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 GEC, Salt Lake City, UT, November 14, 2011 1

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.

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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 sheath edge. 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) • T e = 2.5eV, n e ~ 6x10 9 cm • Non-Maxwellian tails of 3 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 8

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. 11

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. 2006

Multi-dipole device

-60 V, 1.0A

60 cm -30 V P M T Magnets e e Hot Filament e Electrode Plate Z Beam Dump LIF Langmuir Probe Emissive Probe Probe Circuit Laser Pump 70 cm 13

Experimental setup of the laser system Laser Driver Wavelength Meter Chopper Controller I 2 Cell Periscope Power Meter Mirror To Chamber Mirror Optical Chopper Laser Head I 2 Cell Heater Heating Ribbon 14

Multi-dipole Device

PMT EP Ar LIF Laser - Argon + Xenon - Gas pressure: 0.1 ~ 1.0 mTorr - Filament bias: -60 V - Emission current: 1.0 ~ 1.25 A - Electron density: ~ 10 9 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 5d 4 F 7/2 to 6p 4 D 5/2 with the laser of 680.574 nm Relaxation from the state 6p 4 D 5/2 to 6s 4 P 3/2 . 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 V p

Plasma parameters

- Ar 0.7 mTorr - Filament: -60 V, 1.00 A - Electrode: -30 V   0

d

2 

dx

2 

i



n e

)

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 Techniques for Electric Potential Measurements in a Complex Plasma ” 17 2:00 PM –2:15 PM

Maxwell’s Demon is used to control plasma temperature

0.025mm Tungsten wires nicely lined up 18

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

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