Experimental test of instability enhanced collisional friction for

determining ion loss in two ion species plasmas

Noah Hershkowitz

University of Wisconsin – Madison

Annual Meeting of APSNov. 8, 2010 Chicago, IL 1

With one ion species, ion drift velocity vd at the sheath plasma boundary is the Bohm velocity

• The Bohm velocity also is the ion sound velocity in the bulk plasma

• Ions are accelerated to the sheath boundary by presheath electric fields

• For one ion species, Riemann has shown the presheath potential

where is the ion-neutral collision length

vd cs

eTe

x

Background

cs Temi

2

•With 2 or more ion species, Riemann showed that ions satisfy a generalized Bohm criterion

•With only 2 ion species and assuming the equality holds

The generalized Bohm velocity may be satisfied by speeds faster or slower

than the sound speed for a given ion species

Two simple solutions:

(1) all ions attain the same speed at the sheath edge

(2) each species attains its own Bohm speed.

Solution (1) gives a common ion drift velocity at the sheath edge equal to

the ion acoustic speed in a homogeneous plasma with no ion drifts.

•

ninei

csi

2

v i21

n1

ne

cs12

v12 n2

ne

cs22

v22 1

Many authors quite naturally have assumed that solution (2)

applies.

If the plasma is collisionless, then all ions can reach their individual

Bohm velocity at the sheath edge by falling through a potential of Te/2.

In weakly collisional plasmas, ion motion is mobility limited and much

larger potential drops are required to reach the Bohm velocity. Under

these conditions, the potential drop that works for one ion species does

not work for the other ion species.

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Our recent experiments have shown that ions in weakly collisional plasmas containing two ion species of comparable densities nearly reach a common velocity at the sheath edge within errors

The common velocity was the bulk system ion sound velocity

How does the plasma achieve that result?

Ar+Xe LIF & emissive probe data show the difference in flow Ar+Xe LIF & emissive probe data show the difference in flow speeds throughout the presheath is smallspeeds throughout the presheath is small

- Ar 0.5 + Xe 0.2 mTorr- Filament: -60 V, 1.25 A- Electrode: -30 V

- ne = 5.71×109 cm-3, Teff = 0.68 eV

- Cs(Ar) = 1280 m/s, Cs(Xe) = 710 m/s

- Sheath edge from EP

= 0.25 ~ 0.30 cm

- Phase velocity by IAW: 1090 ± 40 m/s- Ion ratios: Ar 0.61 + Xe 0.39

Ar ion speed with respect to z in Ar+Xe plasma

- At the sheath edge: <vrms> = 1080 ± 50 m/s

- The Ar velocity measured from the LIF data at the sheath edge is between the Bohm velocity

of argon and xenon.- The results show that the argon ions also get close to the sound speed of the system at the sheath boundary

when the argon is the lighter species.

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An Ion-Ion beam Instability is observedAn Ion-Ion beam Instability is observed

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Baalrud et al.1,2 have recently argued that ion beam - ion beam instability-enhanced collisional friction establishes the solution of the Bohm Criterion

The relative flow speed of the two ion species with large differences in ion masses was predicted to be limited to a value determined by the instability-enhanced friction, the thermal velocities and relative densities of the ions and their mass differences.

In particular, they predict that individual species’ velocities equal individual species’ Bohm velocities when one species’ density was much larger than the other, and a minimum velocity difference when the ion concentrations are comparable. The predicted velocity diffeence goes to zero as Ti goes to zeero.

[1] S. Baalrud, J. Callen, and C. Hegna, Phys. Rev. Lett. 103, 205002 (2009)[2] S. Baalrud, and C. Hegna, UW-CPTC 10-2 (Dated: April 7, 2010)

Experimental Approach• Plasma is produced in a multi-dipole device by energetic electrons emitted from heated filaments.

• The concentration ratio of the two ion species is determined from the phase velocity of Ion Acoustic Waves in the bulk plasma combined with the measured Te

• Electron temperature is measured with a Langmuir probe.

• Laser Induced Fluorescence determines ion flow velocities and ion temperatures. Both Ar + and Xe+ LIF are employed

• An emissive probe measures the plasma potential profile near a negatively biased plate

• The sheath/presheath boundary is identified from the slope change of the emission current vs bias voltage curve

• Drift velocities of both species at the sheath edge are compared with the solution to the generalized Bohm criterion predicted by the theory.

• A Maxwell demon wire array device is used to heat the plasma for temperature variance

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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 or Helium + 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 Ar metastable ion in state 3d4F7/2 to 4p4D5/2 with the diode laser of 668.614 nm

Relaxation from the state 4p4D5/2 to 4s4P3/2. Observe the fluorescence at 442.72 nm

In Xe excite with 680.574 nm and observe fluorescence at 492.15 nm

It is assumed that the metastable ions are in thermal equilibrium with ground state ions 13

The sheath edge is determined from the change The sheath edge is determined from the change in slope of inflection point vs Vin slope of inflection 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 cm14Wang 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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•MacKenzie et al. successfully heated a plasma by an angular momentum trap of cold electrons with a 60 x 60 cm grid of 0.03mm tungsten wire in a 1-m diameter by 2-m long filament discharge chamber. [1]

•Mackenzie’s Maxwell demon wire array is revisited in a multi-dipole chamber filament discharge in a much simpler incarnation - loops of 0.025mm tungsten filament (about 3 meters in total length) spot-welded onto a conductive probe-shaft covered with electrical insulating material (ceramics and fiber-glass covers) to create an exposed wire-array, which works in spite of the lack of overall geometry.

A Maxwell demon wire array is used to raise A Maxwell demon wire array is used to raise the plasma temperature for investigationthe plasma temperature for investigation

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Note that the plasma after its temperature is Note that the plasma after its temperature is raised satisfies the Bohm’s Criterionraised satisfies the Bohm’s Criterion

Te=0.89eV without demon by Langmuir Probe(Cs = 810.3 m/s)Te=1.71eV with demon by Langmuir Probe (Cs = 1120m/s)Measured IAW velocity = 1111±70m/sMeasured Ion velocity at sheathedge = 1094±70m/s

Ion velocity and potential profile of a Xenon plasma with its temperature doubled by the Maxwell demon.

IAW data tell the same story as LIF data. IAW data tell the same story as LIF data.

Phase velocity at sheath edge Phase velocity at sheath edge 2v 2vbulkbulk

-Neutral Pressures: Argon 0.5mT Xenon 0.2mT- Bulk velocity ~ 1080m/s- Argon – Xenon Ratio ~ 47:53

- Filament: -60 V, 1.25 A

- Electrode: -30 V

-Teff 0.75eV

- Sheath edge from EP

= 0.4± 0.05cm

- Phase velocity by IAW: 1080±

70 m/s

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For Argon-Xenon plasmas, ion temperatures at the sheath/presheath edge are comparable except for low relative ion concentrations

Ion temperatures are calculated by the equation Ti = mi(<v2>-<v>2)1/2/2

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In a Xenon-Helium plasma, however, Xenon temperature rises both when Xenon dominates the plasma and when ion concentrations are comparable

The fractional Xenon ion concentration is much higher than its the fractional neutral concentrations for both Xenon-Argon and Xenon-Helium plasmas because of Penning ionization

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Data shows that Ion-Ion Instability depends both on the relative flow velocity and the relative concentration of the two species.

This was verified in our paper, “Experimental Test of Instability-Enhanced Collisional Friction for Determining Ion Loss in Two Ion Species Plasmas”, Yip, CS; Hershkowitz, N; Severn, G. Phys Rev Lett.  Vol.104  Iss:22  #225003 (2010)

When ion masses are comparable, the theory predicts

Xenon drift velocities measured by LIF are marked by the squares, Argon velocities measured by LIF are marked in circles, solid line is the prediction curve and the dash dotted line is the common sound velocity.

Ar

Xe

23

Xenon and Argon ion sheath velocities measured in Te = 1.80±0.05eV plasmas, notice that Argon velocities were implied by the generalized Bohm Criterion.

Measurements made at a higher temperature (Te = 1.8eV) achieved by the Maxwell demon also confirms the same results.

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When ion masses are very different, the theory predicts

Vc 12

vT12 vT 2

2

where and vTj are the ion thermal velocities

n1m2

n2m1

Our Xenon-Helium drift velocities data: Xenon drift velocities measured by LIF are marked by the squares, Helium velocities infered by Generalized Bohm’s Criterion are marked in circles, dashed line is the prediction curve and the dash dotted line is the common sound velocity.

Xe

He

Conclusions

• The generalized Bohm criterion has been verified for Ar-Xe plasmas

• LIF data are in excellent agreement with the theory based on ion beam - ion beam instability-enhanced collisional friction for weakly collisional Ar-Xe and He-Xe plasmas

• Experiments with Maxwell’s Demon increased Te are also in excellent agreement with collisional friction theory.

• Ions do not fall out of plasmas with their individual Bohm velocities except when their relative concentrations are either very large or very small

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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

Acknowledgements:

My Collaborators

Chi-Shung Yip, University of Wisconsin – Madison and

Greg Severn, University of San Diego

• They predict that individual species’ velocities equal individual species’ Bohm velocities when one species’ density was much larger than the other.

• This experiment is an attempt to verify the collisional friction theory by measuring the ivdfs and other related plasma parameters in a multi-dipole chamber operating with discharges of Argon and Xenon or Argon and Helium with varying concentration ratios.

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