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The technical data in this document (or file) is controlled for export under the International Traffic in Arms Regulations (ITAR),
22 CFR 120-130. Violations of these laws may be subject to fines and penalties under the Arms Export Control Act, 22 U.S.C. 2778.
May contain Georgia Tech proprietary information; Not for public dissemination.
EFFECT OF ION-NEUTRAL COLLISIONS ON SHEATH
POTENTIAL PROFILE
Samuel J. Langendorf, Mitchell L.R. WalkerHigh-Power Electric Propulsion Laboratory, Georgia Institute of Technology, Atlanta, GA 30332 USA
Laura P. Rose, Michael KeidarMicropropulsion and Nanotechnology Laboratory, George Washington University, Washington, D.C. 20052 USA
Lubos Brieda Particle in Cell Consulting LLC, Falls Church, VA 22046
33rd International Electric Propulsion Conference,
The George Washington University, Washington, D.C., USA
October 6 – 10, 2013
2
MOTIVATION
Hall-effect thruster [PPS-100ML] Wall power deposition Performance Wall material erosion LifetimeDudeck, M., et al. "Plasma Propulsion for Geostationary Satellites and Interplanetary Spacecraft." Romanian Journal of Physics 56 (2011): 3-14.
Gridded Ion Engine [NSTAR] Wall (grid) ion optics PerformanceWall (grid) erosion LifetimeGRC – Deep Space 1 Mission <http://www.grc.nasa.gov/WWW/ion/past/90s/ds1.htm> retrieved 2013-09-30.
• The plasma-wall interface is critical in electric propulsion devices.
3
BACKGROUND
• Plasma Sheath:– Non-neutral region that forms near walls interacting with plasma to control fluxes
of + and – charge in order to satisfy the wall boundary condition. – These charged-particle fluxes facilitate power deposition to the wall and
resultant phenomena (erosion, SEE.)
0 2 4 6 8 10 12 14 16 18 20-5
-4
-3
-2
-1
0
Distance from wall ( Debye lengths )
Potential (eφ / kTe )+
+-
-
-+
-
+
+
+
PlasmaSheath
-
+
+ -
+
+
+
-
-
4
BACKGROUND
• Sheath and Presheath:– Multiple regions corresponding to different physical length scales– Near-wall sheath region: non-neutral, scales with Debye length– Quasi-neutral presheath: scales with ion-neutral mean free path
0 2 4 6 8 10 12 14 16 18 20-5
-4
-3
-2
-1
0
Distance from wall ( Debye lengths )
Potential (eφ / kTe )
PresheathTransition
Region
Sheath
~ λD ~ λin
5
BACKGROUND
• Sheath and Presheath:– Multiple regions corresponding to different physical length scales– Near-wall sheath region: non-neutral, scales with Debye length– Quasi-neutral presheath: scales with ion-neutral mean free path
0 2 4 6 8 10 12 14 16 18 20-5
-4
-3
-2
-1
0
Distance from wall ( Debye lengths )
Potential (eφ / kTe )
PresheathTransition
Region
Sheath
~ λD ~ λin
Collisions increase presheath growth
6
BACKGROUND
• Theories for the sheath-presheath potential profile?• Presheath with finite collisionality is difficult to solve analytically
due to multiple length scales (sheath ~ λD , presheath ~ λin )
Theory Collisions? Presheath?
Child-Langmuir, 1913 Bohm, 1949
Sheridan, 1991 Riemann, 1997
• Asymptotic matching, intermediate scale analysis
7
BACKGROUND
• Sheath theory is well-developed1, however:– Sheaths with multiple complications (collisions, secondary
electron emission (SEE), magnetic fields, flowing plasma, non-Maxwellian plasma, warm ions) are still difficult to model.
… (EP devices)
• Experimental measurements are sparse2
– Sheaths are thin, scale with electron Debye length, (often < 1 mm.)
• Thus, current objectives:
1. Experimentally characterize sheaths and presheaths
in low ne, large-sheath environment.
2. Validate theoretical models for sheath scaling.
3. Validate particle-in-cell (PIC) simulation tool.1. Allen, J. E., “The plasma–sheath boundary: Its history and Langmuir's definition of the sheath edge” Plasma Sources Sci. Technol. 18 (2009) 0140042. Hershkowitz, N. “Sheaths: More complicated than you think” Physics of Plasmas 12, 055502 (2005.)
8
EXPERIMENTAL METHOD
• To resolve sheaths, need large Debye length:
• Low ne Plasma Cell– Multidipole-type plasma device selected– Provides stable, spatially uniform, low-density plasma
90 cm
60 cmHeated filaments,
biased below frame
Cusp shaped field
Permanent MagnetsAluminum Frame
-- -
+
ne 1010 – 106 cm-3 Te 0.5 – 10 eV λd 0.05 – 5 mm
9
EXPERIMENTAL METHOD
• Vacuum Chamber – HPEPL VTF-2• Base pressure: 1.9 x 10-9 Torr
Gas Inlet
ActiveCryopumps (6)
Plasma Cell
CM Location(Capacitance Manometer)
L = 9.2 m
4.9 m
Need local pressure measurement?• Transitional flow regime, expect minimal pressure difference between Plasma Cell and CM.• First order COMSOL transitional flow model indicates 0.001 to 0.01 mTorr pressure difference.
p 1–5 mTorr-Ar
λnn 0.5–0.1 m
Kn 0.01–0.1
10
EXPERIMENTAL METHOD
• Place wall material sample in plasma, measure sheath• Diagnostics:
• Emissive Probe Vp(x)
• Planar Langmuir Probe Te, ne
F Filaments
M Permanent Magnets
B Magnetic Field
PLP Planar Langmuir Probe
EP Emissive Probe
W Wall material sample
X Measurement ordinate
Key:
F
B
M
PLP EPW
60 cm
__
X
90 cm
11
RESULTS
• Cases at 1 and 5 mTorr – Argon gas– HP grade BN wall
– Ion mean free path < device length (60 cm)– Debye length ~ emissive probe spatial resolution (0.5 mm)
p = 1 mTorr p = 5 mTorr
λD 1.8 mm 0.45 mm
λin 60 mm 12 mm
λD / λin 0.030 0.037
Length scales of both sheath and presheath observable
12
RESULTS
• Emissive probe results:
0 2 4 6 8 10-10
-8
-6
-4
-2
0
5 mTorr
1 mTorr
Distance from Wall, cm
Pla
sma
Pot
entia
l, V
p = 1 mTorr p = 5 mTorr
Sheath Potential 8.3 V 5.5 V
Sheath Thickness 1.9 cm 1.2 cm
13
EXPERIMENTAL METHOD
• Langmuir probe, determine bulk plasma parameters– Planar probe theory of Knapmiller et al.– Bi-Maxwellian bulk plasma indicated
0 1 2 3 4 5 6 7 8 9 101.0E+5
1.0E+6
1.0E+7
1.0E+8 data
hot
cold
sum
Energy, eV
Ele
ctro
n E
nerg
y D
istr
ibut
ion,
s/m
4
Te_hot = 3.8 eV
Te_cold = 0.7 eV
Knappmiller, S., Robertson, S., Sternovsky, Z., “Method to find the electron distribution function from cylindrical probe data,” Physical Review E, 73(6), 066402, 2006.
14
RESULTS
• Emissive probe (figure) and Langmuir probe (table):
0 2 4 6 8 10-10
-8
-6
-4
-2
0
5 mTorr
1 mTorr
Distance from Wall, cm
Pla
sma
Pot
entia
l, V
p = 1 mTorr p = 5 mTorr
Te_cold 0.8 eV 0.7 eV
Te_hot 8.4 eV 3.8 eV
ne_cold 9.5 x 106 cm-3 1.9 x 108
cm-3
ne_hot 3.7 x 106 cm-3 5.6 x 107
cm-3
ne_total 1.3 x 107 cm-3 2.5 x 108
cm-3
Bulk Plasma Parameters:
15
0 2 4 6 8 10-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
Collisionless
1 mTorr
5 mTorr
Distance from Wall, cm
RESULTS
• Potential profiles, normalized by Vwall
Increased collisionality Growth of presheath
16
ANALYSIS
• Need to predict floating wall potential– For Maxwellian argon plasma, fluid result:
– For a bi-Maxwellian plasma, the Bohm speed shown to be that of a Maxwellian plasma with weighted harmonic mean Te:
Emphasizes cold electron temperature– Alternatively, from solution of Tonks-Langmuir problem with a bi-
Maxwellian plasma:
Emphasizes hot electron temperatureSong, S. B., Chang, C. S., & Choi, D. I., “Effect of two-temperature electron distribution on the Bohm sheath criterion,” Physical Review E, Vol. 55, No. 1, 1213, 1997. Godyak, V. A., Meytlis, V. P., Strauss, H. R., “Tonks-Langmuir Problem for a Bi-Maxwellian Plasma,” IEEE Transactions on Plasma Science, Vol. 23, No. 4, 1995.
17
ANALYSIS
• Floating wall potential, predicted vs. measured:
p = 1 mTorr p = 5 mTorr
Measured 9.0 V 6.5 V
Harmonic Mean Te Prediction 5.5 V 3.8 V
Hot Te Prediction 45.3 V 10.3 V
• Harmonic mean Te shows closer agreement, use that as boundary condition for sheath prediction
18
ANALYSIS
• Comparison to Riemann 1997 fluid asymptotic matching model with predicted wall floating potential:
0 1 2 3 4 5-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
5 mTorr
5 mTorr prediction
1 mTorr
1 mTorr prediction
Distance from Wall, cm
Pla
sma
Pot
entia
l, V
1 mTorr 5 mTorr
λD 1.8 mm 0.44 mm
λin 60 mm 12 mm
Te 1.07 eV 0.73 eV
Vsheath -5.5 eV -3.8 eV
19
ANALYSIS
• Allowing parameters to vary, good fit can be achieved.• R2 > 0.98
0 1 2 3 4 5-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
5 mTorr 5 mTorr fit
1 mTorr 1 mTorr fit
Distance from Wall, cm
Pla
sma
Pot
entia
l, V
1 mTorr 5 mTorr
λD 1.5 mm 1.3 mm
λin 65 mm 19 mm
Te 0.8 eV 0.7 eV
Vsheath -8.4 eV -5.5 eV
20
CONCLUSIONS
1. Experimental measurements of sheaths and pre-sheaths obtained, presheath growth observed.
2. Potential profiles in qualitative agreement with asympotically-matched fluid theory.
3. Experiment agrees more closely to harmonic mean Te method for predicting floating potential in bi-Maxwellian plasma.
Future Work:– Resolve the transition region with higher spatial resolution,
compare fluid and kinetic model scalings.– Validate results against PIC simulation.– Investigate effect of magnetic field.
21
Thank you
Questions?
This work is supported by the Air Force Office of Scientific Research (AFOSR) through Grant FA9550-11-10160
22
EXPERIMENTAL METHOD
• Emissive probe: determine plasma potential in the sheath• Sweep at multiple low emission levels• Identify inflection point (e.g., left figure)• Extrapolate to zero emission plasma potential (e.g., right figure)
-9.8 -9.6 -9.4 -9.2 -9 -8.8 -8.60.0E+0
2.0E-6
4.0E-6
6.0E-6
8.0E-6
1.0E-5
1.2E-5
1.4E-5
1.6E-5
1.8E-5
Inflection Points
Linear Fit
Plasma Potential
Potential (V)
Em
issi
on C
urre
nt (
A)
-20 -15 -10 -5 0 50.0E+0
2.0E+0
4.0E+0
6.0E+0
8.0E+0
1.0E+1
1.2E+1
Probe Bias, V
dI/d
V,
A/V
Smith, J. R., Hershkowitz, N., and Coakley, P., “Inflection point method of interpreting emissive probe characteristics,” Rev. Sci. Instrum. 50 (2), Feb. 1979.
23
BACKUP
Axial distance from magnet (in)
Radial distance from magnet (in)
Bulk plasma largely field-free
(G)
Gaussmeter200
180
160
140
120
100
80
60
40
20
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.00.0 0.2 0.4 0.6 0.8 1.0 1.2
24
COLLABORATION
Measurement
Theory
Simulation
Validate
Validate
Verify
Collaborative research strategy:
25
BACKGROUND
What kind of sheaths to investigate?• Ion-neutral collisions presheath growth
Presheath effects not confined to near-wall sheath region!
• Studies in HET’s have shown presheath-like potential structures permeating the full width of the discharge channel.
ϕ