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

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

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.
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
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