Transcript Slide 1
6th International Conference on the Physics of Dusty Plasmas Garmisch-Partenkirchen, Germany Nonlinear Dust Acoustic Waves, Shocks, and Stationary Structures in a DC Glow Discharge Dusty Plasma Bob Merlino, Jonathon Heinrich, and Su-Hyun Kim 1 Outline • Large amplitude dust acoustic waves – Collision of 2 nonlinear DAW – Dust acoustic shock waves • Observation of stationary, stable dust density structures 2 Dusty plasmas as a model for fluids m mu 0 t x u u c u t x m x (1) Boltzmannelectronsand ions: 1 P(i ,e ) 0 x c (i ,e ) x ci ce c , P Pe Pi u u 1 P u t x m x (2) m mn, c eZn • Equations (1) and (2) are the Euler equations for an ideal fluid • We can effectively treat the dusty plasma as a single fluid system • Unlike with ordinary fluids, dusty plasmas can be studied at the kinetic level 3 Nonlinear acoustic waves • Solution of the nonlinear 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) • For linear waves, u and m are functions of (x cst) • For nonlinear waves u and m are functions of [x (cs + u)t], so that the wave speed depends on wave amplitude • This leads to nonlinear wave steepening and 4 shock formation Dust Acoustic Shock Waves • Unusual features in Saturn’s rings may be due to dust acoustic waves • Astrophysical contexts – In a very strong DASW, compression of the dust may lead to a reduction in dust charge, thus enabling coalescence of like-charged dust – DASW may provide trigger to initiate the condensation of small dust grains into larger ones in dust molecular clouds • Dusty plasmas can be used as model systems for fluid dynamics studies 5 PHYSICAL REVIEW E 69, 067401, 2004 Dust acoustic shock waves B. Eliasson and P. K. Shukla ndust • Used Boltzmann electrons and ions, and the hydrodynamics equations to derive a set of wave characteristic equations which were then solved numerically • Obtained non-stationary solutions of fully nonlinear, non-dispersive, finite-amplitude DA shock waves Position (mm) 6 Experiment side view Anode Nd:YAG Laser Plasma y x B Cylindrical Lens Dust Tray PC CMOS Camera top view B x z • DC glow discharge • Dust trapped in the “anodic” plasma • Dust: kaolin powder ~ 1 micron • Dust density ~ 1010 m3 • Te ~ 23 eV Ti ~ 0.03 eV • Plasma density ~ (1−5)1014 m3 7 Vacuum chamber 1 m in length anode 60 cm dust tray Photro-Fastcam 1024 PCI 1 megapixel video camera 8 Slit introduced to control the geometry of the dust suspension 9 Effect of the slit Without the slit, near-planar Dusty acoustic waves 1 cm Cylindrical waves Shock tube or Laval nozzle 10 11 Collision of 2 nonlinear DAWs Space-time plots Amplitudes The higher amplitude and faster wave catches up with and “consumes” the slower wave. 12 12 13 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. 14 Self-steepening shock Normalized shock profiles of dust density t= 0 10 20 30 40 50 ms Eliasson and Shukla calculations ndust amplitude Position (mm) 15 Shock properties • Shock speed, Vs 75 mm/s • CDA 65-85 mm/s, so, M = VS/CDA ~ 1 • Amplitude decays as (distance)1 • Shock thickness stabilizes to dmin 0.3 mm Limiting shock thickness, d 0.3 mm • dust-neutral collisions: dmin << Vs / ndn • 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 viscosity, hd 20 mm2/s d 0.3 mm • Gupta et al. (PRE 63, 046406, 2001) and Asgari, et al. (POP 18, 013702, 2011) suggested that non-adiabatic dust charge variation could provide a collisionless dissipation mechanism; estimates agree with exp. 17 Dusty Plasma Structurization Morfill &Tsytovich, Plasma Phys. Rep. 26, 727,2000 • Formation of self-organized structures: dust clumps separated by dust voids • Due to constant flux of plasma on dust, dusty plasmas are open systems that are sustained by an ionization source • This property makes dusty plasma susceptible to self-organization • Dusty plasma are unstable to the formation of structures, e.g. ionization instability 18 Ionization instability DAW with ionization and ion drag analyzed by D’Angelo, POP 5, 3155, 1998 • fluctuation decreases dust density locally • increase in electron density due to less absorption on dust • increases ionization in region becomes more positive • ions flow out dragging dust with them • lowers dust density even 19 more instability Dust structurization • For discharge currents ~ 1-10 mA, propagating DAWs are excited • For currents > 15 mA, the dust cloud is spontaneously trans-formed into nested conical regions of high and low dust density that are stationary and stable • This phenomena was observed with various types and sizes of dust and in argon and helium discharges 1 cm 1000 frames 20 3 D view of structure 21 Wavelength dependencies Discharge current Neutral pressure 22 Structure formation mechanisms I. Ionization instability with ion drag force a) Morfill-Tsytovich: maximum growth occurs for 2Di 1 ~ ~ a ni a b) D’Angelo: for the ion drag frequency > critical value, a zero-frequency, (nonpropagating) perturbation grows 23 II. Effect of polarization force (Hamaguchi and Farouki, PRE 49, 4430, 1994) a) present in a dusty plasma in a non-uniform plasma background. b) (Khrapak et al., Phys. Rev. Lett. 102, 245004, 2009) included this effect in the analysis of DAWS—in the presence of waves, the plasma background becomes locally nonuniform, and there is a force on the grains due to the cloud polarization c) Dispersion relation: k pd Di 1 T 4, T e2 Z 4o kTi Di d) for > 1, w is pure imaginary transition to nonpropagating perturbations 24 Summary & Conclusions 1) Spontaneously excited nonlinear DAWs steepen into DA shock waves 2) The shock thickness may be limited by dissipation due to non-adiabatic dust charge variations or strong correlations 3) We have observed the formation of nonpropagating, stable dust density structures that may be due to an ionization/ion drag instability or the effect of the polarization force on dust particles 25 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) n u n0 t x 2 cs n u t n0 x for DA waves cs cDA kTd kT md Zd2 1 (1 Zd ) nd 0 ni 0 , Ti Te 26 Shock amplitude and thickness a)PRE 79, 055401, 2009 b)POP 18, 013702, 2011 27 • Amplitude falls off linearly with distance faster than ~ r 1/2 for cylindrical expansion, indicating presence of dissipation • dmin ndn << shock speed • Mamun & Cairnsa): dissipation due to strong correlations, dmin ~ nd/Vs, nd is the kinematic viscosity, and Vs is shock speed. With nd ≈ 20 mm2/s, VS ≈ 75 mm/s dmin ≈ 0.3 mm, in agreement with measurements • Asgari, et al.b), variation of dust charge as source of dissipation, in agreement with experiment