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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

51st Annual Meeting of the APS Division of Plasma PhysicsAtlanta, GA Nov. 2-6, 2009

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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)

0

2

0

s

n un

t x

cu n

t n x

2

0 0

for DA waves

1 (1 )

,

ds DA

d

d d

d i i e

kT kTc c

m

Z Z

n n T T

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Nonlinear acoustic waves

2

0

0s

uu

t x xcu u

ut x x

2 0

0s

mn

Pc

• 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

PositionAmplitude

t0 t1 t2 t3

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

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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

Anode

Dust Tray

Nd:YAGLaser

CylindricalLens

Bx

y

Plasma

DigitalCamera

PC

z

x

B

sideview

topview

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

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Effect of Slit

anode

1 cm

No Slit

slit

1 cm

Slit position 1

yz

Slit position 2

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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

Average intensity

Shock Speed: Vs 74 mm/s

Estimated DA speed: Cda 60 – 85 mm/s

Vs/Cda ~ 1 (Mach 1)

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Theory: Eliasson & ShuklaPhys. Rev. E 69, 067401 (2004)

• Nonstationary solutions of fully nonlinear nondispersive DAWs in a dusty plasma

nd

ust

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 s1

• 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 / Vs, where d is the dust kinematic viscosity

– Kaw and Sen (POP 5, 3552, 1998) give d 20 mm2/s

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