Mobility in a strongly coupled dusty plasma with gas

The mobility of a charged projectile in a strongly coupled dusty plasma is simulated. A net force $F$, opposed by a combination of collisional scattering and gas friction, causes projectiles to drift at a mobility-limited velocity $u_p$. The mobility ${\mu }_p=u_p/F$ of the projectile's motion is obtained. Two regimes depending on $F$ are identified. In the high-force regime, ${\mu }_p\propto F^{0.23}$, and the scattering cross section ${\sigma }_s$ diminishes as $u_p^{-6/5}$. Results for ${\sigma }_s$ are compared with those for a weakly coupled plasma and for two-body collisions in a Yukawa potential. The simulation parameters are based on microgravity plasma experiments.

Figure 1

Characterization of simulation conditions for $\kappa =2.4$ at two temperatures: (a) $\Gamma =310$ or $T_t=2T_m$ and (b) $\Gamma =62$ or $T_t=10T_m$. The pair correlation functions shown here indicate that the target has a liquidlike structure.

Figure 2

(a) A typical projectile trajectory shown as a curve projected onto the $x$-$z$ plane from a run at $T_t=10T_m$. Also shown is a snapshot of target particle positions within a slab of thickness $\Delta y=1.7a$. (b) Time series of displacements of a representative projectile, showing drift in the $\widehat{x}$ direction and random walk or diffusion in the $\widehat{y}$ and $\widehat{z}$ directions. Data shown are for $F=3.8$. The time series duration corresponds to 610 ms in physical units.

Figure 3

Characterization of regimes using projectile's random velocity $v_{p\perp }$ in the direction $\perp \mathbf{F}$. Two regimes are seen and the transition between them is identified by the intersections of the asymptotes (dashed lines). Speed is normalized here by ${\omega }_{t}a$, which has a value of 31.4 mm/s. Simulations were performed with two sizes $N$ for the number of target particles.

Figure 4

(a) Projectile speed $u_p$ in the direction $\parallel \mathbf{F}$. This drift velocity scales as $u_p\propto F^{1.01\pm 0.12}$ in the low-force regime and $u_p\propto F^{1.23\pm 0.02}$ in the high-force regime. (b) Mobility dependence with $F$. In the high regime (large $F$), we find ${\mu }_p\propto F^{0.23}$. We expect the maximum mobility limit to be ${\left(m_p{\nu }_p\right)}^{-1}$, as indicated by the dashed line, corresponding to the gas drag on a projectile without Coulomb collisions. The power-law scaling of the mobility is the same for two temperatures we simulated.

Figure 5

Scattering cross section ${\sigma }_s$ for target at different temperatures (a) $T_t=2T_m$ and (b) $T_t=10T_m$. The scattering cross section is calculated from Eq. (8) using the results in Fig. 4 for the mobility, which includes the effects due to gas friction. The cross section exhibits a power-law scaling, ${\sigma }_s\propto u_p^{-6/5}$, at the large drift velocity $u_p>\sqrt{k_B{T}_t/m_p}$ shown here.

Figure 6

Comparison of the scattering cross section for a strongly coupled dusty plasma (our data for $T_t=2T_m$ and $10T_m$) with that for classical two-body collision in a Yukawa potential by Lane and Everhart [69] and Hahn et al. [70]. In the range of $0.2<\beta <50$, the cross section in our strongly coupled many-body dusty plasma is generally larger than that for the two-body collision; it also exhibits a single power-law scaling with $\beta$.