Langmuir’s Paradox: Can Ion instability at sheath-edge thermalize the ions too? Chi-Shung Yip Noah...
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Transcript of Langmuir’s Paradox: Can Ion instability at sheath-edge thermalize the ions too? Chi-Shung Yip Noah...
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Langmuir’s Paradox: Can Ion instability at sheath-edge thermalize the ions too?
Chi-Shung YipNoah Hershkowitz
University of Wisconsin – Madison
Greg Severn
University of San Diego
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GEC, Salt Lake City, UT, November 14, 2011
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• 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.
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Pre-sheath and charge exchange explained
Pre-sheath
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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.
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Most electrons on this side should be lost
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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 sheath-edge. replenishing high energy electrons lost due to insufficient sheath potential.
• MHz instabilities near sheaths has been observed by previous researchers. [2]
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[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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8Claire N, Bachet G, Stroth U and Doveil F 2006 Phys. Plasmas 13 062103
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
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Severn et al., 2003
9G. 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
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[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. 2006
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Multi-dipole device
Pump
ProbeCircuit
Emissive Probe
Langmuir Probe
Electrode Plate
-60 V, 1.0A
Hot Filament
-30 V
PMT
Z
LIF
Laser
Magnets
ee
e
70 cm
60 cm
Beam Dump
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Experimental setup of the laser systemExperimental setup of the laser system
OpticalChopper
WavelengthMeter
ChopperController
I2 Cell
PowerMeter
Mirror
Mirror
Periscope
HeatingRibbon
Laser Head
Laser Driver
I2 CellHeater
To Chamber
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Multi-dipole Device
Ar LIF
Laser
PMT
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?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 16
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The sheath edge is determined from the change in slope of The sheath edge is determined from the change in slope of inflection point vs Vinflection point vs Vpp
2
0 2( )i e
de n n
dx
Plasma parameters- Ar 0.7 mTorr- Filament: -60 V, 1.00 A- Electrode: -30 V
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
17For more information about emissive probe techniques, please attend JP Sheehan’s presentation on Wednesday-Abstract: LW3.00001 : “A Comparison of Emissive Probe Techniques for Electric Potential Measurements in a Complex Plasma” 2:00 PM–2:15 PM
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Maxwell’s Demon is used to control plasma temperature
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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. CBET-0903832, and No. CBET-0903783