Ground-state structures of superparamagnetic two-dimensional dusty plasma crystals

Ground-state structures of finite, cylindrically confined two-dimensional Yukawa systems composed of charged superparamagnetic dust grains in an external magnetic field are investigated numerically, using molecular dynamic simulations and lattice summation methods. The ground-state configuration of the system is identified using, as an approximation, the experimentally obtained shape of the horizontal confinement potential in a classical single-layer dusty plasma experiment with nonmagnetic grains. Results are presented for the dependence of the number density and lattice parameters of the dust layer on (1) the ratio of the magnetic dipole-dipole force to electrostatic force between the grains and (2) the orientation of the grain magnetic moment with respect to the layer.

Figure 1

Geometry of the model system. (a) The lattice lies in the $x$-$y$ plane and its structure is characterized by the lattice spacing $b$, the rhombic angle $\phi$, and the aspect ratio $\nu =c/b$. (b) The magnetic moment $\mathbf{M}$ of each grain lies in the $x$-$z$ plane at an angle $\alpha$ to the $x$ axis. The principal lattice axis subtends an angle $\beta$ with the projection of the magnetic moment.

Figure 2

Experimental (a) and MD simulation (b) results for the radial dust density distribution in 2D layer of nonmagnetic dust. Distances are normalized to the observed average central lattice spacing $\langle b\rangle$. The total particle numbers are $\sim 3000$ in the experiment and 5000 in the simulation.

Figure 3

Equilibrium distance $r_{\mathrm{eq}}(\mathbf{M},\alpha )$ for $\alpha <{\alpha }_{\mathrm{th}}$ along the $x$ direction versus $\eta$. For strong magnetic interactions (large $\eta$) the attraction dominates at all distances, thus no equilibrium distance can be found, as indicated by the discontinuation of the lines for $\alpha =0^{\text{o}}$ and ${30}^{\text{o}}$.

Figure 4

Total pair potential energy $U\left(\mathbf{r}\right)=U_E\left(\mathbf{r}\right)+U_M\left(\mathbf{r}\right)$ around a single particle situated at $\mathbf{r}=(0,0)$ at a relative strength of the magnetic interaction to the electrostatic interaction $\eta =0.5$: (a) $\alpha ={60}^{\text{o}}>{\alpha }_{\mathrm{th}}$ and (b) $\alpha ={50}^{\text{o}}<{\alpha }_{\mathrm{th}}$. The potential energy surface is cut at $y=0$ to display the variation of the interaction energy along the $x$ axis. The central particle is shown.

Figure 5

Radial density distribution in the dust layer as a function of $r$ (the distance from the center), for $\alpha ={90}^{\text{o}}$ and several values of $\eta$.

Figure 6

Snapshot of layer for $\alpha ={90}^{\text{o}}$ and $\eta =0.1$

Figure 7

Snapshot of layer for $\alpha ={60}^{\text{o}}$ and $\eta =0.8$.

Figure 8

Average lattice spacing $b$ (in units of ${\lambda }_D$) versus $\eta$, for various values of angle $\alpha$.

Figure 9

Dust particle central density (in units of $1/{\lambda }_D^2$) versus $\eta$, for various values of angle $\alpha$.

Figure 10

Rhombic angle $\phi$ versus $\eta$, for various values of angle $\alpha$.

Figure 11

Aspect ratio $\nu$ versus $\eta$, for various values of angle $\alpha$.

Figure 12

Total potential energy $U\left(\mathbf{r}\right)=U_E\left(\mathbf{r}\right)+U_M\left(\mathbf{r}\right)$ of the lattice experienced by a test particle situated at $\mathbf{r}=(0,0)$. Lattice parameters are taken from the MD simulations for (a) an $\alpha >{\alpha }_{\mathrm{th}}$ and (b) an $\alpha <{\alpha }_{\mathrm{th}}$ configuration.

Figure 13

Lattice spacing $b$ (in units of ${\lambda }_D$) from “infinite” lattice summation and from finite MD simulations versus $\eta$, for $\alpha ={90}^{\text{o}}$ ($\nu =1$, $\phi ={60}^{\text{o}}$).