Compressional and Shear Wakes in a 2D Dusty Plasma Crystal V. Nosenko, J. Goree & Z.W. Ma Univ. of Iowa A. Piel Univ. of Kiel D. Dubin UCSD

charge Q  e separation a = 762  46  m 2D Monolayer 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  n /  t = 0  v= 0

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

Havnes 1995 Existence predicted theoretically, for Saturn’s rings Mach cones in dusty plasmas Samsonov 1999 Discovered experimentally in lab Melzer & Nunomura 2000 Laser excitation of Mach cones

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

Experimental setup scanning mirror

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

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 Gray-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 Gray-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

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

Superposition of wakes

Experimental image produced by two moving laser spots Superposition of wakes

+ Synthesized image = Test of Linear Superposition Experimental image  n/  t maps

Experimental imageSynthesized image Test of Linear Superposition Agreement  linear superposition is true

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) Linearity

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 Linear superposition is true 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