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NO6.00002 Laboratory observations of self-excited dust acoustic shock waves

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### NO6.00002Laboratory observations of self-excited dust acoustic shock waves

51st Annual Meeting of the APS Division of Plasma Physics

Atlanta, GA Nov. 2-6, 2009

R. L. Merlino,

J. R. Heinrich, and S.-H. Kim

University of Iowa

Supported by the U. S. Department of Energy

Linear acoustic waves

- Small amplitude, compressional waves obey the linearized continuity and momentum equations
- n and u are the perturbed densityand fluid velocity
- Solutions: n(x cst) u(x cst)

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

Amplitude

Position

Pulse steepening- A stationary shock is formed if the nonlinearlity is balanced by dissipation
- For sound waves, viscosity limits the
- shock width

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

view

Plasma

Nd:YAG

Laser

Anode

y

B

x

Cylindrical

Lens

Dust Tray

PC

Digital

Camera

top

view

B

x

z

Experiment- 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

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.

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.

Formation of DASW

Shock Speed: Vs 74 mm/s

Estimated DA speed:

Cda 60 – 85 mm/s

Vs/Cda ~ 1 (Mach 1)

Position (mm)

Theory: Eliasson & ShuklaPhys. Rev. E 69, 067401 (2004)- Nonstationary solutions of fully nonlinear nondispersive DAWs in a dusty plasma

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 s1
- mean-free path ~ 0.05 –1 mm, depending on Td

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) givend 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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