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Experiments on ShocksExperiments on Shocksand Dust Structuresand Dust Structures

in Dusty Plasmasin Dusty Plasmas

Robert L. Merlino, Jonathon R. Heinrich, Robert L. Merlino, Jonathon R. Heinrich, Su-Hyun Kim and John K. MeyerSu-Hyun Kim and John K. Meyer

Department of Physics and AstronomyDepartment of Physics and AstronomyThe University of Iowa, Iowa City, Iowa, USAThe University of Iowa, Iowa City, Iowa, USA

Supported by US DOE and NSFSupported by US DOE and NSF

39th EPS Conference & 16th Int. Congress on Plasma PhysicsStockholm, Sweden, July 2-7, 2012

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1. Introduction to dusty plasmasa. What are they

b. Where are they

c. How do you make a dusty plasma

2. Dust acoustic wave

3. Dust acoustic wave experimentsa. Nonlinear dust acoustic waves

b. Dust acoustic shock waves

c. Self-organization in a dusty plasma

4. Conclusions

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Dusty plasma basics

• A four component system, consisting of electrons, ions, neutral atoms and micron size solid dust grains

• The grains are charged by collecting electrons and ions

• The grain acquires a negative chargesince ve > vi

• Dust is floating, so Ie + Ii = 0 Vf ( dust floating potential)• Charge: Qd = Cd Vf = (4oa)Vf

• If the grain radius a = 1 m, Te = 100 Ti = 2.5 eV (Ar) Qd ~ 4000 e.

• Charged dust interacts collectively with the plasma, but on a much longer timescale, 1/pd

PLASMA

D

a

• Properties of dusty plasmas– Dust radius a << D

– md ~ 1012 mp, Qd ~ (103 – 104) e

– (Q/m)d ~ 1; while (e/mp) ~ 108

– Gravity, electric, and ion drag forces important

• Occurrence of dusty plasmas– Comet tails– Planetary rings– Solar and planetary nebulae– Lower ionosphere (mesosphere)– Atmospheric lightning– Industrial plasma processing devices– Magnetic fusion devices 4

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Examples of dusty plasmasNoctilucent clouds formed in the summer mesosphere at75-80 km altitude range; 100 nm water ice, charged

Charged dust clouds aroundsilicon wafers, formed in aplasma processing device; aserious contamination issue

Dusty plasma of charged icecaused by the Space Shuttleengine exhaust

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Spokes in Saturn’s B ring discovered by the Voyager 1 spacecraft

Micron-size particles thought to be lifted electrostatically above the ring plane

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Simple dusty plasma device

• dc or rf glow discharge plasma at 300 – 400 V• argon gas at p ~ 100 - 200 mTorr (10-30 Pa)• micron size glass spheres, but any powder works• image dust using laser and video camera• for a 1m particle, Qd E = md g with E ~ 1 V/cm

QdE

mdg

GAS

anodeanodetrapped

dust

dust trayg

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Dust Acoustic WavesVery low (few–tens Hz) frequency compressional dust density waves

o treat dust as a fluid of charged particles (Shukla, Capri 1989)o electrons and ions are treated as massless Boltzmann response

( , )( , )

cold dust: (1)

electrons and ions: 0 (2)

charge neutrality: (3)

d dd d d d d

e ie i

i e d d

v vm n v eZ n

t x x

pen

x xn n Z n

, and e i d dd d d

d d d

p p n vv v nm n v

t x x t x

(nonlinear) Euler equations for an invicid fluid shock solutions

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Dispersion relation • Linearize (1) and (2) and the continuity equation for the dust, with first order quantities, nd1, vd1, and 1:

• Combine with quasineutrality condition to obtain, by elementary calculation

• DA speed:

2

1/ 22 21 1, whered D

d D Di De Dio

eZn

2 21 1

2 2 2 2

1d d

pd D

n n

x t

20

0

d d ida pd D

i d

n Z kTCk n m

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Dust acoustic wave excitation:ion-dust streaming instability

11 3

15 3

1

0.5 , 2000, ~ 10

40, ~ 10 , 2

1.26 , 5

Parameters: d d d

i i e

r m Z n m

A n m T eV

k mm mm

P = 100 mtorr E0 = 100 V/m

Include ion drift and collisions in fluid theory

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Dusty plasma device

Dust: silica microspheres (1 mm diameter)Plasma: argon, 10 – 20 Pa, ni ~ 1015 m3, Te 100 Ti 2-3 eV

CMOSCamera

Top View

B

Dust Tray

532 nmLaser

Plasma

B

Side View

Anode

g

Lens

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A spontaneously exciteddust acoustic wave

1 cm

anodeanode

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Dust acoustic waves reach high amplitudes(non-linear) with waveforms having sharp

crests and flat troughs

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2nd order (Stokes) wave theory

01 02( , ) cos( ) cos 2x t kx t kx t

Products of 1st order quantities

Nonlinearity generates 2nd harmonic term

• Perturbation analysis: expand (n, v, ) as a series in the small parameter, to second order:

• Insert into momentum and continuity equations

2nd order quantities

SOLUTION

2 2 2 2 2 22 2 1 1

2 2 2 21d d d d

da

n n n nA B

x tx C t x

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Nonlinear dust acoustic wave

)](2cos[)cos()0,( 0201 kxkxx

Second order wave theory can account, qualitatively, for the nonlinear dust acoustic waves.

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Dust Acoustic Shocks• The experimentalsetup was modifiedby adding a slit infront of the anode.• The slit producesa nozzle-like potentialconfiguration that favorsthe formation of highly-compressed dust densitypulses.

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SLIT

ANODE

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Steepening of nonlinear DAW into Dust acoustic shocks

THEORY Shuklaand

Eliasson2012

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Shock position, amplitude, thickness

• The shock speed, VS 75 mm/s, so that VS / Cda T1, where Cda is the dust acoustic speed, so that M T 1.• The shock steepens as it propagates, finally reaching a steady-state width T the interparticle spacing

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Large amplitude dust acoustic shocksP. K. Shukla and B. Eliasson

arXiv:1205.5947v1, (submitted to PRL)

• Fully nonlinear theory of arbitrary amplitude DA shocks taking into account strong coupling effects, polarization force, dust collisions with neutrals, dust fluid shear and bulk viscosities

• Use the generalized hydrodynamic equations

visco-elasticrelaxation time

polarizationforce term

viscosityeffects

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Scaling of amplitude and thickness• The Shukla/Eliasson (SE)

theory reproduces the evolution of the shock speed, amplitude and width.

• Theory uses a model for viscosity that depends on coupling strength

• By comparing the theory and exp. Shock profiles, a value for the kinetic viscosity can be obtained: 20 mm2/s

Experiment

Theory

pdT t

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Collision of 2 shock waves

Space-time plots

Amplitudes

A unique property of shock waves is the fact that when a faster shock overtakes a slower shock,

they combine into a single shock.

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Structurization in dusty plasmasG. Morfill & V. Tsytovich, Plasma Phys. Rep. 26, 727,2000

• Dusty plasmas are susceptible to the spontaneous formation of self-organized structures: dust clumps separated by dust voids

• The constant flux of plasma on the dust particles must be balanced by an ionization source (open system)– may give rise to ionization instabilities,

– coupled with the ion drag force

• Structurization may evolve from non-propagating dust acoustic waves

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Ionization /ion drag instability

1. A fluctuation decreasesthe dust density in region

2. Less absorptionof electrons leadsto higher electrondensity in region

3. More electrons leadsto higher ionization rate,further increasingplasma density

4. Increase in ion densityleads to more dust beingpushed out of region bythe ion drag force VOID

void

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Non-propagating DA waves

I. D’Angelo (PoP 5, 3155, 1998)included the effects of ionizationand the ion drag force onDA waves.

0

r i

Ion Drag Coefficient

s1

II. Khrapak et al., (PRL 102, 245004, 2009) included the effect of the polarization force on DA waves. The polarization force is due on dust is present when there is a non-uniform plasma background, so that

the dispersion relation then becomes where depends on the polarization force. When > 1, a purely growing instability is found.

2 2( ) 2D D pol d D Dr F Q

1dak C

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Dust structurization

• For discharge currents ~ 1-10 mA, propagating DAWs are excited

• For currents > 15 mA, the dust cloud is spontaneously trans-formed into nested conical regions of high and low dust density that are stationary and stable

• This phenomena was observed with various types and sizes of dust and in argon and helium discharges

• Heinrich et al., PRE 84, 026403, 2011

1 cm

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Stationary Dust Structures

1 cm

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3D Views

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Summary

• In 2014, it will be 25 years since Padma Shuklasuggested the existence of the DA wave at the1st Capri Workshop on Dusty Plasmas.

• The DA wave continues to be studied both theoretically and experimentally, with several papers appearing each month examining various aspects of this basic dust mode.

• This talk has focused on two aspects of the DA wave– Nonlinear DA waves and shocks– Spontaneous structure formation in dusty plasmas

• The interest in the DAW derives from its importance in space, laboratory, and astrophysical dusty plasmas as a mechanism for triggering dust condensation and structrurization.

Lunar Dust Acoustic Waves• In January 2012, NASA plans to launch the

LADEE mission (Lunar Atmosphere and Dust Environment Explorer).

• One of the purposes of this mission is to study the nature of the dust lofted above the lunar surface and reported by the Apollo astronauts as “moon clouds”

• It is conceivable that dust acoustic waves could be observed, in situ, in the moon clouds.

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