Transverse oscillations in a singlelayer dusty plasma under microgravity

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Transverse oscillations in a single-layer dusty
plasma under microgravity
B. Liu J. Goree The University of Iowa V.E.
Fortov, A.M. Lipaev, V.I. Molotkov, O. F.
Petrov Joint Institute for High Temperatures,
Russian Academy of Sciences, Moscow, Russia G.
E. Morfill, H. M. Thomas, H. Rothermel, A.
Ivlev Max Planck Institute for Extraterrestrische
Physik, Garching, Germany
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Goal

• Observe out-of-plane transverse motion
• in a single-layer dusty plasma
• under microgravity
• Identify possible driving damping mechanisms
  for the motion

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Out-of-plane transverse motion under gravity

• Particles oscillate in a potential well formed by
  gravity and electric force
• A transverse wave arises from the interactions
  between particles

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Motivation
Previous work
Simulations crystal Qiao Hyde, PRE
2003 liquids Donko, Hartman Kalman, PRE 2004
Theory crystal Vladimirov, Yaroshenko
Morfill, Phys. Plasmas, 2006
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Out-of-plane transverse motion under gravity
Dispersion relation
Small k optical-like mode negative
dispersion Large k positive dispersion
Vladimirov, Yaroshenko, Morfill, Phys. Plasmas,
2006
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Ion drag force
Momentum is imparted to the particle
_
Orbit force Ion orbit is deflected
Collection force Ion strikes particle
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Formation of void

• Ion drag pushes particles outward
• balanced by an inward electric force
• produces a particle-free region, i.e., void

particles
Ionization source Positive plasma
potential Outward ion flow
void
J. Goree, G. E. Morfill, V. N. Tsytovich S. V.
Vladimirov PRE 1999
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Thermophoretic force
cold gas
Particles are pushed toward regions of cold gas
Fthermophoretic
hot gas
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Single-layer dusty plasma under microgravity

• A single-layer dusty plasma
• formed at a voids edge
• balance of three forces
• electric
• ion drag force
• thermophoretic (small)

ÑTgas
thermo- phoretic
QE
ion drag
side view
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Plasma chamber of PK-3 Plus

• RF power is applied symmetrically to the two
  electrodes (push-pull configuration)
• Cameras view through side windows.

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Experiment parameters
rf power 13.56 MHz 43.8 VPP gas neon 0.12
torr Tgas 301 K particle 6.81 mm diameter
ÑTgas 0.047 K/cm
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Image overview camera
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Real time movie high-resolution camera
25 frames/sec Our results are based on this video
the z direction is out-of-plane compared to the
single layer
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What we measure

• Deinterlacing smooth raw image
• Particles
• measure x,z position
• trace from frame to frame
• calculate vx,z velocity

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Kinetic temperature
Results
Calculate mean-square velocity fluctuation as
temperature
Tx 312 K Tz 287 K
particle
gas
Tgas 301 K
Conclusion Tparticle Tgas Þ Driving force
is mainly Brownian motion due to gas atoms
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Wave spectrum calculation
For a given wave number kx

• Calculate time series of currents

transverse (out-of-plane)

• Perform FFT, yielding

Repeat the above for various kx, combine to yield
a wave spectrum

• wave intensity as a function of kx and w
• plotted with color indicating intensity

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Wave spectrum result
Wave energy is concentrated in a frequency band
20 lt w lt 40 s-1 independent of wave number
wave spectrum
Frequency content, but no conspicuous dispersion
relation
Compare to theory simulations Similar
optical-like mode Different no dispersion
observed
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Power spectrum
wave spectrum
power spectrum
fit to damped-driven harmonic oscillator (white
noise)

• Averaging wave spectrum over all wave numbers
  yields a power spectrum
• Fitting power spectrum yields the damping rate

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Damping rate
in the molecular-flow regime, Epstein
drag Ngas gas number density a particle
radius V relative velocity of particle gas
Results from fitting power
spectrum Epstein prediction
n 24 s-1
nE 17.6 1.8 s-1
Þ Gas friction accounts for most of the observed
damping
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Summary

• A single-layer suspension was observed under
  microgravity conditions
• Confinement of the single layer is attributed to
  a balance of electric ion drag forces
• Tparticle Tgas
• indicates the driving force was mainly due to
  collisions with gas atoms
• Particle motion is characterized using wave
  spectrum, revealing
• particles oscillate with a distinctive frequency
  band
• no dispersion was detected
• damping is mostly due to gas drag

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dusty.physics.uiowa.edu
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Ion drag force
Ratio of ion drag to electric force

• Ion drag force
• can be larger than electric force near the plasma
  center
• is smaller than electric force in sheath region

a 1 ?m Te 1 eV n 3 ?109 cm-2
sheath
plasma center
Khrapak, Ivlev, Zhdanov Morfill, Phys. Plasmas
2005
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Gas drag force
in the molecular-flow regime, Epstein
drag Ngas gas number density a particle
radius V relative velocity of particle and
gas
damping rate
particle mass
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Non-uniformity