Kinetic Characterization of Strongly Coupled Systems

We propose a simple method to determine the local coupling strength $\Gamma$ experimentally, by linking the individual particle dynamics with the local density and crystal structure of a 2D plasma crystal. By measuring particle trajectories with high spatial and temporal resolution we obtain the first maps of $\Gamma$ and temperature at individual particle resolution. We employ numerical simulations to test this new method, and discuss the implications to characterize strongly coupled systems.

Figure 1

Plasma crystal Einstein (PCE) frequency ${\Omega }_E$ normalized to ${\Omega }_0=(Q^2/m{\Delta }^3{)}^{1/2}$ versus screening parameter $\kappa =\Delta /\lambda$, as calculated from Eq. (1). Plotted curves are for 1D chain, 2D hexagonal lattice, and 3D bcc, fcc, and hcp lattices. The inset shows the ratio of frequency ${\Omega }_{\mathrm{NN}}$ calculated in the nearest-neighbor approximation to the PCE frequency. $({\Omega }_{\mathrm{NN}}/{\Omega }_0{)}^2$ in dependence on $\kappa$ is $4e^{-\kappa }(1+\kappa +\frac{1}{2}{\kappa }^2)$ (1D chain), $3e^{-\kappa }(1+\kappa +{\kappa }^2)$ (2D hexagonal lattice), $\frac{8}{3}{e}^{-\kappa }{\kappa }^2$ (3D bcc lattice) and $4e^{-\kappa }{\kappa }^2$ (3D fcc, hcp, and random hcp lattices).

Figure 2

(a),(d) Distribution of velocities $v_x$ (red dots) and $v_y$ (blue dots) with Maxwellian fits (solid lines). (b),(e) Distribution of displacements $x$ (red dots) and $y$ (blue dots) of particles in their nearest-neighbor cage, solid lines are Gaussian fits. We chose the bin size of the histograms to be larger than the measurement error. (c),(f) Particle trajectories in their respective nearest-neighbor cells during the measurement time of $\simeq 12.3\mathrm{s}$ (colors correspond to the progression of time). (a)–(c) [(d)–(f)] represent stationary (nonstationary) trajectories, respectively.

Figure 3

2D maps of local crystal parameters. The voronoi cell around each particle is color coded according to the value of the particular measured quantity (the scales are shown in the bars on the right side of each picture). The circles indicate the position of the sevenfold to fivefold pair defect. Top panel: Experiment. (a) Particle temperature $T$, (b) coupling parameter $\tilde{\Gamma }$, (c) interparticle distance $\Delta$, and (d) bond order parameter ${\Psi }_6$. Blue cells seen at the upper edge of Fig. 3b represent nonstationary particles, with a trajectory example shown in Fig. 2f. The (compressing) wires are arranged along the vertical image axis to the left and right of the plasma crystal. Bottom panel: MD simulation. (e) Sample particle trajectory during $\simeq 10\mathrm{s}$, colors correspond to the time progression, (f) coupling parameter $\tilde{\Gamma }$, (g) interparticle distance $\Delta$, (h) and bond order parameter ${\Psi }_6$.