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

2 1.Introduction to dusty plasmas a.What are they b.Where are they c.How do you make a dusty plasma 2.Dust acoustic wave 3.Dust acoustic wave experiments a.Nonlinear dust acoustic waves b.Dust acoustic shock waves c.Self-organization in a dusty plasma 4.Conclusions

3 Dusty plasma basics 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 charge since v e > v i Dust is floating, so I e + I i = 0  V f ( dust floating potential) Charge: Q d = C d V f = (4  o a)V f If the grain radius a = 1  m, T e = 100 T i = 2.5 eV (Ar)  Q d ~  4000 e. Charged dust interacts collectively with the plasma, but on a much longer timescale, 1/  pd PLASMA D a

Properties of dusty plasmas –Dust radius a << D –m d ~ m p, Q d ~ (10 3 – 10 4 ) e –(Q/m) d ~ 1; while (e/m p ) ~ 10 8 –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 4

5 Examples of dusty plasmas Noctilucent clouds formed in the summer mesosphere at 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 ice caused by the Space Shuttle engine 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 Simple dusty plasma device dc or rf glow discharge plasma at 300 – 400 V argon gas at p ~ mTorr (10-30 Pa) micron size glass spheres, but any powder works image dust using laser and video camera for a 1  m particle, Q d E = m d g with E ~ 1 V/cm QdEQdE mdgmdg GAS anode trapped dust dust tray g

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9 Dust Acoustic Waves Very low (few–tens Hz) frequency compressional dust density waves o treat dust as a fluid of charged particles (Shukla, Capri 1989) o 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, n d1, v d1, and  1 : Combine with quasineutrality condition to obtain, by elementary calculation DA speed:

11 Dust acoustic wave excitation: ion-dust streaming instability P = 100 mtorr E 0 = 100 V/m  Include ion drift and collisions in fluid theory

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

13 A spontaneously excited dust acoustic wave 1 cm anode

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

15 2 nd order (Stokes) wave theory Products of 1 st order quantities Nonlinearity generates 2 nd harmonic term Perturbation analysis: expand  (n, v,  ) as a series in the small parameter,  to second order:         Insert into momentum and continuity equations 2nd order quantities SOLUTION

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 THEORY Shukla and Eliasson 2012

20 Shock position, amplitude, thickness The shock speed, V S  75 mm/s, so that V S / C da T 1, where C da is the dust acoustic speed, so that M T 1. The shock steepens as it propagates, finally reaching a steady-state width  T the interparticle spacing

21 Large amplitude dust acoustic shocks P. K. Shukla and B. Eliasson arXiv: v1, (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 visco-elastic relaxation time polarization force term 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:  20 mm 2 /s Experiment Theory

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

24 Structurization in dusty plasmas G. 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

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

26 Non-propagating DA waves I.D’Angelo (PoP 5, 3155, 1998) included the effects of ionization and the ion drag force on DA waves. 0 rr ii Ion Drag Coefficient s1s1 II. Khrapak et al., (PRL 102, , 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.

27 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 Heinrich et al., PRE 84, , cm

28 Stationary Dust Structures 1 cm

29 3D Views

30 Summary In 2014, it will be 25 years since Padma Shukla suggested the existence of the DA wave at the 1 st 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.

Lunar Dust Acoustic Waves In January 2012, NASA plans to launch the LADEE mission (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. 31