Symbolic transfer entropy analysis of the dust interaction in the presence of wakefields in dusty plasmas

The method of symbolic transfer entropy has been applied to analyze the behavior of charged-particle systems under the influence of an ion focus (wakefield) in a dusty plasma. Using long-run experiments under various plasma and trapping conditions, it is revealed from the transfer entropy that information is transported from the upper particle in an ion flow to the lower. The information transfer increases with smaller interparticle distance and with reduced height in the sheath. This can be consistently explained by the formation of the ion focus by an ion flow in the sheath. From the analysis of two-particle and many-particle systems, the symbolic entropy transfer can be judged as a reliable measure for information asymmetry, and hence interaction asymmetry, in dusty plasma systems.

Figure 1

Particle trajectories of the two-particle system at discharge powers of (a) 1.2 W, (b) 1.4 W, and (c) 1.6 W at a gas pressure of 8 Pa. Directionality index $T^S$ in false colors for the three situations at (d) 1.2, (e) 1.4, and (f) 1.6 W. The directionality index is calculated taking the $x$, $y$ and $z$ coordinate of the upper versus the coordinates of the lower particle.

Figure 2

Directionality index $T_{xx}^S$ for the $x$ components of the upper and lower particle trajectory. In (a) $T_{xx}^S$ is shown as a function of interparticle distance, whereas in (b) it is given as a function of height above the lower electrode. The particle trajectories of the outlier in (a) and (b), which is marked by the arrow, are shown as an inset.

Figure 3

Particle trajectories of a three-particle system at discharge powers of (a) 0.8 W, (b) 1.2 W, and (c) 1.6 W at a gas pressure of 6 Pa together with the directionality index $T^S$ in false colors. The directionality index is calculated taking the $x$ and $y$ coordinates of the three particles against each other. The color bar is nearly the same as in Fig. 1.

Figure 4

(a) Directionality index $T_{xx}^S$ in false colors for a system with 30 particles (color bar as in Fig. 1). Here, the $x$-time series of all particles are calculated against each other. The particle number is counted from top to bottom. (b) Trajectories of the 30 particle system. See text for details.