measurement of the charge of a particle in a dusty plasma jerome fung, swarthmore college july 30,...
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![Page 1: Measurement of the Charge of a Particle in a Dusty Plasma Jerome Fung, Swarthmore College July 30, 2004](https://reader036.vdocument.in/reader036/viewer/2022062313/56649d555503460f94a31ef9/html5/thumbnails/1.jpg)
Measurement of the Charge of a Particle in a Dusty Plasma
Jerome Fung, Swarthmore College
July 30, 2004
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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
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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
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plasma = electrons + ions Plasma
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What is a dusty plasma?
small particle of solid matter
• becomes negatively charged
• absorbs electrons and ions
& neutral gas
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Solar system• Rings of Saturn• Comet tails
Fundamental science• Coulomb crystals• Waves
Manufacturing• Particle contamination
(Si wafer processing)
Who cares about dusty plasmas?
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Dusty Plasma Crystals
• Small (micron-sized) particles in plasma disperse into 2-D lattice
• Exhibits properties of solid crystal– Order of crystal lattice
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Making Dusty Plasma Crystals
Argon RF plasma
20 mTorr
8 - 20 W
Polymer microspheres
diameter 8.09 0.18 m
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Voilà!
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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
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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
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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!
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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)
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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
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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)
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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
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Sound Speed Methods
• Charge determined from material properties of plasma crystal
• Natural phonons
• Laser-induced pulses– Longitudinal– Transverse
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Longitudinal Pulse
QuickTime™ and aDV/DVCPRO - NTSC decompressor
are needed to see this picture.
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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
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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.