dusty plasmas in basic science, astronomy, industry & fusion

Dusty plasmas in basic science, astronomy, industry & fusion

John GoreeThe Univ. of Iowa

The growth of dusty plasmas as a field of research

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

YEAR82 84 86 88 90 92 94 96 98 00 02 04

N = N0 e( T / 3.9 )

Inspec DatabaseSubject Heading: Dusty Plasma(s)

Outline

1. What is dust?2. Formation of dust

• Fusion• Industry• Astronomy

3. Dust charge4. Forces acting on dust5. Some physics experiments:

• Voids under microgravity conditions• Strongly-coupled vs. Weakly-coupled

Plasmas• Waves & Instabilities• Shear flow• Wakes

What is dust?“Dust” = small particles of solid matter, 10 nm – 1 mm, usually

dielectric

Astronomy: “dust”

M16 pillarCredit: NASA, HST, J. Hester & P. Scowen (ASU)

Semiconductor industry“particulates” or “particles”

G.S. Selwyn, Plasma Sources Sci. Tehcnol. 3, 340 (1994)

Safety Issues for fusion

RadiologicalDust:

• activated• retains tritium• ITER safety limit: 350 kg Tungsten dust

Fire & chemical explosionHydrogen:

• stored in dust• released during accidental exposure to:

• air• steam

• ITER safety limit: 6 kg dust allowed on hot surfacesPhil SharpeFusion Safety Program, Idaho National Laboratory

Dust in Fusion Plasmas Workshop2005

What is dust?

Formation of dust

Formation

Produced in the gas phase• Nucleation• Coagulation

Purchased from vendor

What’s the source of dust in a plasma?

Produced on surfaces• Flaking of deposited films• Bubbles & blistering of

surfaces

Fusion: various shapes of dust collected from the Tore Supra tokamak

Phil SharpeFusion Safety Program, Idaho National Laboratory

Formation: tokamaks

Composition is mainly: • carbon• constituents of stainless steel

Formation: tokamaksTungsten dust formation: flaking from He bubbles

N. Ohno, S. Takamura, Dai. Nishijima“Formation and Transport of Dust in the Divertor Plasma Simulators”

Divertor Plasma Simulator NAGDIS-II

Surface Temp.: 2200 KFlux: 8.3×1022 m-2s-1

Ion Energy: 15 eVTime: 104 s

Poloidal Limiter

High Z dust is emitted from the Mo poloidal limiter.

Observation of High Z Dust in TRIAM-1M by Fast Framing Camera, 4500 fps

Formation: tokamaks

N. Ohno, S. Takamura, Dai. Nishijima“Formation and Transport of Dust in the Divertor Plasma Simulators”

A lesson from the semiconductor industryParticles were always there, but you didn’t know it until you used the right diagnostics:

G.S. Selwyn, Plasma Sources Sci. Tehcnol. 3, 340 (1994)

cameraimagingin-situ

electron microscopy ex-situ

Formation: gas phaseGas-phase formation in

astrophysics:

• Vapor flowing outward from a carbon star cools & nucleates dust

• Dust grains then grow by “coagulation”

M16 pillar, Credit: NASA, HST, J. Hester & P. Scowen (ASU)

Formation: gas phaseGas-phase

formation

G. Praburam and J. GoreeAstrophys. J 1995

Formation: gas phaseCauliflower particles grow in the gas phase:

Gary Selwyn, IBM, 1989 Ganguly et al., J. Vac. Sci. Technol. 1993

intact fractured

Formation: gas phase

Particles grownby sputtering tungsten

D. Samsonov and J. GoreeJ. Vac. Sci. Technol. A 1999

300 nm

Coagulated particles consisting of 3+ cauliflowers

Particles grownby sputtering graphite

Particles grownby sputtering aluminum

Polymer microspheres:• melamine-formaldehyde• diameter 8.09 0.18 m• used in basic science experiments• introduced into plasma with a “salt shaker”

Formation: purchased from vendor

Outline

Charging: mechanisms

Charging by collecting electrons and ions only negative charge

Ielectron collection

+ Iion collection

Goree, Plasma Sources Sci. Technol. 1994

+ Iion collection

+ Ielectron emission

e- +Electron emission

•secondary emission due to e- impact•photoemission•thermionic

positive charge

Charging: mechanismsParticles immersed in a plasma collect currents:

Itotal = Ielectron collection + Iion collection + Ielectron emission

Each of these currents depends on the potential V of the particle

Equilibrium:

Itotal = 0 at the “floating potential” V:

Q = CV

is capacitance of sphere of radius a

surfacepotential V

Charging: mechanismsCharging by collecting electrons & ions only

Consider a particle that is suddenly exposed to plasma:

• Initially it collects electrons more rapidly than ions, due to higher vte

• Eventually it reaches equilibrium “floating potential”:

Hydrogen, Ti = Te

V = -2.5 kTe

• Example:Parameters:

Te= 1 eV

a = 1 mCharge: Q = - 1737 e

+ Iion collection

Forces

• Fusion• Industry• Astronomy• Pure physics

3. Dust charge4. Forces acting on dust5. Some pure physics experiments:

• Strongly-coupled vs. Weakly-coupled Plasmas

• Waves & Instabilities• Shear flow• Wakes

Forces

Forces acting on a particle

Ion drag a2 big for high-density plasmas

Radiation pressure a2 if a laser beam hits particle

Gas drag a2 requires gas

Thermophoretic force a2 requires gas

Coulomb QE a provides levitation

Lorentz Q v B a tiny except in astronomy

Gravity a3 tiny unless a > 0.1 m

Ion drag force

Orbit force: Ion orbit is deflected

Collection force: Ion strikes particle

Momentum is imparted to the dust particle

Void is due to ion drag

D. Samsonov and J. GoreeInstabilities in a Dusty Plasma with Ion Drag and IonizationPhysical Review E Vol. 59, 1047-1058, 1999

Dust (laser light scattering from a horizontal laser sheet)

Ion drag force

Plasma: • RF parallel-plate• glow discharge• argon gas

Dust:• nm size• carbon• grown by sputtering

graphite target

Void is due to ion drag

D. Samsonov and J. GoreeInstabilities in a Dusty Plasma with Ion Drag and IonizationPhysical Review E Vol. 59, 1047-1058, 1999

Dust (laser light scattering from a horizontal laser sheet)

Ion drag force

Plasma: • RF parallel-plate• glow discharge• argon gas

Dust:• nm size• carbon• grown by sputtering

graphite target

How ion drag produces a void:

J. Goree, G. E. Morfill, V. N. Tsytovich and S. V. Vladimirov, Theory of Dust Voids in Plasmas, Physical Review E Vol. 59, 7055-7067, 1999

Ion drag force

Ionization sourcePositive plasma potl

Outward ion flow

dust void

Ion drag force

J. Goree, G. E. Morfill, V. N. Tsytovich and S. V. Vladimirov, Theory of Dust Voids in Plasmas, Physical Review E Vol. 59, 7055-7067, 1999

E. C. Whipple, Rep. Prog. Phys. 44, 1198 (1981)

Two contributions:

• Orbit force (this is the usual drag force for Coulomb collisions, except that ln is problematic)

• Collection force (ions actually strike the particle)

Depends on ion velocity ui

Force ni

Orbit forcefrom Rosenbluth potential

Collection forcefrom OML model

0.01 0.1 1 10 100io

ion velocity / ion thermal velocity

Te / Ti = 60, mi = 40 amu, D = 130 mIon drag is normalized by 4 ni a2 Te / (Ti/Te)0.5

Ion drag force

0.01 0.1 1 10

ion velocity / ion thermal velocity

Ion drag force

Data computed March 2005 using the same code as in J. Goree, G. E. Morfill, V. N. Tsytovich and S. V. Vladimirov, Theory of Dust Voids in Plasmas, Physical Review E Vol. 59, 7055-7067, 1999

• Fusion edge plasma parameters:

• Te = Ti, deuterium mass

Te / Ti = 1, mi = 2 amu, D = 13 mIon drag is normalized by 4 ni a2 Te / (Ti/Te)0.5

Ion drag force

Gas drag

molecular-flow regime

Epstein:

• Ngas gas atom: number density• mgas mass• cgas mean thermal speed • V velocity of particle with respect to

the gas• dimensionless, ranges from 1.0 to

P. Epstein, Phys. Rev. 23, 710 (1924).

M. J. Baines, I. P. Williams, and A. S. Asebiomo, Mon. Not. R. Astron. Soc. 130,

63 (1965).

VacmNF gasgasgas2

Gas drag force

Stokes-flow regime

Radiation pressure force

Radiation pressure

B. Liu, V. Nosenko, J. Goree and L. Boufendi, Phys. Plasmas (2003).

cIaqF laser

incident laser

momentum imparted to microsphere

transparent microsphere

cIaF laser

radiation

Physics experiments

• Fusion• Industry• Astronomy• Pure physics

• Microgravity conditions• Strongly-coupled vs. Weakly-coupled

Physics experiments

Remainder of this talk:

All experiments performed with polymer microspheres

EquipotentialContours (RF glow discharge)

electrode

positive

potential

electrode

With gravity, particles sediment to high-field region 2-D layer

Without gravity, particles fill 3-D volume

Microgravity conditions

Microgravity conditionsTo obtain a 3D dust suspension, use zero g conditions:Parabolic flights, NASA KC-135

Parabolic flights, NASA KC-135

“strongly coupled”dusty plasma: Q bigstar interior: r smallpure-ion plasma: T small

Strongly-coupled vs. weakly-coupled plasmas

> 1 plasma is like a solid or a liquid << 1 plasma is like a gas

energy kinetic particleenergy potential cleinterparti

Coulomb coupling parameter:

Physics experiments

Waves in a weakly-coupled dusty plasma

Parameter:gas: Argonp = 1.0 .. 2.5 Pani = 1015 m-3

B = 20 .. 80 mT

dust:MF-spheresd = 1 µmnd = 0.5 .. 3 x 1011 m-3

particles

anodic plasma

RF-discharge

camera

dust tray

plasma column probes

Anode:UA = 50 .. 100 VIA = 3 .. 12 mA

Dusty Plasma Research, A. Piel, 2005 41

Courtesy Alexander Piel, Kiel University, Germany, 2005

Dust acoustic wave experiment: Kiel Univ.

Time lapse 1:10 p = 2.5 PaIA = 10 mAB = 20 mT

Dust acoustic wave experiment: Kiel Univ.

Dusty Plasma Research, A. Piel, 2005 42

Courtesy Alexander Piel, Kiel University, Germany, 2005

Physics experiments

Shear flow in a strongly-coupled dusty plasma (plasma crystal).

Shear flow in a 2D dusty plasma

two Ar+ laser beams:• 0.61 mm width• rastered into vertical sheets

vide o cam e ra(top v iew)

lower elec trod e

m icros pheres

Ar laserbeam 1

Ar laserbeam 2

m od ulator

scanningm irrors

m od ulator 1

scanningm irrors

vide o cam e ra(sid e view)

Ar+ laser pushes particles

low power: slow deformation, rotationmedium power: plastic deformation, flow high power: melting the lattice

undisturbed monolayer

Transport: radiation pressure

Shear flow in a strongly-coupled dusty plasma

Zoom-in view

A 2D liquid, observed at an atomistic level

Video data:

Data recorded: x & v for each particlei.e., a kinetic approach

Next step in analysis: convert to a continuum approach, by spatial averaging

particle’s x,y position measured in each video frame

Velocity profiles

-5 0 5

distance y (mm)

Plaser

= 3.41 W

2.00 W

1.44 W

1.04 W0.82 W

Navier-Stokes equation

vv)(/3)/(vvvvEp

v fluid velocity areal mass density

(2D)p pressure (2D)/ kinematic viscosity

(2D) second viscosity (2D)E gas drag

0)(v)(v2

Navier-Stokes equation reduces to:

kinematic viscosityE gas drag coefficient

Our experiment:

/t = 0

/x = 0

vy = 0

Velocity profiles fit to Navier-Stokes

-5 0 5

distance y (mm)

laser = 3.41 W

2.00 W

1.44 W

1.04 W0.82 W

Results: viscosity vs. inverse temperature

100 1000

coupling parameter

0.53 0.42

r / w Dwater at STP (3D)

high temperature

viscosity hasa minimum

low temperaturey 1/Ty

Physics experiments

Waves in a strongly-coupled dusty plasma

Waves: two modes in a lattice

S & P waves in seismology

Only the P wave passes through the core of Earth – because the core is liquid

Theory for a triangular lattice, 0°Wang, Bhattacharjee, Hu , PRL (2000)

0 2 4wavenumber ka/

acoustic limit

compressional

Wave dispersion relation – 2D triangular lattice

Longitudinal wave

k Laser incident here

f = 1.8 Hz

Nunomura, Goree, Hu, Wang, Bhattacharjee Phys. Rev. E 2002

Random particle motion

No Laser!

S. Nunomura, Goree, Hu, Wang, Bhattacharjee, AvinashPRL 2002

Wave spectrum

-6.0 -4.0 -2.0 0.0 2.0 4.0 6.0

Longitudinal mode6.0

k (mm-1)

ka/-2.0 -1.5 -1.0 0.5 0.0 0.5 1.0 1.5 2.0

Transverse mode

& sinusoidally-excited waves

Mach Cones

Courtesy of Dan Dubin, UCSD

Mach cone angle

C = U Sin U

kSupersonic disturbance

Acoustic wavefronts

Lateral wakeTransverse Wake

Ship’s wake

airWake pattern is

determined bydispersion relation

Mach cone

Lateral & transverse wakes

kHas both features:

• Mach Cone• Lateral & transverse wakes

plasma crystal

Dan Dubin, Phys. Plasmas 2000

Wakes in a dusty plasma

V/CL = 1.17

Mach cone excitation

Nosenko et al. PRL 2002

Speed map for compressional Mach cone

particle speed v (m/s)

The Early History of Dusty Plasmas

• The first observations of a dusty plasma in the laboratory were made by Langmuir.

• He reported these observations on September 18, 1924 at an address at the Centenary of the Franklin Institute in Philadelphia.

• “. . . we have observed some phenomena of remarkable beauty which may prove to be of theoretical interest.”

Langmuir, Found and Dittmer, Science, vol. 60, No. 1557, p 392 (1924)

2 – 4 Torr Argon

tungstenglobules

0.01 -0.1 mm

negativeparticles

Langmuir’s Streamer Discharge

Langmuir’s Observations

• small tungsten ‘globules’ were sputtered into the discharge from the filament

• these globules could be made to move upward and their motions could easily be followed visually

• by concentrating a beam of sunlight into the tube, he could see a ‘very intense scattering’ from the particles

Langmuir’s conclusions

• Langmuir concluded that since the walls of the tube are negatively charged, the particles must also be negatively charged because they do not deposit on the walls

• the negatively charged particles is surrounded by a positive ion shielding cloud

• the negative particles can lose their charge when moving through an ion sheath, and the resulting neutral particles can condense into larger solid particles

formation resulting from graphite sputtering:

• Graphite targets were sputtered by Ar+ in a glow discharge

• Particles grew in the gas phase

• Particles (white) are imaged here resting on the graphite lower electrode

G. Praburam and J. GoreeCosmic Dust Synthesis by Accretion and CoagulationAstrophysical Journal Vol. 441, pp. 830-838, 1995

D. Samsonov and J. GoreeParticle growth in a sputtering dischargeJ. Vac. Sci. Technol. A 1999

Log lambda used in code log_lambda = max([3.,alog(debye_length / max([b_c,b_pi]))]) ; John's ad-hoc Coulomb logarithm ; corresponds to impact parameters ranging from ; the one that causes pi/2 scattering or collection on grain ; whichever is bigger, to the Debye length ; the outermost max function assures a nearly zero log lambda if the ; Debye length is shorter than the other length ; minimum value of 3 is suggested by Tsytovich (private communication)

Formation: gas phaseExplanation proposed for cauliflower shape:

The origin of the bumpy shape has been attributed to columnar growth.

If true, column size will depend on temperature

J.A. Thornton, J. Vac. Sci. Technol. A 11, 666 (1974).

columnar growth, for thin films on a planar surface, using sputter deposition

lo we r e le c tro d e

up p e r e le c tro d e

Gas-phase formation resulting from sputtering:

• Targets were sputtered by Ar+ in a glow discharge• Particles grew in the gas phase

tu rb op um p

g rou nd ed p la te

v acu um v esse lin s id e w all

g as in le t

p ow e rede lec trod e

g ro u n d edelec trod e

la se r sh ee t= 4 88 n m

g ro u n dsh ie ld

formation resulting from sputtering:

partic

le dia

00 50 100 150 200 250 300

tim e (se c )

ensity

Growth of carbon particles, from sputtering graphite in an rf discharge

Particles grownby sputtering titanium

Spherical-shaped primary particles that have coagulated into aggregates consisting of a few spheres.

The surface of theparticles appears smoother than that of the graphite.

Particles grownby sputtering stainless steel

Formation: gas phaseParticles grownby sputtering copper

Particles grownby sputtering

Growth rate varies tremendously, depending on the material

Charging: electron depletion

0.01 0.1 1 10 100 1000

normalized particle number density P

floating potentialof particle

plasma potential

Electron depletion

When the density N of negatively-charged dust is high:

• Dust potential is reduced

• Dust charge is reduced

• Plasma potential is altered

33 /695 cmcmmeV nNaTP

Charging: secondary emission

)/2exp()/(4.7)( mmm EEEEE

Secondary electron emission (electron impact)

For mono-energetic electrons:

Graphite in bulk:m = 1

Em = 400 eV

For small particles, yield is bigger than for bulk, because of bigger solid angles for secondary electrons to escape particle

Goree, Plasma Sources Sci. Technol. 1994 0

0 2 4 6 8 10

E / Em

Charging : secondary emissionSecondary electron emission (electron impact)

For Maxwellian electrons:

Meyer-Vernet* provides formulae for electron current, result:

• Polarity of particle’s charge switches from negative to positive

• Occurs for Te in range 1 – 10 eV, depending on m

Other electron emission processes:• photoemission due to UV (very common in

space)• thermionic emission (uncommon?)

*Meyer-Vernet, Astron. Astrophys. 105,98 (1982)

+ Iion collection

+ Ielectron emission

Charging: charging time

Typically 1 sec for a 1 micron grain in a glow discharge

K= -1510 secfor hydrogen, Te = Ti

Charging time

A particle’s charge:• Can change at a finite rate, as plasma conditions change• Fluctuates randomly as individual electrons & ions are collected

Characteristic time scale is called “charging time, can be defined as:• charge / current of one of the two incident species“floating potential V

Charging: stochastic fluctuationsCharge fluctuations

Stochastic, due to collection of individual electrons and ions at random times

Q 0.5 (Q/e)1/2

0 0 .5 1 .0 1.5 2 .0 2 .5 3 .0

t (m sec)

continuous d iscre te

charging tim e

vv)(/3)/(vvvvEp

v fluid velocity areal mass density

(2D)p pressure (2D)/ kinematic viscosity

(2D) second viscosity (2D)E gas drag

Comparison: experiment & MD simulation

●equilibriumsimulation

▲ non-equilibriumexperiment

this talk

normalized by0.1

1 10 100 1000

coupling parameter inverse temperature 1/T

Wave spectrum

-6.0 -4.0 -2.0 0.0 2.0 4.0 6.0

Longitudinal mode6.0

k (mm-1)

ka/-2.0 -1.5 -1.0 0.5 0.0 0.5 1.0 1.5 2.0

Transverse mode

& theory

Formation: tokamaksDust formation: flaking

J. Winter, Phys. Plasmas 7, 3862 (2000)

dusty plasmas in basic science, astronomy, industry & fusion

transport of dust

various shapes of dust

formation of dustwhat

observation of high

gas phaseparticles grownby

gas phasecauliflower

gas phasegasphase formationg

divertor plasma simulatorsdust

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