No6 00002 laboratory observations of self excited dust acoustic shock waves
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51 st 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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NO6.00002 Laboratory observations of self-excited dust acoustic shock waves

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No6 00002 laboratory observations of self excited dust acoustic shock waves

51st Annual Meeting of the APS Division of Plasma Physics

Atlanta, GA Nov. 2-6, 2009

NO6.00002Laboratory 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


Linear acoustic waves

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

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


Pulse steepening

t0 t1 t2 t3

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

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


Experiment

side

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


Effect of slit

No Slit

1 cm

slit

Slit position 1

Slit position 2

y

z

Effect of Slit

anode

1 cm


No6 00002 laboratory observations of self excited dust acoustic shock waves

SLIT POSITION 1


Confluence of 2 nonlinear daws

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.


No6 00002 laboratory observations of self excited dust acoustic shock waves

SLIT POSITION 2


Formation of da shock 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

Average intensity

Formation of DASW

Shock Speed: Vs  74 mm/s

Estimated DA speed:

Cda  60 – 85 mm/s

 Vs/Cda ~ 1 (Mach 1)


Theory eliasson shukla phys rev e 69 067401 2004

ndust

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

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


Limiting shock thickness

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


Conclusions

Conclusions


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