Experiments on Shocks and Dust Structures in Dusty Plasmas

1. 39th EPS Conference & 16th Int. Congress on Plasma Physics Stockholm, Sweden, July 2-7, 2012 Experiments on Shocksand Dust Structuresin Dusty Plasmas Robert L. Merlino, Jonathon R. Heinrich, Su-Hyun Kim and John K. Meyer Department of Physics and AstronomyThe University of Iowa, Iowa City, Iowa, USA Supported by US DOE and NSF

2. Introduction to dusty plasmas • What are they • Where are they • How do you make a dusty plasma • Dust acoustic wave • Dust acoustic wave experiments • Nonlinear dust acoustic waves • Dust acoustic shock waves • Self-organization in a dusty plasma • Conclusions

3. A four component system, consisting of electrons, ions, neutral atoms and micron size solid dust grains The grains are charged by collecting electrons and ions The grain acquires a negative chargesince ve > vi Dust is floating, so Ie + Ii = 0  Vf( dust floating potential) Charge: Qd = Cd Vf = (4peoa)Vf If the grain radius a = 1 mm, Te = 100 Ti = 2.5 eV (Ar) Qd ~  4000 e. Charged dust interacts collectively with the plasma, but on a much longer timescale, 1/pd a lD Dusty plasma basics PLASMA

4. Properties of dusty plasmas • Dust radius a << lD • md ~ 1012 mp, Qd ~ (103 – 104) e • (Q/m)d ~ 1; while (e/mp) ~ 108 • Gravity, electric, and ion drag forces important • Occurrence of dusty plasmas • Comet tails • Planetary rings • Solar and planetary nebulae • Lower ionosphere (mesosphere) • Atmospheric lightning • Industrial plasma processing devices • Magnetic fusion devices

5. Examples of dusty plasmas Noctilucent clouds formed in the summer mesosphere at75-80 km altitude range; 100 nm water ice, charged Charged dust clouds around silicon wafers, formed in a plasma processing device; a serious contamination issue Dusty plasma of charged icecaused by the Space Shuttleengine exhaust

6. Spokes in Saturn’s B ring discovered by the Voyager 1 spacecraft Micron-size particles thought to be lifted electrostatically above the ring plane

7. QdE mdg Simple dusty plasma device GAS trapped dust anode anode g dust tray • dc or rf glow discharge plasma at 300 – 400 V • argon gas at p ~ 100 - 200 mTorr (10-30 Pa) • micron size glass spheres, but any powder works • image dust using laser and video camera • for a 1mm particle, Qd E = md g with E ~ 1 V/cm

9. Dust Acoustic Waves • Very low (few–tens Hz) frequency compressional dust density waves • treat dust as a fluid of charged particles (Shukla, Capri 1989) • electrons and ions are treated as massless  Boltzmann response (nonlinear) Euler equations for an invicid fluid  shock solutions

10. Dispersion relation • Linearize (1) and (2) and the continuity equation for the • dust, with first order quantities, nd1, vd1, and j1: • Combine with quasineutrality • condition to obtain, by • elementary calculation • DA speed:

11. Dust acoustic wave excitation:ion-dust streaming instability Include ion drift and collisions in fluid theory P = 100 mtorr E0 = 100 V/m

12. B B Lens Plasma Anode g 532 nm Laser Side View Dust Tray Top View CMOS Camera Dusty plasma device Dust: silica microspheres (1 mm diameter) Plasma: argon, 10 – 20 Pa, ni ~ 1015 m3, Te  100 Ti  2-3 eV

13. A spontaneously exciteddust acoustic wave anode 1 cm

14. Dust acoustic waves reach high amplitudes(non-linear) with waveforms having sharp crests and flat troughs

15. 2nd order (Stokes) wave theory • Perturbation analysis: expandh = (n, v, j) as a series in the • small parameter, e to second order: h = h0 + e h1 + e2 h2 • Insert into momentum and continuity equations Products of 1st order quantities 2nd order quantities SOLUTION Nonlinearity generates 2nd harmonic term

16. Nonlinear dust acoustic wave  Second order wave theory can account, qualitatively, for the nonlinear dust acoustic waves.

17. Dust Acoustic Shocks • The experimental • setup was modified • by adding a slit in • front of the anode. • The slit produces • a nozzle-like potential • configuration that favors • the formation of highly- • compressed dust density • pulses.

18. SLIT ANODE

19. Steepening of nonlinear DAW into Dust acoustic shocks Shukla and Eliasson 2012 THEORY

20. Shock position, amplitude, thickness • The shock speed, VS 75 mm/s, so that VS / CdaT1, • where Cda is the dust acoustic speed, so thatM T 1. • The shock steepens as it propagates, finally reaching • a steady-state width dT the interparticle spacing

21. Large amplitude dust acoustic shocksP. K. Shukla and B. Eliasson arXiv:1205.5947v1, (submitted to PRL) • Fully nonlinear theory of arbitrary amplitude DA shocks taking into account strong coupling effects, polarization force, dust collisions with neutrals, dust fluid shear and bulk viscosities • Use the generalized hydrodynamic equations polarization force term visco-elastic relaxation time viscosity effects

22. Scaling of amplitude and thickness • The Shukla/Eliasson (SE) theory reproduces the evolution of the shock speed, amplitude and width. • Theory uses a model for viscosity that depends on coupling strength • By comparing the theory and exp. Shock profiles, a value for the kinetic viscosity can be obtained: n 20 mm2/s Experiment Theory

23. Collision of 2 shock waves A unique property of shock waves is the fact that when a faster shock overtakes a slower shock,they combine into a single shock. Space-time plots Amplitudes

24. Structurization in dusty plasmasG. Morfill & V. Tsytovich, Plasma Phys. Rep. 26, 727,2000 • Dusty plasmas are susceptible to the spontaneous formation of self-organized structures: dust clumps separated by dust voids • The constant flux of plasma on the dust particles must be balanced by an ionization source(open system) • may give rise to ionization instabilities, • coupled with the ion drag force • Structurization may evolve from non-propagating dust acoustic waves 24 24

25. Ionization /ion drag instability 4. Increase in ion density leads to more dust being pushed out of region by the ion drag force  VOID 1. A fluctuation decreases the dust density in region void 2. Less absorptionof electrons leadsto higher electrondensity in region 3. More electrons leadsto higher ionization rate, further increasing plasma density

26. D’Angelo (PoP 5, 3155, 1998)included the effects of ionizationand the ion drag force onDA waves. wi wr s1 II. Khrapak et al., (PRL 102, 245004, 2009) included the effect of the polarization force on DA waves. The polarization force is due on dust is present when there is a non-uniform plasma background, so that the dispersion relation then becomes where  depends on the polarization force. When  > 1, a purely growing instability is found. 0 Ion Drag Coefficient Non-propagating DA waves

27. Dust structurization 1 cm 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 Heinrich et al., PRE 84, 026403, 2011 27

28. Stationary Dust Structures 1 cm

29. 3D Views

30. Summary • In 2014, it will be 25 years since Padma Shuklasuggested the existence of the DA wave at the1st Capri Workshop on Dusty Plasmas. • The DA wave continues to be studied both theoretically and experimentally, with several papers appearing each month examining various aspects of this basic dust mode. • This talk has focused on two aspects of the DA wave • Nonlinear DA waves and shocks • Spontaneous structure formation in dusty plasmas • The interest in the DAW derives from its importance in space, laboratory, and astrophysical dusty plasmas as a mechanism for triggering dust condensation and structrurization.

31. Lunar Dust Acoustic Waves • In January 2012, NASA plans to launch the LADEEmission (Lunar Atmosphere and Dust Environment Explorer). • One of the purposes of this mission is to study the nature of the dust lofted above the lunar surface and reported by the Apollo astronauts as “moon clouds” • It is conceivable that dust acoustic waves could be observed, in situ, in the moon clouds.