Magnetic Field Blocks Two-Dimensional Crystallization in Strongly Coupled Plasmas

Crystallization in a two-dimensional strongly coupled plasma from a rapidly cooled fluid is found to be efficiently blocked by an external magnetic field. Beyond a threshold of the magnetic field strength $B$, the relaxation time to the equilibrium crystal increases exponentially with $B$, which is attributed to an impeded conversion of potential to kinetic energy. Our finding is opposed to the standard picture of two-dimensional freezing of one-component systems which does not exhibit a nucleation barrier and opens the way to keep two-dimensional fluids metastable over long times.

Figure 1

Top: sketch of the quenching process. Bottom: configuration snapshot of a quarter of the simulation box (${\Gamma }_i=140$) before and after the quench at different magnetic fields (after a time ${\omega }_{p}t=24000$). The color indicates the number of nearest neighbors: 5 [light gray (yellow)], 6 (black), 7 [dark gray (red)], and other (purple).

Figure 2

(a) Temporal evolution of $T^{*}$ for ${\Gamma }_i=140$ for $\beta =0$ to $\beta =2$ (top to bottom curve). The quench takes place at ${\omega }_{p}t=0$; the excursion of the temperature to zero is not shown. (b) Coupling parameter ${\Gamma }_f$ at a time ${\omega }_{p}t=24000$ after the quench as a function the initial coupling parameter ${\Gamma }_i$. (c) Corresponding structural order parameter ${\Delta }_6$ after the quench as a function of ${\Gamma }_i$, indicating a liquid for ${\Delta }_6\gtrsim 0.1$ and a crystal for ${\Delta }_6\lesssim 0.1$.

Figure 3

${\Gamma }_i=140$ (a) Relaxation time scale of the kinetic temperature [cf. Fig. 2a]. (b) Kinetic energy per particle at a time ${\omega }_{p}t=24000$ after the quench. (c) Mean-squared displacement $u_r(t)$ after the quench for $\beta =0.0,0.8,0.9,2.0,1.2$ (bottom to top curve at large times). (d) The value of $u_r(t)$ at ${\omega }_{p}t=4000$, a measure of the long-time diffusivity of the system.

Figure 4

(a)–(c) Solution of Eq. (3) for $\beta$ as indicated. The dashed white lines indicate equipotential lines. (d) Maximum kinetic energy [the value of $\dot{x}(t{)}^2+\dot{y}(t{)}^2$] attained in Eq. (3) up to ${\omega }_{p}t=300$ as a function of $\beta$. The values of $\beta$ of (a)–(c) are indicated by vertical lines [36].

Figure 5

(a)–(c) Single particle in a rigid cage of six neighbors (see the text) at $\beta$ as indicated. The dashed white lines indicate equipotential lines. (d) Maximum kinetic energy attained by the particle with six (black line), five (lower gray line), and seven (upper gray line) nearest neighbors. The values of $\beta$ of (a)–(c) are indicated by vertical lines. The jitter in the curves is specific to the initial conditions [36].