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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