Instabilities in bilayer complex plasmas: Wake-induced mode coupling

Stability principles for bilayer complex plasmas are studied. To mimic bilayer crystals and identify the main melting mechanism of such structures, a simple binary-chain model is employed. This approach provides adequate representation of the collective effects and accurate description of the interaction nonreciprocity, associated with the wake-mediated interparticle forces. It is shown that the wake-induced coupling of the wave modes sustained in different crystalline layers can trigger the dynamical instability. Furthermore, the mode coupling is demonstrated to be a universal instability mechanism, operating also in bilayer fluids. General stability criteria for the crystalline and fluid bilayers are derived.

Figure 1

Typical example of the particle potential in a streaming plasma, obtained from the kinetic wake model (see text for details). Shown is the unit-charge potential $\varphi (R,z)$, the ion flow is directed downward, the distance is in units of the spatial scale $\lambda$. (a) The potential profile along the vertical axis, $\varphi (0,z)$. (b) Lines of constant $\varphi$ in the vicinity of the particle. The dashed line is the locus of the horizontal inflection points, ${\partial }^2\varphi /\partial R^2=0$, due to the potential well of the wake. The thick solid line indicates the contour of $\varphi (R,z)=0$.

Figure 2

A sketch showing two major regular structures for the binary-chain setup.

Figure 3

Amplitude of the potential of a flat modulated charged layer. Shown are examples of the amplitude $\mathrm{\Phi }(z,k)$ for three different values of wave number $k$, plotted versus the height $z$ with respect to the layer. The results are derived from the kinetic wake model for a constant mean free path of ions, $z$ and $k$ are normalized with the spatial scale $\lambda , \zeta =0.3$, and $\tau =0.5$ (see text for details).

Figure 4

Characteristics of the wave mode coupling in a fluid bilayer system with the height difference $H$. (a) Examples of the coupling factor $\mathrm{\Gamma }(H,k)$, calculated for the potential amplitudes $\mathrm{\Phi }(z,k)$ shown in Fig. 3. (b) Absolute value of the “minimum” coupling factor $|{\mathrm{\Gamma }}_{\min }|\equiv |\mathrm{\Gamma }(H_{\min },k_{\min })|$, corresponding to the global negative minimum of $\mathrm{\Gamma }$ at $H_{\min }$ and $k_{\min }$. The three curves are plotted versus the collision parameter $\zeta$ for $\tau =0.5$ (see text for details).

Figure 5

Stability diagram for a regular structure.