Measurement of the Charge of a Particle in a Dusty Plasma

Jerome Fung, Swarthmore College

July 30, 2004

Introduction• What is a dusty plasma?

• Why do we care about dusty plasmas?

• Making dusty plasma crystals

• The importance of electric charge

• Theory: Vertical resonance methods

• Preliminary results

• Sound speed methods

What is a plasma?• Plasma: ionized gas

– Contains positive ions, negative electrons, and neutral particles

– 4th state of matter: hotter than gases– Most abundant state of matter in the universe:

found in stars, fluorescent light bulbs!

High Voltage

CathodeAnode Low Pressure Gas

P L A S M A

plasma = electrons + ions Plasma

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- -

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What is a dusty plasma?

small particle of solid matter

• becomes negatively charged

• absorbs electrons and ions

& neutral gas

Solar system• Rings of Saturn• Comet tails

Fundamental science• Coulomb crystals• Waves

Manufacturing• Particle contamination

(Si wafer processing)

Who cares about dusty plasmas?

Dusty Plasma Crystals

• Small (micron-sized) particles in plasma disperse into 2-D lattice

• Exhibits properties of solid crystal– Order of crystal lattice

Making Dusty Plasma Crystals

Argon RF plasma

20 mTorr

8 - 20 W

Polymer microspheres

diameter 8.09 0.18 m

Voilà!

Particle Interactions and Forces

• Electrostatic ( Fe = q E )– Levitating sheath electric field– Horizontal particle confinement– Interparticle interactions

• Gravitational ( Fg = m g )

• Ion drag force, gas drag, thermophoresis

qE

mg

∑F = 0

Charge matters!

• Electrostatic force is the most significant– Many interactions, all depend on q– Most experiments/theory require knowledge of q

• Measurement techniques– Vertical Resonance (Melzer et al., Phys. Lett. A

191,1994)– Variation of vertical resonance (Goree)– Sound speed methods

• Natural phonons• Laser-induced longitudinal / transverse waves

Vertical Resonance Method• Key idea: modulate levitating RF electric field to “shake”

crystal up and down, measure amplitude of oscillation– In practice, modulate voltage on electrodes– View oscillations via side view video camera

• Observe resonance measure resonance frequency ⇒ ⇒determine particle charge!

Vertical Resonance: Theory

Damped, driven oscillator equation:

€

m˙ ̇ x = qE(x, t) − mg − mβ ˙ x

Resonance frequency:

€

ωo2 =

qnie

mεo

ni = plasma ion density (ions/unit volume)

Vertical Resonance: Issues• Original method: requires measurement of ion

density– Must be measured with a Langmuir probe in the bulk

plasma, above the sheath– Problem: method requires extrapolation of ion density in

bulk plasma to sheath– Large uncertainties in q, ~50% in original papers

• Modified method– Does not require ion density measurement– Makes assumption about the variation of the sheath

electric field, which has been tested experimentally– Should result in smaller uncertainties

Preliminary Results: Resonance Curve

ni ≈ 2 × 1015 m-3

ωo/2π = 10.08 ± 0.01 Hz

m ≈ 4.2 × 10-13 kg

q ≈ 3000 e

0

0.2

0.4

0.6

0.8

1

1.2

0 5 10 15 20

Resonant Response: July 08

Frequency (Hz)

Vertical Resonance: Variation• Assumes linear dependence on height for the electric field in the sheath• Uses more easily measured quantities (e.g. plasma potential) instead of ion density

q ≈ 9000 e

Sound Speed Methods

• Charge determined from material properties of plasma crystal

• Natural phonons

• Laser-induced pulses– Longitudinal– Transverse

Longitudinal Pulse

QuickTime™ and aDV/DVCPRO - NTSC decompressor

are needed to see this picture.

Conclusions

• Knowing charge necessary for lots of interesting experiments / theory with dusty plasma crystals

• Charge measured with 2 vertical resonance methods

• Further analysis of data from these methods and from sound speed methods is ongoing

Acknowledgements

This project would not have been possible without the advice and assistance of Dr. Bin Liu and my advisor, Prof.John A. Goree.

Several useful discussions with V. Nosenko and K. Pachawere also had.

Work supported by an NSF REU grant.