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

1. 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

2. 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)

3. 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

4. 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

5. 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

6. 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

8. No Slit 1 cm slit Slit position 1 Slit position 2 y z Effect of Slit anode 1 cm

9. SLIT POSITION 1

10. 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.

11. SLIT POSITION 2

12. 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.

13. Average intensity Formation of DASW Shock Speed: Vs  74 mm/s Estimated DA speed: Cda  60 – 85 mm/s  Vs/Cda ~ 1 (Mach 1)

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

15. 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

16. 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

17. Conclusions