15th Topical Conference on RF Power in PlasmasMay 20 –22, 2003 Jackson Hole, Wyoming

Waves and Instabilities inDusty Plasmas

Bob MerlinoUniversity of Iowa

Outline

• What is a dusty plasma?• Where are dusty plasmas?• Charging of dust particles• Waves in dusty plasmas

Dusty Plasmas

• Dust represents much of the solid matter in the universe and this component often coexists with the ionized matter forming a dusty plasma.

• Dust is often present in laboratory plasmas as well either by choice or circumstance.

plasma = electrons + ions Plasma

+

-

+

+

+

+

+

++

- -

-

-

--

-

+

-

What is a dusty plasma?

D

• Debye shielding

small particle of solid matter

• becomes negatively charged

• absorbs electrons and ions

Importance of Charged Dust

the dust acquires an electrical charge and thus is subject to electromagnetic as well as gravitational forces

the charged dust particles participate in the collective plasma processes

DUSTY PLASMASNatural Man-made

1. Solar nebula2. planetary rings3. interstellar medium4. comet tails5. noctilucent clouds6. Lightning7. snow

1. Microelectronic processing

2. rocket exhaust3. flames4. fusion devices5. H bomb

Our solar system accumulated out of a dense cloud of gas and dust, forming everything that is now part of our world.

Rosette Nebula

A flame is a very weakly ionized plasma that contains soot particles.

An early temperature measurement in a dusty plasma.

Comet Hale-Bopp

Spokes in Saturn’s B Ring

Voyager 2Nov. 1980

Cassini-HuygensJuly 2004

Semiconductor Processing System

PUMP

gas

13.56 MHz

substrate

EqE

mg

dust

silane (SiH4) + Ar + O2 → SiO2 particles

Semiconductor Manufacturing

dustSi

Physics TodayAugust 1994

Dusty Plasma

DUST

Dust Charging Processes

• electron and ion collection• secondary emission• UV induced photoelectron

emission

Total current to a grain = 0

Σ I = Ie + Ii + Isec + Ipe = 0

The Charge on a Dust GrainIn typical lab plasmas Isec = Ipe = 0

Electron thermal speed >> ion thermal speed so the grainscharge to a negative potential VS relative to the plasma, untilthe condition Ie = Ii is achieved.

electronrepulsion

ion enhancement

a2

2

exp

1

e Se e

e e

i Si i

i i

kT eVI en am kT

kT eVI en am kT

π

π

=

= −

Q = (4πεoa) VS

Typical Lab Plasma

• For T e = Ti = T in a hydrogen plasma

VS = − 2.5 (kT/e)

• If T ≈ 1 eV and a = 1 µm,

Q ≈ − 2000 e

• Mass: m ≈ 5 × 1012 mp

Dust Charge Measurements

0

0.5

1

1.5

2

0 20 40 60 80 100 120Diameter (micron)

2

0

0.5

1

1.5

0 20 40 60 80 100 120 140 160Electron Energy (eV)

Glass

Graphite

Walch, Horanyi, & Robertson,Phys. Rev. Lett. 75, 838 (1995)

Waves in dusty plasmas

• electrostatic dust ion-cyclotron waves (EDIC)• dust ion acoustic waves (DIA)• dust ion acoustic shocks (DIAS)• dust acoustic waves (DA)• Dust cyclotron mode• Strongly coupled dusty plasmas

Effect of dust on plasma waves

• the presence of dust modifies the characteristics of the usual plasma modes, even at frequencies where the dust does not participate in the wave motion

• the dust provides an immobile charge neutralizing background

i e d dn n Z n= +

Dust Modes

• new, low frequency (~ few Hz) modes in which the dust grains participate in the wave motion appear in the dispersion relations

• the dust dynamics can be observed visually since the dust motion can be imaged and recorded on tape

Quasineutrality in dusty plasmas

• For low frequency waves the condition holds in both zero and first order i e d dn n Z n= +

• defining: we characterize the

dusty plasma using the quantity

which is the fraction of negative charge on

the dust grains

do ion nε =

dZε

Fluid theory of Low frequency electrostatic waves in dusty plasmasThree component plasma: electrons, ions, negative dust

. ( ) 0

. ( )

( ) 0. i e d d

nI n vt

vII n m n m v v q nt

q n v BIII n n Z n

αα α

αα α α α α α α α

α α α

ϕ

∂+∇⋅ =

∂∂

+ ⋅∇ + ∇∂

− × =

= +

New Phenomena in Dusty Plasmas

• Unlike ordinary plasma, or plasmas containing negative ions, the charge on a dust grain is not constant, but fluctuates with the local plasma potential.

• This leads to new damping effects and new mechanisms for wave growth.

Fluid theory: mode frequencies

• for ion and electron modes we treat the dust as an immobile negative background

• for dust modes we can neglect the electron and ion inertia terms

• For excitation conditions (growth rates, critical drifts, etc.) we must use kinetic theory

Dust Ion Acoustic Mode

• DIA: ion-acoustic wave modified by dust

• Dispersion relation:

( )

12

|| 1i e

pi i d

kT kTvK m m Z

CDIA

ωε

= = +

−

= εΖ0 1

vp

DIA – Kinetic TheoryDust acoustic waves are normally heavily Landau dampedin a plasma with Te = Ti. However the presence of negativelycharged dust can drastically reduce the damping.

1 312 22 2

8

11

e

i

TTe e

ri i

d

m T em T

Z

δπγ ω δ δ

δε

− = − +

==

- γ

εZ

Dust Ion Acoustic Wave Experiment

LANGMUIRPROBE

Ta Hot Plate rotating dustdispenser

end plate

probe

K oven

1.0

1.1

1.2

1.3

1.4

1.5

PHA

SE V

ELO

CIT

Y

0 0.5 1εZ d

(a)

DIA

phas

e sp

eed ki/kr

0.0

0.5

1.0

Ki/K

r

0 0.5 1εZd

DIA

(b)

DIA - Conclusion

• Ion acoustic waves which would otherwise not propagate in a plasma with Te = Ti can propagate in a plasma with a sufficient amount of negatively charged dust.

• In the presence of negative dust, the wave phase velocity increases, decreasing the effect of ion Landau damping.

Experimental setup

CsHP

LP

Dust Dispenser

(a)G

PG

Rotating

EPB

(b)n

z

DIA Shocks – results

DIA Shocks – results

EDIC: fluid theory• Electrostatic ion-cyclotron waves excited by electron current

along the magnetic field

• Propagate at large angle to B

2 2

2 2

2

2

(1i e

cii i d

c Di IA

kT kTKm m Z

K C

ωε⊥

⊥

= Ω + + −

= Ω +

Electrostatic dust ion-cyclotoninstability (EDIC)

EDIC- kinetic theory results

1/(1 )dZδ ε= −v d

e/vet

h

• EIC instability driven bycurrent along B

• As more negative charge iscarried by the dust, thecritical drift needed to excite the instabilitydecreases

• the instability is easier toexcite in a dusty plasma

V. W. Chow & M. Rosenberg, Planet. Space Sci. 44, 465 (1996)

Dust acoustic waves( ) 0

0

0; 0

d d d

d d dd d d d d d

ee e

e d d

n n vt x

v v nm n v kT eZ nt x x x

n nkT en kT enx x x x

n n Z n

ϕ

ϕ ϕ++ +

+

∂ ∂+ =

∂ ∂∂ ∂ ∂ ∂ + + − = ∂ ∂ ∂ ∂

∂ ∂∂ ∂− = + =

∂ ∂ ∂ ∂

= +

Dustdynamics

Quasineutrality

Electrons& Ions

Combining the dust momentum equation with the plasma equations we see that (for the case of cold dust, Td =0).

( )dd d e

vm n p px x +

∂ ∂= − +

∂ ∂where pe + p+ is the total pressure due toelectrons and ions.

In the dust acoustic wave the inertial isprovided by the massive dust particles and the electrons and ions provide the restoring force

DA Dispersion relation

Monochromatic plane wave solutions for Te = Ti = T

11DA d

d

kTf C Zm

ελε

−= =

+

dust masswhere ε = ndo/n+o

DUST IN A GLOW DISCHARGE

N2

Vacuumvessel

PS

+

BAnode

Dust Tray

Anode Glow Plasma

Dust: kaolin (aluminum silicate)

E

Levitated Grains

QE

mg

Dust Acoustic Wave Image

wavefronts

DAMovie

Dust Acoustic WaveDispersion Relation

theory0

4

8

12

16

0 50 100 150 200ω (s-1 )

K (c

m-1

)

Electrostatic dust cyclotron mode

• EDIC – involves cyclotron motion of the dust – magnetized dust

• Dispersion relation:

2 2 2 2

2 2 2

11 ( / )(1 )

dcd d

d i e d

cd DA

kTK Zm T T Z

K C

ω εε⊥

⊥

= Ω + + + − = Ω +

Gyroradius of dust particles

d dd

d

m vreZ B

=

3, , dd d d

d

kTm a Z a vm

∝ ∝ =

12

dr a∝

Gyroradius of dust particles

0.01

0.1

1

10

0.001 0.01 0.1 1 10

[Td=0.025 eV][Td=1.0 eV][Td = 0.1 eV]

dust radius (microns)

B = 800 G

Solid state dusty plasmas

In a typical plasma2 2 4 1o

d

e Z dkTπε

Γ = <<

• In a dusty plasma the interaction energy is multiplied by which can be very large, so that Γ > 1 is possible

2dZ

• The dust grains may thenarrange themselves in aregular lattice.

Coulomb CrystalJohn Goree – Univ. Iowa

triangular lattice with hexagonal symmetry

Waves in strongly coupleddusty plasmas

• The presence of short scale correlations gives rise to novel modifications of the collective behavior

• Both compressional and transverse shear waves are possible

Compressional and shear waves

Summary/Conclusions

• Dusty plasmas are not uncommon in the lab and are ubiquitous in the Universe

• Presence of dust modifies both the excitation and propagation of plasma waves

• New, very low frequency dust modes • Collective fluctuations in dusty plasmas

may provide mechanism for structuring