Waves in two-dimensional superparamagnetic dusty plasma liquids

Wave dispersion relations in the strongly coupled liquid phase of a two-dimensional system of dust grains interacting via both Yukawa and dipole interactions are investigated. The model system comprises a layer of charged superparamagnetic grains in a plasma in an external, uniform magnetic field $\mathbf{B}$ whose magnitude and direction can be varied. Because the induced magnetic dipole moments of the grains lie along $\mathbf{B}$, the interaction between the grains becomes anisotropic as $\mathbf{B}$ is tilted with respect to the layer. The theoretical approach uses a reformulated quasilocalized charge approximation that can treat dipole interactions, combined with molecular dynamics simulations. The mode dispersion relations are found to depend on the relative strengths of the Yukawa and dipole interactions and the direction of wave propagation in the plane.

Figure 1

Geometry of the model system. (a) The dust layer lies in the $x\text{−}y$ plane and the magnetic moment $\mathbf{M}$ of each grain lies in the $x\text{−}z$ plane at an angle $\alpha$ to the $x$ axis. (b) The angle between the wave vector $\mathbf{k}$ and the $x$ axis is $\chi$.

Figure 2

Equilibrium pair correlation function in the dust layer as a function of polar angle $\theta$ and $\overline{r}$, for parameters $\overline{\kappa }=1$, with (a) $\Gamma =100$ and $\eta =0$, (b) $\alpha ={60}^{\circ }$, $\Gamma =25$, and $\eta =1$. For the parameters in (b), $g\left(\overline{r}\right)$ is shown in (c) for $\theta =0^{\circ }$ (red, solid curve) and $\theta ={90}^{\circ }$ (blue, dashed curve).

Figure 3

The color maps are the (a) longitudinal and (b) transverse fluctuation spectra generated by the simulations for a Yukawa system with $\Gamma =100$ and $\overline{\kappa }=1$. The solid and dashed curves are the QLCA wave dispersion relations for the two modes obtained from Eq. (7) as a function of $ka$ for these parameters.

Figure 4

Polarization angles of the two QLCA eigenmodes obtained from (7). Solid (red) curve corresponds to the higher frequency mode, while dashed (blue) curve corresponds to the lower frequency mode. Parameters are $\Gamma =25$ and $\overline{\kappa }=1$, with (a) $\eta =0$, (b) $\alpha ={60}^{\circ }$, $\eta =0.5$, and $\chi ={30}^{\circ }$.

Figure 5

The color maps are the longitudinal fluctuation spectra generated by the simulations. Parameters are $\Gamma =25$, $\overline{\kappa }=1$, and $\alpha ={60}^{\circ }$, with the values of $\eta$ and $\chi$ shown in the figure. The solid and dashed curves are the QLCA wave dispersion relations for the two modes obtained from Eq. (7) as a function of $ka$ for these parameters.

Figure 6

The color maps are the transverse fluctuation spectra generated by the simulations. Parameters are the same as in Fig. 5. The solid and dashed curves are the QLCA wave dispersion relations for the two modes obtained from Eq. (7) as a function of $ka$ for these parameters.

Figure 7

Longitudinal (red, solid curve) and transverse (purple, dashed curve) sound speeds as a function of propagation angle $\chi$ obtained from the QLCA expression (7) using (11) and expanding the exponential function for small $k$. Parameters are $\overline{\kappa }=1$, with (a) $\Gamma =100$ and $\eta =0$, (b) $\alpha ={60}^{\circ }$, $\Gamma =100,$ and $\eta =0.5$.