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Mach Cones in a 2D Dusty Plasma Crystal

Mach Cones in a 2D Dusty Plasma Crystal. J. Goree Dept. of Physics and Astronomy, University of Iowa with results from V. Nosenko, Z. Ma, and D. Dubin. Supported by DOE, NASA, NSF. electrons + ions = plasma. small particle of solid matter. absorbs electrons and ions.

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Mach Cones in a 2D Dusty Plasma Crystal

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  1. Mach Conesin a 2D Dusty Plasma Crystal J. Goree Dept. of Physics and Astronomy, University of Iowa with results from V. Nosenko, Z. Ma, and D. Dubin Supported by DOE, NASA, NSF

  2. electrons + ions = plasma small particle of solid matter • absorbs electrons and ions • becomes negatively charged • Debye shielding What is a dusty plasma?

  3. polymer microspheres • » 8 mm diameter Particles

  4. Different - dusty plasma has: • gaseous background • 105´ charge • no inherent rotation • gravity effects • Yukawa potential Comparison ofdusty plasma & pure ion plasmas Similar: • repulsive particles • Crystals & liquids • 2D or 3D suspensions • direct imaging • laser-manipulation of • particles

  5. Forces Acting on a Particle • Coulomb • trapping potential • inter-particle • µr1 Gravity µr3 • Gas drag • Ion drag • Thermophoresis • µr2

  6. electrode Equipotential contours electrode Without gravity, particles fill 3-D volume positive potential QE With gravity, particles sediment to high-field region Þ2-D layer possible mg electrode electrode Electrostatic trapping of particles

  7. top-view camera laser illumination vacuum chamber side-view camera chamber

  8. Experimental conditions • Polymer microspheres • diameter 8.69 ± 0.17 mm Gas Ar, 15 mTorr RF plasma 13.56 MHz 20 W

  9. All experiments in this talk: a monolayer of particles Þ2D physics Triangular lattice with hexagonal symmetry Lattice • charge Q» -13000 e • separation a = 762 ± 46 mm

  10. Pair correlation function • Many peaks in g(r) • Translation order length » 9a Þ Ordered lattice

  11. Compressional and shear waves

  12. Dispersion relations in 2D triangular lattice

  13. Mach cones (in air) Shock wave behind an f-18 courtesy of D. Dubin

  14. C = U Sin m U m Mach cone angle m courtesy of D. Dubin

  15. Lateral wake Transverse Wake Wake behind a ship courtesy of D. Dubin

  16. scanning mirror Experimental setup

  17. Get top view images of the lattice • Determine particle positions Data analysis method • Trace particle orbits • Calculate particle velocity, number density

  18. Laser manipulation of particles radiation force Ar laser beam 0.2 - 1 W • motion of laser spot: • ^ to radiation force direction shown here, • || motion is also possible

  19. V Shear wave Mach cone V/Cl = 0.51

  20. Speed map for compressional Mach cone particle speed v (mm/s)

  21. Lateral wake Transverse Wake Wake behind a ship courtesy of D. Dubin

  22. speed map for compressional Mach cone particle speed v (mm/s)

  23. ¶n/¶t Schlieren map Ñ´vvorticity map Vector velocity map 2 mm 2 mm 2 mm V/Cl= 2.23: compressional wave Mach cone Grey-scale speed map small Ñ´v Þ not shear waves Big ¶n/¶t Þ compressional waves

  24. ¶n/¶t Schlieren map Ñ´vvorticity map 2 mm 2 mm 2 mm V/Cl = 0.51: shear wave Mach cone Grey-scale speed map Vector velocity map big Ñ´v Þ shear waves small ¶n/¶t Þ not compressional

  25. Ct = 5.8 mm/s Cl = 22.1 mm/s Test of Mach cone angle relation

  26. 2 mm Comparison to MD simulation Experiment MD simulation by Z.W. Ma V/Cl = 0.51

  27. Compressional & Shear wave Mach cones Scanning parallel to radiation force direction, V/Cl = 1.35 Shear wave Mach cone

  28. Theory of wakes in a 2D plasma crystal Dubin, Phys. Plasmas 2000 • Wakes with dispersion: c = c(k) ºw/k • Wave equation • Phase mixing Þ cancellation everywhere • except where constructive interference • occurs (loci of stationary phase)

  29. calculation by Dubin V/Cl > 1: Mach cone and lateral wakes Mach cone lateral color mapexperimental ¶n/¶t Schlieren map • V/Cl = 1.21 • k = 1.14 • no fitting parameter

  30. 2 mm V/Cl < 1: transverse wake transverse ¶n/¶t Schlieren map • V/Cl = 0.51 • k = 1.14

  31. Summary • Mach cones were observed in a 2D dusty plasma crystal • Shear wave & Compressional Waves • Compressional wave: Rich wake structure was observed for both supersonic and undersonic excitation, consisting of multiple lateral and transverse wakes • Shear Wave: had a single-cone structure • In far field, the wake structure in experiment is comparable to Dubin’s theory of wakes in dusty plasma crystal

  32. Solar system • Rings of Saturn • Comet tails • Manufacturing • Particle contamination • (Si wafer processing) • Nanomaterial synthesis • Basic physics • Coulomb crystals • Waves Who cares about dusty plasmas?

  33. 160 80 0 Dusty plasma publications in APS & AIP journals 9 months data in 1999

  34. Coulomb force • Interparticle interaction is repulsive Coulomb (Yukawa) • External confinement by natural electric fields present in plasma

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