Transcript Slide 1

51st Annual Meeting of the APS Division of Plasma Physics
Atlanta, GA Nov. 2-6, 2009
NO6.00002
Laboratory observations of
self-excited dust acoustic
shock waves
R. L. Merlino,
J. R. Heinrich, and S.-H. Kim
University of Iowa
Supported by the U. S. Department of Energy
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Linear acoustic waves
• Small amplitude,
compressional waves
obey the linearized
continuity and
momentum equations
• n and u are the
perturbed density
and fluid velocity
• Solutions: n(x  cst)
u(x  cst)
n
u
 n0
t
x
cs2 n
u

t
n0 x
for DA waves
cs  cDA 
kTd   kT
md
   Zd2 1   (1   Zd )
  nd 0 ni 0 ,
  Ti Te
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Nonlinear acoustic waves


u
u

0
t
x
x
u
u cs2 
u

0
t
x
 x
  mn
P0
c 
0
2
s
• Solution of these equations, which apply to
sound and IA waves (Montgomery 1967) show that
compressive pulses steepen as they propagate, as
first shown by Stokes (1848) and Poisson (1808).
• Now, u and  are not functions of (x  cst), but
are functions of [x  (cs + u)t], so that the wave
speed depends on wave amplitude.
• Nonlinear wave steepening  SHOCKS
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Pulse steepening
t1
t2
t3
Amplitude
t0
Position
• A stationary shock is formed if the
nonlinearlity is balanced by dissipation
• For sound waves, viscosity limits the
shock width
4
Importance of DASW
• Unusual features in Saturn’s rings may be
due to dust acoustic waves
• DASW may provide trigger to initiate the
condensation of small dust grains into
larger ones in dust molecular clouds
• Since DASW can be imaged with fast
video cameras, they may be used as a
model system for nonlinear acoustic wave
phenomena
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Experiment
side
view
Plasma
Nd:YAG
Laser
Anode
y
x
B
Cylindrical
Lens
Dust Tray
PC
Digital
Camera
top
view
B
 DC glow discharge plasma
 P ~ 100 mtorr, argon
 kaolin powder
 size ~ 1 micron
 Te ~ 2-3 eV, Ti ~ 0.03 eV
 plasma density
~ 1014 – 1015 m-3
x
z
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7
anode
Effect of Slit
No Slit
1 cm
y
slit
Slit position 1
z
Slit position 2
1 cm
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SLIT POSITION 1
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Confluence of 2 nonlinear DAWs
• With slit in position 1, we observed one DAW
overtake and consume a slower moving DAW.
• This is a characteristic of nonlinear waves.
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SLIT POSITION 2
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Formation of DA shock waves
• When the slit was
moved to a position
farther from the anode,
the nonlinear pulses
steepened into shock
waves
• The pulse evolution
was followed with a 500
fps video camera
• The scattered light
intensity (~ density) is
shown at 2 times
separated by 6 ms.
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Formation of DASW
Shock Speed: Vs  74 mm/s
Estimated DA speed:
Cda  60 – 85 mm/s
 Vs/Cda ~ 1 (Mach 1)
Average intensity
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Theory: Eliasson & Shukla
Phys. Rev. E 69, 067401 (2004)
ndust
• Nonstationary solutions of fully nonlinear
nondispersive DAWs in a dusty plasma
Position (mm)
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Shock amplitude and thickness
• Amplitude falls off
roughly linearly with
distance
• For cylindrical shock,
amplitude ~ r 1/2
• Faster falloff may
indicate presence of
dissipation
• Dust-neutral collision
frequency ~ 50 s1
• mean-free path
~ 0.05 –1 mm,
depending on Td
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Limiting shock thickness
• Due to dust-neutral collisions
• Strong coupling effects (Mamun and Cairns, PRE
79, 055401, 2009)
– thickness d ~ nd / Vs, where nd is the dust
kinematic viscosity
– Kaw and Sen (POP 5, 3552, 1998) give nd  20 mm2/s
–  d  0.3 mm
• Gupta et al (PRE 63, 046406, 2001) suggest that
nonadiabatic dust charge variation could provide
a collisionless dissipation mechanism
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Conclusions
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