dusty plasmas in basic science, astronomy, industry & fusion john goree the univ. of iowa

Dusty plasmas in basic science, astronomy, industry & fusion

John GoreeThe Univ. of Iowa

The growth of dusty plasmas as a field of research

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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 charge

4. Forces acting on dust

5. 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

Radiological

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

Fire & chemical explosion

Hydrogen:• stored in dust• released during accidental exposure to:

• air• steam

• ITER safety limit: 6 kg dust allowed on hot surfaces

Phil SharpeFusion Safety Program, Idaho National Laboratory

Dust in Fusion Plasmas Workshop2005

What is dust?

Formation of dust

1. What is dust?


3. Dust charge




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: tokamaks

Tungsten 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

2 m

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

Ion Energy: 15 eVTime: 104 s

Dust

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 industry

Particles 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 phase

Gas-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)


Gas-phase formation

G. Praburam and J. GoreeAstrophys. J 1995


Cauliflower particles grow in the gas phase:

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

intact fractured


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

1. What is dust?


3. Dust charge




Charging: mechanisms

Charging by collecting electrons and ions only

negative charge

Ielectron collection

+ Iion collection

H+

e-

_

Goree, Plasma Sources Sci. Technol. 1994


+ Iion collection

+ Ielectron emission

H+

e-

e- +

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

positive charge


Particles 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

C = a

is capacitance of sphere of radius a

H+

e-

e-

a

surfacepotential V


Charging 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 m

Charge: Q = - 1737 eGoree, Plasma Sources Sci. Technol. 1994


+ Iion collection

H+

e-

_

Forces

1. What is dust?

2. Formation of dust• Fusion• Industry• Astronomy• Pure physics

3. Dust charge


5. Some pure physics experiments:• Strongly-coupled vs. Weakly-coupled


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)

Glow

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

1

10

0.01 0.1 1 10 100io

n d

rag

forc

e,

norm

aliz

ed

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

V-2

V

V2

Ion drag force

0.1

1

10

100

1000

0.01 0.1 1 10

ion

dra

g fo

rce

, no

rma

lize

d

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

1.442

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

3

4

Gas drag force

Stokes-flow regime

Radiation pressure force

Radiation pressure

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

c

IaqF laser

laser

2

incident laser

momentum imparted to microsphere

transparent microsphere

c

IaF laser

radiation

2

Physics experiments

1. What is dust?

2. Formation of dust• Fusion• Industry• Astronomy• Pure physics

3. Dust charge


5. Some physics experiments:• Microgravity conditions• Strongly-coupled vs. Weakly-coupled


Physics experiments

Remainder of this talk:

All experiments performed with polymer microspheres

EquipotentialContours (RF glow discharge)

electrode

electrode

positive

potential

electrode

electrode

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

Without gravity, particles fill 3-D volume

QE

mg

Microgravity conditions


To obtain a 3D dust suspension, use zero g conditions:

Parabolic flights, NASA KC-135


video


“strongly coupled”

dusty plasma: Q big

star interior: r small

pure-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

Tk

rQ

B

02 4/

energy kinetic particle

energy potential cleinterparti

Coulomb coupling parameter:

Physics experiments

Next:

Waves in a weakly-coupled dusty plasma

Parameter:gas: Argonp = 1.0 .. 2.5 Pan

i = 1015 m-3

B = 20 .. 80 mT

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

particles

anodic plasma

anode

3 cm

RF-discharge

camera

dust tray

plasma column probes

Anode:U

A = 50 .. 100 V

IA = 3 .. 12 mA

Dusty Plasma Research, A. Piel, 2005 41

Courtesy Alexander Piel, Kiel University, Germany, 2005

Dust acoustic wave experiment: Kiel Univ.

15 mm

Time lapse 1:10p = 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

Next:

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

RF

m icros pheres

VCR

yx

Ar laserbeam 1

Ar laserbeam 2

m od ulator

scanningm irrors

m od ulator 1

scanningm irrors

vide o cam e ra(side 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 particle

i.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

-6

-4

-2

0

2

4

6

-5 0 5

distance y (mm)

par

ticle

vel

ocity

vx (

mm

/s)

Plaser

= 3.41 W

2.00 W

1.44 W

1.04 W

0.82 W


Navier-Stokes equation

vv)(/3)/(vvvv

Ept

21

v fluid velocity areal mass density

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

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

0)(v)(v

2

2

ydy

ydx

Ex

Navier-Stokes equation reduces to:

kinematic viscosityE gas drag coefficient

Our experiment:

2D

/t = 0

/x = 0

vy = 0


Velocity profiles fit to Navier-Stokes

-6

-4

-2

0

2

4

6

-5 0 5

distance y (mm)

par

ticle

vel

ocity

vx (

mm

/s)

Plaser

= 3.41 W

2.00 W

1.44 W

1.04 W

0.82 W

Results: viscosity vs. inverse temperature

0

1

2

3

4

100 1000

kin

emat

ic v

i sco

sit y

(

mm

2/ s

)

coupling parameter

y

0.36

0.53

0.42

r / w D

water at STP (3D)

high temperature

viscosity hasa minimum

low temperaturey 1/Ty

Physics experiments

Next:

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

Fre

quen

cy

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

0

1

2

3

0 2 4

wavenumber ka/

acoustic limit

compressional

shear

Wave dispersion relation – 2D triangular lattice

Longitudinal wave

4mm

k Laser incident here

f = 1.8 Hz

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

Random particle motion

No Laser!

4mm

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

Wave spectrum

-6.0 -4.0 -2.0 0.0 2.0 4.0 6.0

6.0

4.0

2.0

0.0

Longitudinal mode6.0

4.0

2.0

0.0

k (mm-1)

f (H

z)f (

Hz)

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

/

0

3.0

2.0

1.0

0.0

4.0

/

0

3.0

2.0

1.0

0.0

4.0

5

10

15

En

erg y

den

s ity

/ k B

T (

10-

3m

m2s)

k

a

= 0°

Transverse mode

& sinusoidally-excited waves


Mach Cones

Courtesy of Dan Dubin, UCSD

Mach cone angle

C = U Sin U

kSupersonic disturbance

Acoustic wavefronts

cone


Lateral wakeTransverse Wake

Ship’s wake

k


water

air

Wake pattern is determined bydispersion relation

Mach cone

Lateral & transverse wakes

k

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)

A

2 – 4 Torr Argon

tungstenglobules

0.01 -0.1 mm

negativeparticles

C

S

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


Gas-phase 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)


Explanation 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 o p um p

g ro u n d ed p la te

v acu u m v esse lin s id e w all

g as in le t

p o w e rede lec tro d e

g ro u n d ede lec tro d e

lase r sh ee t= 4 88 n m

4 c m

g ro u n dsh ie ld


Gas-phase formation resulting from sputtering:


dus

t pa

rtic

le d

iam

ete

r (nm

)

100

400

300

200

00 50 100 150 200 250 300

tim e (se c )

10 6

10 7

10 8

10 9

10 10

dus

t num

be

r de

nsity

(cm

-3)

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



Particles grownby sputtering copper




Particles grownby sputtering

Growth rate varies tremendously, depending on the material

Charging: electron depletion

0.01

0.1

1

10

0.01 0.1 1 10 100 1000

pote

ntia

l (n

orm

aliz

ed b

y el

ectr

on te

mpe

ratu

re)

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:

Yield

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


0

0.2

0.4

0.6

0.8

1

1.2

0 2 4 6 8 10

yie

ld

/

m

E / Em

Charging : secondary emission

Secondary 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

H+

e-

e- +

Charging: charging time

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

3

cmm

eV

na

TK


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 fluctuations

Charge fluctuations

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

Q 0.5 (Q/e)1/2


-20

-15

-10

-5

0

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

t (m sec)

continuous d iscre te

char

ge n

um

be

r N

charging tim e


vv)(/3)/(vvvv

Ept

21

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

a

Q

0

2

2

normalized by0.1

1

1 10 100 1000

norm

aliz

ed k

inem

atic

vis

cosi

ty

coupling parameter inverse temperature 1/T

Wave spectrum

-6.0 -4.0 -2.0 0.0 2.0 4.0 6.0

6.0

4.0

2.0

0.0

Longitudinal mode6.0

4.0

2.0

0.0

k (mm-1)

f (H

z)f (

Hz)

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

/

0

3.0

2.0

1.0

0.0

4.0

/

0

3.0

2.0

1.0

0.0

4.0

5

10

15

En

erg y

den

s ity

/ k B

T (

10-

3m

m2s)

k

a

= 0°

Transverse mode

& theory


Formation: tokamaks

Dust formation: flaking

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

dusty plasmas in basic science, astronomy, industry & fusion john goree the univ. of iowa

Documents

dust dust grains

dust charge

transport of dust

source of dust

fusion radiological

various shapes of dust

gas phase gasphase formation

idaho national laboratory