Wake-Mediated Propulsion of an Upstream Particle in Two-Dimensional Plasma Crystals

The wake-mediated propulsion of an “extra” particle in a channel of two neighboring rows of a two-dimensional plasma crystal, observed experimentally by Du et al. [Phys. Rev. E 89, 021101(R) (2014)], is explained in simulations and theory. We use the simple model of a pointlike ion wake charge to reproduce this intriguing effect in simulations, allowing for a detailed investigation and a deeper understanding of the underlying dynamics. We show that the nonreciprocity of the particle interaction, owing to the wake charges, is responsible for a broken symmetry of the channel that enables a persistent self-propelled motion of the extra particle. We find good agreement of the terminal extra-particle velocity with our theoretical considerations and with experiments.

Figure 1

Channeling of an extra particle in a simulated complex plasma crystal. (a) The particles are sketched in gray, their wake charges in black. The unperturbed channel is visualized by dashed lines on the semitransparent crystal plane. During the passage of the extra particle floating above the crystal from left to right, its wake attracts the channel particles (thick arrows shown for two particles). Because of the small displacement $\delta y$ of the channel particles, the repulsive particle interaction is stronger behind the extra particle than in front of it, leading to a propulsion of the extra particle (thin arrow). (b) Horizontal particle positions with respect to the extra particle between $t_1=1.35$ and $t_2=1.49\mathrm{s}$. The position of the extra particle is indicated by a cross. The relative positions were fitted by straight dotted lines for $-0.4\mathrm{mm}<\mathrm{\Delta }x<0$. (c) Horizontal (top view) particle positions color coded with respect to time between $t_1$ and $t_2$. (d) The same for the $xz$ projection (side view); here, only the extra particle and the two neighboring rows that form the channel are shown. (e) Horizontal particle positions from experiment 5 of Ref. [5].

Figure 2

Local particle density $n$ in the reference frame of the extra particle, showing the pronounced wave structure behind the extra particle (lateral wake [36, 37]).

Figure 3

(a) Variation of the kinetic energy (black) and the potential energy [red (gray)] of the extra particle as a function of time. The dashed line of slope $765\mathrm{eV}/\mathrm{s}$ is to guide the eye. (b) The same for a crystal confined horizontally by a parabolic confinement. The dashed line has a slope of $781\mathrm{eV}/\mathrm{s}$.

Figure 4

Magnitude of the extra-particle velocity as a function of time, for different initial velocities $v_0$. The extra particle with $v_0=5\mathrm{mm}/\mathrm{s}$ (bold line) exits the channel at $t\approx 1.4\mathrm{s}$ while the others stay in the same channel and reach a constant velocity $v_s$. The inset shows $v_s$ as a function of damping rate $\nu$. The error is no larger than the symbol size. The predicted value of Eq. (3) is shown as a black line.