1980
). 49.
V. N.
Popov
, “Thermal properties of mercury on the basis of model potentials
,” High Temp.
50
, 700
–707
(2012
). 50.
P.-Y. C. R.
Taunay
, “Scaling laws in orificed thermionic hollow cathodes,” Ph.D. thesis (Princeton University, 2020).51.
52.
P.-Y. C. R.
Taunay
, C. J.
Wordingham
, and E. Y.
Choueiri
, “Open electric propulsion with an application to thermionic orificed hollow cathodes,” in AIAA Propulsion and Energy Forum (AIAA, 2020), AIAA Paper No. 2020-3638.53.
I. G.
Mikellides
, I.
Katz
, D. M.
Goebel
, and J. E.
Polk
, “Hollow cathode theory and experiment. II. A two-dimensional theoretical model of the emitter region
,” J. Appl. Phys.
98
, 113303
(2005
). 54.
L.
Cassady
, “Lithium-fed arc multichannel and single-channel hollow cathode: Experiment and theory,” Ph.D. thesis (Princeton University, 2006), p. 15.55.
G.
Sary
, L.
Garrigues
, and J.-P.
Boeuf
, “Hollow cathode modeling: I. A coupled plasma thermal two-dimensional model
,” Plasma Sources Sci. Technol.
26
, 55007
(2017
). 56.
E.
Buckingham
, “On physically similar systems; illustrations of the use of dimensional equations
,” Phys. Rev.
4
, 345
–376
(1914
). 57.
58.
D. M.
Goebel
, I.
Katz
, J. E.
Polk
, I. G.
Mikellides
, K. K.
Jameson
, T.
Liu
, and R.
Dougherty
, “Extending hollow cathode life for electric propulsion in long-term missions,” in Space Conference & Exhibit (AIAA, 2004), AIAA Paper No. 2004-5911.59.
P.-Y. C. R.
Taunay
, C. J.
Wordingham
, and E. Y.
Choueiri
, “Physics of thermionic orificed hollow cathodes. Part 2: Scaling laws and design rules
,” Plasma Sources Sci. Technol.
(submitted) (2022
).60.
M.
Capacci
, M.
Minucci
, and A.
Severi
, “Simple numerical model describing discharge parameters in orificed hollow cathode devices,” in 33rd AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit (AIAA, 1997), AIAA Paper No. 1997-2791.61.
M.
Newville
, T.
Stensitzki
, D. B.
Allen
, and A.
Ingargiola
, “LMFIT: Non-linear least-square minimization and curve-fitting for Python” (2014).62.
F.
Pedregosa
, G.
Varoquaux
, A.
Gramfort
, V.
Michel
, B.
Thirion
, O.
Grisel
, M.
Blondel
, P.
Prettenhofer
, R.
Weiss
, V.
Dubourg
, J.
Vanderplas
, A.
Passos
, D.
Cournapeau
, M.
Brucher
, M.
Perrot
, and E.
Duchesnay
, “Scikit-learn: Machine learning in Python
,” J. Mach. Learn. Res.
12
, 2825
–2830
(2011
); available at: https://scikit-learn.org/63.
H.
Akaike
, “A new look at the statistical model identification
,” IEEE Trans. Automat. Contr.
19
, 716
–723
(1974
). 64.
C. H.
Chang
and E.
Pfender
, “Nonequilibrium modeling of low-pressure argon plasma jets; Part I: Laminar flow
,” Plasma Chem. Plasma Process.
10
, 473
–491
(1990
). 65.
D. J.
Santeler
, “Exit loss in viscous tube flow
,” J. Vac. Sci. Technol. A
4
, 348
–352
(1986
). 66.
67.
P.-Y. C. R. Taunay eppdyl/cathode–database: An open database of thermionic orificed hollow cathode-data (Version 1.0.2) [
Computer Software
]. Zenodo, (2021). 68.
P.-Y. C. R. Taunay pytaunay/total-pressure-cathodes-controlling-mechanisms (Version 1.1.0) [
Computer Software
]. Zenodo, (2021). © 2022 Author(s). Published under an exclusive license by AIP Publishing.
2022
Author(s)
You do not currently have access to this content.