Waves in a 2D Dusty Plasma Crystal

J. Goree S. Nunomura, V. Nosenko

Univ. of Iowa

Work supported by DOE, NASA, NSF

electrons + ions = plasma Plasma

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What is a dusty plasma?

D

• Debye shielding

small particle of solid matter

• becomes negatively charged

• absorbs electrons and ions

Solar system• Rings of Saturn• Comet tails

Basic physics• Coulomb crystals• Waves

Manufacturing• Particle contamination

(Si wafer processing)

• Nanomaterial synthesis

Who cares about dusty plasmas?

9 0 9 1 9 2 9 3 9 4 9 5 9 6 9 7 9 8 9 9 *

*1999 publications are morenumerous than shown here.At the time this figure was prepareddata was available onlyfor Jan - Oct. 1999

0

80

1609 months data

in 1999

Dusty plasma publications in APS & AIP journals

Gas

Ar, 15 mTorr

RF plasma

capacitively-coupled

13.56 MHz

20 W

Te = 2.6 eV

ni = 1.271015 m-3

Polymer microspheres

diameter 8.69 0.17 m

Experimental conditions

Modified GEC chamber

top-viewcamera

laser illumination

side-viewcamera

vacuum chamber

Big upper window, no upper electrode

Forces Acting on a Particle

Coulomb • trapping potential • inter-particle particle radius1

Gravity

particle radius3

Radiation pressure from laser beam

particle radius3

Laser manipulation of particles

= push the particles with an Ar laser beam

Electrostatic trapping of particlesEquipotentialcontours

electrode

electrode

positive

potential

electrode

electrode

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

Without gravity, particles fill 3-D volume

QE

mg

Particle confinement

– Particles repel each other

– External confinement by natural electric fields present in plasma

Laboratory results:

monolayer with 19 particles

view from top camera

Laboratory results:

monolayer with 948 particles

particles triangulation

view from top camera

triangular (hexagonal) lattice

separation a mm

Laboratory results:

monolayer with many particles

Compressional and shear waves

Dispersion relation (phonon spectrum)

0

0.5

1

1.5

2

2.5

3

3.5

0 2 4

wavenumber ka/

Fre

quen

cy

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

compressional

shear

02 = Q2 / 40 m a3

/k = shear sound speed

/k = compressional sound speed

• The shear wave is:– slow– propagates only in a solid

• The compressional wave is:– fast– propagates in solids & liquids

Compressional & shear waves

• Pulse propagation

• Sine wave excitation

Here, we show two kinds of experiments

Data analysis method

• Trace particle orbits

• Calculate particle velocity, number density

• Get top view images of the lattice

• Determine particle positions

Particle Manipulation with Ar laser

chopper

Ar laserbeam

scanningmirror

chopper

Ar laserbeam

scanningmirror

chopper

Ar laserbeam

scanningmirror

chopper

Ar laserbeam

scanningmirror

4 mm 4 mm/sx

y

t = 0.1 s 0.4 s 0.7 s 1.0 s

LASER EXCITATION

Velocity map for pulse propagation

0 1 2 3 40

10

20

30

40

k (mm-1)

0=15.1s-1

/a = 4.05 mm-1

Closed symbol: krOpen symbol: ki

0 1 2 3 40

10

20

30

40

k (mm-1)

0=15.1s-1

/a = 4.05 mm-1

Closed symbol: krOpen symbol: ki

Dispersion relations for sinusoidal excitation

Experiment: S.Nunomura et al. PRL 2001

Theory: Wang et al. PRL 2001

Compressional wave Shear wave

Summary

• 2D plasma crystals

• Laser manipulation of particles

• Excite shear wave & compressional waves

• Measure dispersion relation, compare to theory

HeNe laserhorizontalsheet

video camera(top view)

micro lens

lower electrodeRF

microspheres Ar laserbeam

servoamp

funcgenscope

framegrabber

scanningmirror

to chopper

chopper

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Experimental setup