1. Phonons in a 2D Yukawa triangular lattice: linear and nonlinear experiments Dept. of Physics and Astronomy, University of Iowa supported by DOE, NASA, NSF V.Nosenko, S.Nunomura, and J.Goree

2. 2D Yukawa triangular lattice Yukawa interparticle interaction, where  is screening parameter:

3. Phonons in a 2D Yukawa triangular lattice

4. wavenumber ka/  Frequency   Theory for a triangular lattice Wang et al. PRL 2001 Frequency normalized by   :     Q     ma  Dispersion relation (phonon spectrum)

5. electrons + ions = plasma Experimental system: Dusty Plasma Debye shielding D absorbs electrons and ions small particles of solid matter becomes negatively charged

6. gas Ar at 2 mTorr RF plasma 13.56 MHz 20 W Experimental conditions Polymer microspheres diameter 8.69  0.17  m charge  10000 e

7. Experimental setup

8. 2D lattice External confinement natural electric fields in plasma gravity mg F sheath The lattice is characterized by screening parameter:

9. Comparison of dusty plasma & colloids Similar: Different - dusty plasma has: Like-charged particles Yukawa potential 2D or 3D suspensions Direct imaging Laser-manipulation of particles Gaseous background 10 5  less dissipation 10 5  less volume fraction

10. Dispersion relations for both modes Experiment: S.Nunomura et al. Theory: Wang et al. PRL 2001 Longitudinal wave Transverse wave

11. 2D lattice can be modeled as a network of masses connected by springs to the nearest neighbors 2D triangular (hexagonal) lattice Response: linear nonlinear

12. Triangular (hexagonal) lattice separation a = 0.5 -1.0 mm areal fraction (0.6 - 2.4)  10 -4 2D lattice Pair correlation function: Many peaks in g(r) Translation order length  9a  Ordered lattice

13. These profiles show pulse propagation Particle velocity profiles

14. Theory of nonlinear sound waves in 3D liquid (Landau & Lifshitz, Fluid Mechanics) C- wave propagation speed C 0 - sound speed v- particle speed  - adiabatic coefficient

15. Normalization: by C min, the pulse propagation speed for lowest laser power indication of nonlinearity Pulse propagation speed vs. pulse amplitude  

16. Summary In 2D triangular (hexagonal) Yukawa lattice Longitudinal and transverse phonons were detected and their dispersion relations were measured. Nonlinear effects in pulse propagation of the longitudinal wave were observed for large amplitudes (Mach numbers M > 0.07).

17. Pulse propagation speed vs. laser power Pulse propagation speed depends on: particle number density (i.e.  excitation laser power  indication of nonlinear effect                 

18. Deviation from proportionality v   n/n is further evidence of nonlinearity Pulse amplitude (particle speed) vs. Pulse amplitude (number density)

19. Dispersion relations:  dependence Experiment: S.Nunomura et al. Theory: Wang et al. PRL 2001 Longitudinal wave Transverse wave