Langmuir’s Paradox: Can Ion
instability at sheath-edge
thermalize the ions too?
Chi-Shung Yip
Noah Hershkowitz
University of Wisconsin – Madison
Greg Severn
University of San Diego
1
GEC, Salt Lake City, UT, November 14, 2011
Pre-sheath and charge exchange
explained
• Ions travel through a potential
drop into the sheath boundary to
accelerate to Bohm’s velocity.
• The potential drop affects only
charge particles
• Neutral atoms are not charged
• If charge exchange occurs, ions
will be born from a zero drift
velocity Maxwellian of the neutral
gas.
Pre-sheath
2
Langmuir’s Paradox
• As old as plasma physics itself!
• Originally found by Langmuir.
• Energetic electrons on the tail of the Maxwellian
distribution of a plasma are not confined by the plasma
potential.
• Notice that in his experiment, ionization mostly comes
from electrons on the tail of the Maxwellian, so his
plasma should not have existed.
• However Langmuir found that electrons are
Maxwellian up to 50eV (with his Langmuir probe), so
there must be an additional mechanism in electron
thermalization.
3
4
Most electrons
on this side
should be lost
5
But what is this mechanism?
• In Langmuir’s experiment, the electron-electron
scattering collision length is far greater than the
tube diameter, so electron-electron scattering
without additional assumptions does not explain
the phenomena.
• Various explanations have been proposed:
sheath scattering, photons scattering, sheath
oscillations, etc.
• None of them gives a satisfactory answer to the
paradox.
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The Baalrud theory
• Baalrud et al. resolved the Langmuir’s Paradox in the
following way[1]:
• Ion Acoustic Instability in the presheath, increases the
electron-electron and ion-ion collisional cross section
of an otherwise stable plasma by 100 times
• This quickly thermalizes electrons near the sheathedge. replenishing high energy electrons lost due to
insufficient sheath potential.
• MHz instabilities near sheaths has been observed by
previous researchers. [2]
[1] S. D. Baalrud and C. C. Hegna, “Kinetic Theory of the Presheath and
the Bohm Criterion,” Plasma Sources Science and Technology
[2] D. Gabor, E. A. Ash, and D. Dracott, Nature 176, 916 (1955).
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A “two stage” ion velocity distribution
phenomenon is found in previous experiments
• Claire et al. measured ion
velocity distribution
functions (ivdfs) throughout
the pre-sheath.
• Plasma created in a 80 cm
long x 40 cm diam. filament
discharge device.
• Neutral pressure 1.8 x 10-4
mbar (0.135 mTorr)
• Te = 2.5eV, ne ~ 6x109cm3
• Non-Maxwellian tails of
ivdfs are seen as ions
enters pre-sheath, and
thermalizes as they goes
into sheath edge
Claire N, Bachet G, Stroth U and Doveil F 2006 Phys. Plasmas 13 062103
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Severn et al., 2003
G. D. Severn, X. Wang, E. Ko, and N. Hershkowitz, Phys. Rev. Lett. 90, 145001 (2003).
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This is also resolved by the
Baalrud theory
• The Baalrud theory explains the “two stage
pre-sheath with the following:
• Ions entering the beginning of the presheath
will first become non-Maxwellian due to charge
exchange
• As ions travel towards the sheath edge, they
will thermalize into a Maxwellian distribution
due to ion acoustic instability enhanced
friction.
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Experimental Approach
• Pre-sheath lengths are proportional to the ion neutral
collision length which is inversely proportional to
neutral pressure
• According to Baalrud et al. ion acoustic instability will
not have adequate distance to grow as pre-sheath
shortens.
• Experiments were set up to measure ivdfs throughout
presheaths to verify previous findings.
• Control experiments at higher pressures were setup
to find the existence of a threshold pressure where
this phenomena cease occuring.
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Experimental Setup
• Plasma is produced in a multi-dipole device by energetic
electrons emitted from heated filaments.
• Electron temperature is measured with a Langmuir probe.
• Laser Induced Fluorescence determines ion flow velocities and
ion temperatures. Xe+ LIF is employed
• An emissive probe measures the plasma potential profile near a
negatively biased plate [3]
• The sheath/presheath boundary is identified from the slope
change of the emission current vs bias voltage curve
[3] Wang X, Hershkowitz N. Simple way to determine thee edge of an electro-free sheath
with an emissive probe, REVIEW OF SCIENTIFIC INSTRUMENTS 77, 4, 043507. 200612
Multi-dipole device
P
M
T
Magnets
-60 V, 1.0A
e
60 cm
LIF
e
Hot Filament
e
Electrode Plate
-30 V
Langmuir Probe
Z
Emissive Probe
Probe
Circuit
Laser
Beam Dump
Pump
70 cm
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Experimental setup of the laser system
Periscope
Chopper
Controller
Wavelength
Meter
Power
Meter
Mirror
I2 Cell
To Chamber
Mirror
Laser Driver
Optical
Chopper
Laser Head
I2 Cell
Heater
Heating
Ribbon
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Multi-dipole Device
PMT
Ar LIF
Laser
EP
- Argon + Xenon
- Gas pressure: 0.1 ~ 1.0 mTorr
- Filament bias: -60 V
- Emission current: 1.0 ~ 1.25 A
- Electron density: ~ 109 cm-3
- Electron temperature: ~ 1 eV
- Using the filament of the emissive probe
as an aiming point of the laser.
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How does the LIF work?
Optical excitation of Xe
metastable ion in state
5d4F7/2 to 6p4D5/2 with the
laser of 680.574 nm
Relaxation from the state
6p4D5/2 to 6s4P3/2. Observe
the fluorescence at 492.15
nm
It is assumed that the metastable ions are in thermal
equilibrium with ground state ions
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The sheath edge is determined from the change in slope of
inflection point vs Vp
Plasma parameters
- Ar 0.7 mTorr
- Filament: -60 V, 1.00 A
- Electrode: -30 V
d 2
 0 2  e(ni  ne )
dx
Where is the sheath edge?
- Emitted electrons from the probe reduces the curvature of potential.
- The reduction in the curvature of the potential increases as the emission increases.
- The inflection point becomes more positive with the increased emission in a sheath.
- An electron-free sheath is identified as the position where the inflection point changes
from increasing with emission to decreasing with emission.
- From the figure, the sheath edge is determined to be 0.35 ~ 0.40 cm
For more information about emissive probe techniques, please attend JP Sheehan’s
presentation on Wednesday-Abstract: LW3.00001 : “A Comparison of Emissive Probe 17
Techniques for Electric Potential Measurements in a Complex Plasma” 2:00 PM–2:15 PM
Maxwell’s Demon is used to
control plasma temperature
0.025mm
Tungsten wires
nicely lined up
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At higher pressure charge
exchange tail persists
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At low pressure, Claire et al.’s
phenomenon are replicated
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Summary
• Preliminary data recreated phenomenon by Claire et
al.
• A higher pressure case where ion acoustic instability
no longer thermalize non-Maxwellian tails of ivdfs,
seems to be found. This is consistent with Baalrud’s
predictions.
• Further LIF experiments will be performed at additional
pressures to obtain complete spectrum of change in
the phenomena.
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This work was supported by U.S.
Department of Energy Grants No.
DE-FG02-97ER54437 and No. DE
FG02- 03ER54728, National Science
Foundation Grants No. CBET0903832, and No. CBET-0903783
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