Electron density fluctuations in collisional dusty plasma with variable grain charge

The kinetic theory of electric fluctuations in a collisional weakly ionized dusty plasma is formulated with due regard to the grain charging dynamics. The correlation functions of electron and ion density are obtained by considering their collisions with neutrals described within the Bhatnagar-Gross-Krook model. The electron density correlation spectra in isothermal and nonisothermal plasma are calculated for various values of grain density, grain size, and ion collisionality.

Figure 1

Electron (dashed lines) and ion (solid lines) charging frequencies ${\nu }_{\text{ch}}^{\alpha }/{\omega }_{pi}$ vs ion-neutral collision frequency ${\nu }_{in}$ in isothermal ($\tau =1$) argon plasma for $a/{\lambda }_D=1$, 0.15, 0.01.

Figure 2

Ion-grain collision frequency ${\nu }_{ig}/{\omega }_{pi}$ vs ion-neutral collision frequency in isothermal ($\tau =1$) argon plasma for $P=0.5$ (solid lines) and $P=0.8$ (dashed lines), $a/{\lambda }_D=1$, 0.15, 0.01.

Figure 3

Normalized electron density correlation spectra ${\langle \delta n_{\alpha }^2\rangle }_{\mathbf{k}\omega }{\omega }_{pi}/n_i$ in ordinary nonisothermal ($\tau =100$) argon plasma for ${\nu }_{in}/{\omega }_{pi}=0,2\times {10}^{-4},5\times {10}^{-4},1\times {10}^{-3},2\times {10}^{-3}$; $k/k_{Di}=0.1$.

Figure 4

Normalized electron density correlation spectra ${\langle \delta n_{\alpha }^2\rangle }_{\mathbf{k}\omega }{\omega }_{pi}/n_i$ in ordinary nonisothermal ($\tau =100$) argon plasma for ${\nu }_{in}/{\omega }_{pi}=0.02, k/k_{Di}=0.1, P=0,0.2,0.5$. Dashed line corresponds to Eq. (35) and plasma particle susceptibility (36) including collisions with grains ${\nu }_{\alpha }={\nu }_{\alpha n}+{\nu }_{\alpha g}, a/{\lambda }_D=0.15$. Dotted line corresponds to Eq. (32).

Figure 5

Normalized electron density correlation spectra ${\langle \delta n_{\alpha }^2\rangle }_{\mathbf{k}\omega }{\omega }_{pi}/n_i$ in nonisothermal ($\tau =100$) argon plasma for ${\nu }_{in}=0.02{\omega }_{pi}, a/{\lambda }_D=0.15, k/k_{Di}=0.05,0.1,0.2, P=0,0.2,0.5$; $a/{\lambda }_D=0.01$ (dotted line) and $a/{\lambda }_D=1$ (dashed line). Insert is the maximum value of normalized electron correlation function vs $k/k_{Di}$.

Figure 6

Normalized electron density correlation spectra ${\langle \delta n_{\alpha }^2\rangle }_{\mathbf{k}\omega }{\omega }_{pi}/n_i$ in nonisothermal ($\tau =10$) argon plasma for $k/k_{Di}=0.1, {\nu }_{in}/{\omega }_{pi}=0.02,0.1,0.5,2, P=0$ (solid lines), and $P=0.5$; $a/{\lambda }_D=0.15$ (dashed line).

Figure 7

Normalized electron density correlation spectra ${\langle \delta n_{\alpha }^2\rangle }_{\mathbf{k}\omega }{\omega }_{pi}/n_i$ in isothermal ($\tau =1$) argon plasma for ${\nu }_{in}=0.02{\omega }_{pi}, a/{\lambda }_D=0.15, k/k_{Di}=0.05,0.1,0.2$, and $P=0,0.2,0.5$.

Figure 8

Normalized electron density correlation spectra ${\langle \delta n_{\alpha }^2\rangle }_{\mathbf{k}\omega }{\omega }_{pi}/n_i$ in isothermal ($\tau =1$) argon plasma for ${\nu }_{in}=0.02{\omega }_{pi}, k/k_{Di}=0.1, P=0,0.5,0.8, a/{\lambda }_D=0.01$ (dashed lines), and $a/{\lambda }_D=1$ (solid lines).