1. R. L. Merlino, J. R. Heinrich, and S.-H. Kim University of Iowa
51st Annual Meeting of the APS Division of Plasma Physics
Atlanta, GA Nov. 2-6, 2009
NO 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

2. 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)

3. Nonlinear acoustic waves
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

4. Pulse steepening
Position
Amplitude
t t t t3
A stationary shock is formed if the nonlinearlity is balanced by dissipation
For sound waves, viscosity limits the
shock width

5. 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

6. Experiment  DC glow discharge plasma  P ~ 100 mtorr, argon
Anode
Dust Tray
Nd:YAG
Laser
Cylindrical
Lens B x y
Plasma
Digital
Camera PC z
side
view
top
 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

8. Effect of Slit No Slit Slit position 1 Slit position 2 y z anode slit
1 cm
Slit position 1 y z
Slit position 2
1 cm

9. SLIT POSITION 1

10. 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.

11. SLIT POSITION 2

12. 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.

13. Formation of DASW Shock Speed: Vs  74 mm/s Estimated DA speed:
Average intensity
Shock Speed: Vs  74 mm/s
Estimated DA speed:
Cda  60 – 85 mm/s
 Vs/Cda ~ 1 (Mach 1)

14. Theory: Eliasson & Shukla Phys. Rev. E 69, 067401 (2004)
Nonstationary solutions of fully nonlinear nondispersive DAWs in a dusty plasma
ndust
Position (mm)

15. 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

16. Limiting shock thickness
Due to dust-neutral collisions
Strong coupling effects (Mamun and Cairns, PRE 79, , 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, , 2001) suggest that nonadiabatic dust charge variation could provide a collisionless dissipation mechanism

17. Conclusions