Melting scenarios for three-dimensional dusty plasma clusters

The melting transition of finite three-dimensional dust clouds (Yukawa balls) from a solid-like to a liquid-like state is systematically studied with high spatial and temporal resolution of the individual grains by means of stereoscopy. Two different melting scenarios are reported: Melting is induced first by an increase of plasma power, and second by laser-induced heating. The experiments confirm that melting starts with a loss of orientational correlation, followed by a loss of the radial order upon further heating. While the plasma-power melting is driven via the ion wakefield, laser heating provides a more equilibrium scenario. The internal loss of correlations is well captured by the triple correlation function (TCF) which is insensitive to particle exchanges and the rotation of the cluster as a whole. The critical Coulomb coupling parameter for $N=35$ is determined as ${\Gamma }_{\mathrm{crit}}\approx 570$. The experimental findings are in good agreement with thermodynamic Monte Carlo simulations.

Figure 1

Scheme of the experimental setup used for the melting experiments. The particles confined in the glass box are illuminated by a Nd:YAG laser from two sides and manipulated by a diode laser from one side. The full 3D dynamics of all particles is measured with three orthogonal high-speed cameras.

Figure 2

Structure of the investigated Yukawa balls. (a) $N=32$ for the plasma-induced melting experiment and (b) $N=35$ for the laser-induced melting experiment. The structure of the balls is influenced by the ion focus (see text).

Figure 3

Scheme of the centered triple correlation function $g(r_1,r_2,\phi )$: $r_1$ ($r_2$) denotes the distance from the trap center to the first (second) particle and $\phi$ is the angle between the two vectors with respect to the trap center.

Figure 4

Trajectories of the Yukawa ball with $N=32$ particles for (a) 1.9 W, (b) 2.3 W, (c) 2.7 W, and (d) 3.9 W. (e)–(h) $\overline{g}(r_2,\phi )$ for the corresponding clusters in (a)–(d).

Figure 5

Side view of the cluster trajectories for $N=32$ for an rf power of (a) 2.7 W and (b) 3.9 W.

Figure 6

(a) Angular correlation $g\left(\phi \right)$ and (b) radial correlation $g\left(r\right)$ for a change of plasma power. For better visibility, the maximum of the correlation functions is normalized to unity and the curves are plotted with a constant offset of 1.

Figure 7

(a) Kinetic dust temperature as a function of applied plasma power for the three spatial directions. (b) Velocity distribution of all spatial directions for 2.7 W.

Figure 8

Interparticle distance fluctuation (IDF) as function of applied plasma power. The error bars indicate the standard deviation of the individual IDF.

Figure 9

Interparticle distance fluctuations for each particle in the $\rho$-$z$ plot. The size of the markers corresponds to the magnitude of the fluctuations $u_i$. (a)–(d) Variation of plasma power.

Figure 10

Trajectories for the Yukawa ball with $N=35$ particles for laser heating with (a) 0 mW, (b) 50 mW, (c) 100 mW, and (d) 160 mW. (e)–(h) $\overline{g}(r_2,\phi )$ for the corresponding clusters in (a)–(d).

Figure 11

(a) Angular correlation $g\left(\phi \right)$ and (b) radial correlation $g\left(r\right)$ for a change of laser power. For better visibility the maximum of the correlation functions is normalized to unity and the curves are plotted with a constant offset of 1.

Figure 12

(a) Kinetic dust temperature as function of applied laser power. The solid lines represent parabolic fits to the experimental data. (b) Velocity distribution for a laser power of 160 mW.

Figure 13

Interparticle distance fluctuation (IDF) as function of applied laser power. The error bars indicate the standard deviation of the individual IDF.

Figure 14

Interparticle distance fluctuations for each particle in the $\rho$-$z$ plot. The size of the markers corresponds to the magnitude of the fluctuations $u_i$. (a)–(d) Variation of laser power.

Figure 15

TCF obtained from Monte Carlo calculations for $N=32$, $\kappa =1.26$, and $\Gamma \approx 12,150,1600,$ and $16000$. The grains form shells in the range $12<{\Gamma }_{\mathrm{crit}}^{\mathrm{rad}}<150$ and become localized within the shells (orientational ordered) for $150<{\Gamma }_{\mathrm{crit}}^{\mathrm{ang}}<1600$.

Figure 16

(a) Angular correlation $g\left(\phi \right)$ and (b) radial correlation $g\left(r\right)$ for a change of coupling strength in the Monte Carlo simulations for $N=32$. For better visibility the maximum of the correlation functions is normalized to unity and the curves are plotted with a constant offset of 1.