Transcript Slide 1

Observations of Linear and
Nonlinear Dust Acoustic Waves*
Bob Merlino, Jon Heinrich
Su Hyun Kim and John Meyer
Department of Physics and Astronomy
The University of Iowa, Iowa City, Iowa
*Supported by DOE and NSF
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Introduction
• The DAW is the most basic dust density wave
involving motion of the dust particles
• Dispersion relation:  k  D pd  Cda
• Often reaching very high amplitudes with nonsinusoidal waveforms, may develop into shocks
• Very difficult to see the linear growth phase, except at
high neutral pressures where it is nearly quenched
• Observations discussed in this talk:
– Linear growth of DAWs in a drifting dusty plasma
– Nonlinear DAWs and second order wave theory
– Secondary dust waves associated with nonlinear DAWs
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Dust acoustic waves (DAW)
• The DAW wave is spontaneously excited in gas
discharge dusty plasmas by an ion-dust
streaming instability
• Dispersion relation from fluid theory
– finite Td
– Collisions of electrons, ions and dust with neutrals
– DC electric field E0
1   i   e   d  0, where
j  
 pj2
  ku   ku
j0
2 2

i


k
VTj

j0
jn
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Ion-dust streaming instability
P = 100 mtorr
E0 = 100 V/m
Parameters: rd  0.5 m, Z d  2000, nd ~ 1011 m 3
Ai  40, ni ~ 1015 m3 , Te  2 eV
k  1.26 mm1 ,    5 mm 
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DAWs in discharge plasmas
Phys. Plasmas 16, 124501, 2009
• DAWs are often observed in
discharge dusty plasmas at
low neutral pressures
• Solid lines are numerical
solutions of the dispersion
relation for various
experimental parameters
• The region below a curve
signifies that the mode is
unstable
• The points correspond to
different experiments
• Ion drift in discharges are
sufficient for instability
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Dusty plasma device
B
Lens
Plasma
532 nm
Laser
Anode
g
Side View
B
Dust Tray
Top View
CMOS
Camera
Dust: silica microspheres (1 mm diameter)
Plasma: argon, 10 – 20 Pa, ni ~ 1015 m3, Te  100 Ti  2-3 eV
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DAWs excited in a drifting dust cloud
ion drift
• A secondary dust
suspension is trapped
by a biased grid 15 cm
from the anode.
• When the bias on the
grid is switched off,
the grid returns to its
floating potential, and
the secondary cloud is
released.
• The secondary cloud
begins drifting toward
the anode.
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Drifting dust cloud and DAWs
• When the center of cloud is about 10 cm from the anode, dust
acoustic waves begin to be excited in the quiescent dust cloud.
• The DAWs begin being excited when they reach the point where
the ion drift is sufficient to drive the ion-dust streaming instability
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Growth rate measurement
rd = 0.5 m silica microspheres
t = 0.09 s
t = 0.03 s
nd / ndo
nd / ndo
t = 0.06 s
t t==00s s
Distance from anode (cm)
FIT
Time (s)
nd
 0.2
nd
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Comparison to DAW (F, K) theory
Growth rate
f (K)
g (F)
g (K)
Wavelength (m)
Growth rate (s1)
Frequency (Hz)
f (F)
Frequency
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Nonlinear dust acoustic waves
Spontaneously excited DA waveforms are non-sinusoidal,
DA waves often grow
typically with sharp wave crests
to very high amplitudes and flat wave troughs
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2nd order DA wave theory
• Simple fluid theory (Stokes’ waves in ocean wave theory)
• expand x  (nd, ud, j) as a series in the small parameter, e to
second order: x  x0  e x1  e2 x2
 2 nd 2
 2 nd21
 2 nd21
1  2 nd 2

 A
B
2
2
2
2
xt
x
Cda t
x
SOLUTION
nd ( x, t )  nd1 cos(kx  t )  nd 2 cos  2  kx  t  
Nonlinearity generates 2nd harmonic term
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Compare 2nd order theory to data
Exp.
Theory
• The fit has a second harmonic amplitude of 30% of the first
harmonic amplitude.
• 2nd order theory captures sharp crests and flat troughs.
• Higher order theory provides qualitative and quantitative
corrections over linear theory – this was a first start.
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Secondary dust density waves
Primary DAW
Secondary DDW
• Secondary dust density
waves (SDDW) were
observed in the troughs
of high amplitude DAWs
• The SDDW propagated
in the direction opposite
to the primary DAW
• SDDW grow in thedust
that is displaced by the
nonlinear DAW and then
restored back
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Dust Density (arb)
0
50
100
Position (arb)
150
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Secondary dust density waves
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Dust-dust streaming instability
(M. Rosenberg)
• We considered the possibility
that the SDDW were excited by a
dust-dust streaming instability
between the background dust and
the restoring dust drift.
• The kinetic dispersion relation
was obtained and solved for the
parameters of the experiment.
• The theory give values for the
frequency and wavelength (for
max. growth) that fit the results
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Summary
• The linear growth of DAWs was observed in a
drifting dusty plasma
• The measured growth rates agreed well with
the kinetic theory of DAWs
• High amplitude (nonlinear ) DAWs exhibit
non-sinusoidal waveforms that seem to be
accounted for by second-order DAW theory
• Secondary DDW were observed in the
presence of nonlinear DAW which may be
excited by a dust-dust streaming instability
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