Phase transition of three-dimensional finite-sized charged dust clusters in a plasma environment

The dynamics of a harmonically trapped three-dimensional Yukawa ball of charged dust particles immersed in plasma is investigated as function of external magnetic field and Coulomb coupling parameter using molecular dynamics simulation. It is shown that the harmonically trapped dust particles organize themselves into nested spherical shells. The particles start rotating in a coherent order as the magnetic field reaches a critical value corresponding to the coupling parameter of the system of dust particles. The magnetically controlled charged dust cluster of finite size undergoes a first-order phase transition from disordered to ordered phase. At sufficiently high coupling and strong magnetic field, the vibrational mode of this finite-sized charged dust cluster freezes, and the system retains only rotational motion.

Figure 1

Organization of the charged dust particle cluster containing $N=32$ particles at $\mathrm{\Gamma }=514.38$ and $B=0\mathrm{T}$. (a) A snapshot of the shell configuration of the dust cluster. The filled circles represent particles on the inner shell, and the open circles represent the outer shell particles. (b) The trajectories of the particles for $1.0\times {10}^5$ time steps. (c) The radial position of the particles measured from the center of the simulation box at the final time step of the simulation.

Figure 2

Trajectories of the dust particles for three different values of the applied magnetic field strengths (a) $B=0.001\mathrm{T}$, (b) $B=0.4$ T, and (c) $B=0.6$ T, for $\mathrm{\Gamma }=21.11$.

Figure 3

Trajectories of the dust particles at two different coupling strengths (a) $\mathrm{\Gamma }=15.43$, (b) $\mathrm{\Gamma }=12.86$ keeping magnetic field fixed at $B=0.6$ T.

Figure 4

Variation of the variance of block averaged inter-particle distance fluctuation ($\sigma$) to the strength of the magnetic field $B$ for fixed $\mathrm{\Gamma }=21.107216$.

Figure 5

Plot of trajectories of the dust particles at the critical magnetic field strength $B_c=0.5010114\mathrm{T}$, for three different coupling strengths: (a) $\mathrm{\Gamma }=21.107211$, (b) ${\mathrm{\Gamma }}_c=21.107216$, and (c) $\mathrm{\Gamma }=21.107219$

Figure 6

Variation of the VIDF with coupling parameter at the critical magnetic field $0.5010114\mathrm{T}$.

Figure 7

The $B\text{−}T$ phase diagram separating ordered-to-disordered rotational phase of the finite-sized system of dust particles. The circles indicate numerically obtained data points and the straight line is the critical line satisfying the equation of state $B_c=A\sqrt{T_c}$ with $A=5.8\times {10}^{-3}{\mathrm{T}\mathrm{K}}^{-1/2}$.

Figure 8

The radial distribution function $g\left(r\right)$ with $\mathrm{\Gamma }$ at (a) $B=0\mathrm{T}$, (b) $B=0.5\mathrm{T}$.