Effect of strong coupling on the dust acoustic instability

In a plasma containing charged dust grains, the dust acoustic instability (DAI) can be driven by ions streaming through the dust with speed less than the ion thermal speed. When the dust is strongly coupled in the liquid phase, the dispersion relation of the dust acoustic modes changes in a way that leads to an enhancement of the growth rate of the DAI. In this paper, we show how strong coupling enhances the DAI growth rate and consider application to microgravity experiments where subthermal ion flows are in general possible.

Figure 1

(a) Real frequency ${\omega }_r$ and (b) growth rate $\gamma$ normalized to ${\omega }_{pd}$ versus $k{\lambda }_{Di}$ obtained by solving (5). Parameters are ${\nu }_d=0$, $T_e/T_i=100$, $n_i/n_e=2$, $V_{0i}/v_i=0.2$, $V_{0e}/v_e=0$, and ${\omega }_{pd}/{\omega }_{pi}=1\times {10}^{-4}$. With strong coupling, $\Gamma =725$, $\kappa =3$ (magenta, dashed curves), $\Gamma =300$, $\kappa =2$ (red, solid curves), and the weakly coupled fluid case, obtained by setting $D_L\left(k\right)=0$ (black, dot-dash curves).

Figure 2

(a) Real frequency ${\omega }_r$ and (b) imaginary part of frequency $\gamma$ normalized to ${\omega }_{pd}$ versus $k{\lambda }_{Di}$ obtained by solving (5). The parameters are: $m_i/m_p=40$, $T_e/T_i=154$, $n_i/n_e=8$, ${\omega }_{pd}/{\omega }_{pi}=3\times {10}^{-5}$, and ${\nu }_d/{\omega }_{pd}=0.3$. The weakly coupled case, setting $D_L\left(k\right)=0$, is shown for $V_{0i}/v_i=0.4$ (black, dash-dot curves) and $V_{0i}/v_i=0.8$ (blue, dashed curves). The strongly coupled case with $\Gamma =300$, $\kappa =2$, is shown for $V_{0i}/v_i=0.6$ (red, solid curves).

Figure 3

(a) Real frequency ${\omega }_r$ and (b) imaginary part of frequency $\gamma$ normalized to ${\omega }_{pd}$ versus $k{\lambda }_{Di}$ obtained by solving (5). The parameters are: $m_i/m_p=20$, $T_e/T_i=233$, $n_i/n_e=2$, ${\omega }_{pd}/{\omega }_{pi}=1.35\times {10}^{-4}$, ${\nu }_d/{\omega }_{pd}=0.58$, and $V_{0i}/v_i=0.9$. Weakly coupled case, setting $D_L\left(k\right)=0$ (black, dashed curves). Strongly coupled case, with $\Gamma =300$ and $\kappa =2$ (red, solid curves).

Figure 4

Real frequency ${\omega }_r$ and imaginary part of frequency $\gamma$ normalized to ${\omega }_{pd}$ versus $k{\lambda }_{Di}$ obtained by solving (2), using (3) for all three charged species. The parameters for the dashed curves are: $m_i/m_p=40$, $T_e/T_i=154$, $T_e/T_d=0.1$, $Z_d=3500$, $n_d/n_i=2.5\times {10}^{-4}$, $m_d/m_p=1.4\times {10}^{14}$, ${\nu }_d/{\omega }_{pd}=0.3$, ${\nu }_i/{\omega }_{pi}=0.16$, ${\nu }_e/{\omega }_{pi}=53$, $V_{0i}/v_i=0.8$, and $V_{0e}/v_e=0.05$. The parameters for the dotted curves are: $m_i/m_p=20$, $T_e/T_i=233$, $T_e/T_d=0.58$, $Z_d=1500$, $n_d/n_i=3.3\times {10}^{-4}$, $m_d/m_p=8.2\times {10}^{11}$, ${\nu }_d/{\omega }_{pd}=0.58$, ${\nu }_i/{\omega }_{pi}=0.5$, ${\nu }_e/{\omega }_{pi}=85$, $V_{0i}/v_i=0.9$, and $V_{0e}/v_e=0.06$.