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

– polymer microspheres –  8  m diameter Particles

Comparison of dusty plasma & pure ion plasmas Similar: repulsive particles Crystals & liquids 2D or 3D suspensions direct imaging laser-manipulation of particles Different - dusty plasma has: gaseous background 10 5  charge no inherent rotation gravity effects Yukawa potential

Gas drag Ion drag Thermophoresis  r 2 Forces Acting on a Particle Coulomb trapping potential inter-particle  r 1 Gravity  r 3

Electrostatic trapping of particles Equipotential contours electrode positive potential electrode With gravity, particles sediment to high-field region  2-D layer possible Without gravity, particles fill 3-D volume QE mg

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

Gas Ar, 15 mTorr RF plasma MHz 20 W Polymer microspheres diameter 8.69  0.17  m Experimental conditions

charge Q  e separation a = 762  46  m Lattice All experiments in this talk: a monolayer of particles  2D physics Triangular lattice with hexagonal symmetry

Pair correlation function  Ordered lattice Many peaks in g(r) Translation order length  9a

Compressional and shear waves

Dispersion relations in 2D triangular lattice

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

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

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

Experimental setup scanning mirror

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

Laser manipulation of particles Ar laser beam W motion of laser spot:  to radiation force direction shown here, || motion is also possible radiation force

Shear wave Mach cone V/C l = 0.51 V

Speed map for compressional Mach cone particle speed v (  m/s)

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

speed map for compressional Mach cone particle speed v (  m/s)

V/C l = 2.23: compressional wave Mach cone Grey-scale speed map 2 mm Vector velocity map 2 mm  n  t Schlieren map 2 mm  v  vorticity map Big  n/  t  compressional waves small  v  not shear waves

V/C l = 0.51: shear wave Mach cone Grey-scale speed mapVector velocity map  n  t Schlieren map 2 mm  v  vorticity map small  n/  t  not compressional big  v  shear waves

Test of Mach cone angle relation C l = 22.1 mm/s C t = 5.8 mm/s

Comparison to MD simulation MD simulation by Z.W. MaExperiment 2 mm V/C l = 0.51

Compressional & Shear wave Mach cones Scanning parallel to radiation force direction, V/C l = 1.35 Shear wave Mach cone

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

V/C l > 1: Mach cone and lateral wakes color map experimental  n/  t Schlieren map no fitting parameter  = 1.14 V/C l = 1.21 calculation by Dubin Mach cone lateral

2 mm V/C l < 1: transverse wake transverse  = 1.14 V/C l = 0.51  n/  t Schlieren map

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

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

months data in 1999 Dusty plasma publications in APS & AIP journals

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