Connecting the wakefield instabilities in dusty plasmas

The wakefield, or ion focus, formed by ions streaming past dust particles trapped in the plasma sheath leads to two types of instabilities: the Schweigert instability in multilayer systems and the mode-coupling instability that already appears in single-layer dust systems. Here, a model is presented that treats both types of instability in a common description. The parameter space for the onset of the instabilities is determined. A new variant of the mode-coupling instability is found to arise from the interaction among the layers. For weak confinement, all instabilities continuously merge into each other. For stronger confinement of the dust mainly the Schweigert type of instability is observed.

Figure 1

Scheme of the modeled system consisting of a two-layer chain of particles with equilibrium distances $b$ in the horizontal and $d+d_{+}$ in the vertical direction. The horizontal and vertical excursions from the equilibrium are indicated by arrows. The ion focus is modeled by a positive point charge $q$ with a vertical distance $d_{+}$ below a negative dust particle of charge $Q$.

Figure 2

Dispersion relation of the two-layer system for a separation of upper and lower layer, of (a) $d/b=5$, (b) $d/b=0.37$, and (c) $d/b=0.32$. The other parameters are fixed as $\tilde{q}=0.5,\widetilde{d_{+}}=0.4$, and ${\omega }_0^2/{\omega }_h^2=8$. The solid lines indicate the real part of the frequency $\omega$ in units of ${\omega }_h$, and the dashed line indicates the imaginary part. The dash-dotted line indicates the horizontal component of the oscillation amplitude of the unstable mode.

Figure 3

Color-coded (gray scale) imaginary part of the wave frequency as a function of the wave vector $kb$, the interparticle distance $\tilde{d}=d/b$, and the ion-focus charge $\tilde{q}=q/Q$. The mode-coupling regime is indicated by $m$ for large interlayer distances, the Schweigert instability (marked by $S)$ is found for large values of $kb$, and the interlayer mode coupling is denoted by $m^{☆}$. Shown are slices through the instability range at $\tilde{q}=0.1,0.3,0.5$, and $0.7$ for ${\omega }_0^2/{\omega }_h^2=8$ and $d_{+}/b=0.4$. The black solid contour lines encircle regions with $V_x>0.9$.

Figure 4

Same as Fig. 3, but for ${\omega }_0^2/{\omega }_h^2=20$.