Spectra of ion density and potential fluctuations in weakly ionized plasmas in the presence of dust grains

The spectral densities of ion density and electrostatic potential fluctuations are derived in the framework of a self-consistent kinetic model of partially ionized dusty plasmas in the low-frequency regime. Neutral gas density can be responsible for significant modifications of the fluctuation level, hence the inclusion of the effect of neutrals is essential for a more realistic comparison with experiments, especially if spectral measurements are intended for dust diagnostic purposes. Comparison with the multicomponent model, attractive due to its simplicity as compared to the self-consistent one, is carried out to establish its limits of validity. Numerical calculations are performed for parameters typical of low-temperature plasma discharges. A criterion is derived for the omission of plasma discreteness in the low-frequency regime.

Figure 1

Spectral density of the ion density fluctuations as a function of the normalized frequency $\omega /k{v}_{Td}$ for the full (red bottom line) and the multicomponent (blue top line) kinetic models for different wave numbers $k{\lambda }_{Di}$. The plasma and dust parameters are $n_i={10}^{11}$ cm${}^{-3}$, $P_n=10$ Pa, $T_e=3$ eV, $a=50$ nm, and $P=0.01$. The levels of fluctuations in a dust-free plasma for increasing $k{\lambda }_{Di}$ are $S_{\mathit{k},\omega }^i/n_i=1.5\times {10}^{-7},1\times {10}^{-8},2.6\times {10}^{-10},$ and $2.2\times {10}^{-10}$ s, respectively.

Figure 2

Spectral density of the electrostatic potential fluctuations as a function of the normalized frequency $\omega /k{v}_{Td}$ for the full (red top line) and the multicomponent (blue bottom line) kinetic models for different wave numbers $k{\lambda }_{Di}$ and the parameters of Fig. 1. The levels of fluctuations in a dust-free plasma for increasing $k{\lambda }_{Di}$ are $S_{\mathit{k},\omega }^{\phi }/e^2=6\times {10}^{-4},4\times {10}^{-5},7\times {10}^{-7},$ and $2.4\times {10}^{-7}$ cm s, respectively.

Figure 3

Spectral density of the ion density fluctuations as a function of the normalized frequency $\omega /k{v}_{Td}$ for the full (red bottom line) and the multicomponent (blue top line) kinetic models for varying dust radii. The parameters are $n_i={10}^{11}$ cm${}^{-3}$, $P_n=10$ Pa, $T_e=3$ eV, $P=0.01,$ and $k{\lambda }_{Di}=0.05$. For increasing radius the dust densities are $n_d=4.8\times {10}^6,2.3\times {10}^6,4.3\times {10}^5,$ and $2.1\times {10}^5$ cm${}^{-3}$. The level of fluctuations in a dust-free plasma is $S_{\mathit{k},\omega }^i/n_i=2.6\times {10}^{-10}$ s.

Figure 4

Spectral density of the ion density fluctuations as a function of the normalized frequency $\omega /k{v}_{Td}$ for the full (red bottom line) and the multicomponent (blue top line) kinetic models for varying dust densities. The parameters are $n_i={10}^{11}$ cm${}^{-3}$, $P_n=10$ Pa, $T_e=3$ eV, $a=50$ nm, and $k{\lambda }_{Di}=0.05$. For increasing $P$ the dust densities are $n_d=4.8\times {10}^5,2.4\times {10}^6,4.8\times {10}^6,$ and $2.3\times {10}^7$ cm${}^{-3}$. The level of fluctuations in a dust-free plasma is $S_{\mathit{k},\omega }^i/n_i=2.6\times {10}^{-10}$ s.

Figure 5

Spectral density of the ion density fluctuations as a function of the normalized frequency $\omega /k{v}_{Td}$ for the full kinetic model for varying pressure. The parameters are $n_i={10}^{11}$ cm${}^{-3}$, $T_e=3$ eV, $a=50$ nm, $P=0.01$, and $k{\lambda }_{Di}=0.05$. The level of fluctuations in a dust-free plasma for increasing pressure is $S_{\mathit{k},\omega }^i/n_i=1.2\times {10}^{-10},5.3\times {10}^{-10},1.8\times {10}^{-9},5\times {10}^{-9},1\times {10}^{-8},$ and $2.3\times {10}^{-8}$ s, respectively.

Figure 6

Spectral density of the ion density fluctuations as a function of the normalized frequency $\omega /k{v}_{Td}$ for the full kinetic model for varying electron temperature. The parameters are $n_i={10}^{11}$ cm${}^{-3}$, $P_n=10$ Pa, $a=50$ nm, $P=0.01$, and $k{\lambda }_{Di}=0.05$. For increasing $T_e$ the dust charge number is $Z_d=12$, 50, 87, 207, 257, 303, and 346. The level of fluctuations in a dust-free plasma for increasing $T_e$ is $S_{\mathit{k},\omega }^i/n_i=9\times {10}^{-8},6\times {10}^{-9},1.7\times {10}^{-9},2.6\times {10}^{-10},1.6\times {10}^{-10},1.2\times {10}^{-10}$, and $9\times {10}^{-11}$ s, respectively.