Measurement of the Charge of a Particle in a Dusty Plasma

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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!

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What is a dusty plasma?
neutral gas
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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
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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

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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
Resonance frequency
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
?o/2p 10.08 0.01 Hz
m 4.2 10-13 kg
q 3000 e
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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
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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. Pacha were
also had. Work supported by an NSF REU grant.