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 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

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)

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 Position Amplitude t0 t1 t2 t3 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

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

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

SLIT POSITION 1

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.

SLIT POSITION 2

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: Average intensity 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) Nonstationary solutions of fully nonlinear nondispersive DAWs in a dusty plasma ndust Position (mm)

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 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) give nd  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