Influence of dust-particle concentration on gas-discharge plasma

A self-consistent kinetic model of a low-pressure dc glow discharge with dust particles based on Boltzmann equation for the electron energy distribution function is presented. The ions and electrons production in ionizing processes as well as their recombination on the dust-particle surface and on the discharge tube wall were taken into account. The influence of dust-particle concentration $N_d$ on gas discharge and dust particles parameters was investigated. It is shown that the increase of $N_d$ leads to the increase of an averaged electric field and ion density, and to the decrease of a dust-particle charge and electron density in the dusty cloud. The results were obtained in a wide region of different discharge and dusty plasma parameters: dust particles density ${10}^2–{10}^8{\text{cm}}^{-3}$, discharge current density ${10}^{-1}–{10}^1\text{mA}/{\text{cm}}^2$, and dust particles radius 1, 2, and $5\mu \text{m}$. The scaling laws for dust-particle surface potential and electric filed dependencies on dust-particle density, particle radius and discharge currents were revealed. It is shown that the absorption of electrons and ions on the dust particles surface does not lead to the electron energy distribution function depletion due to a self-consistent adjustment of dust particles and discharge parameters.

Figure 1

(Color online) Dust-particle surface potential (lines), ${\phi }_s$, and axial electric field (symbols), $E_z$, dependencies on dust-particle concentration, $N_d$, for different dust-particle radii: solid line and circles for $r_0=1\mu \text{m}$, dashed line and squares for $r_0=2\mu \text{m}$ and dashed dotted line and triangles for $r_0=5\mu \text{m}$. $N_g=1.75\cdot {10}^{16}{\text{cm}}^{-3}$, and $j_z=1\text{mA}/{\text{cm}}^2$. Helium.

Figure 2

(Color online) Charged particle concentration dependencies on dust-particle concentration, $N_d$, for different discharge current densities; symbols present results for $j_z=10\text{mA}/{\text{cm}}^2$: circles for $n_e$, squares for $n_i$, and triangles for $N_d{Z}_d$, and lines for $j_z=1\text{mA}/{\text{cm}}^2$: solid line for $n_e$, dashed line for $n_i$, and dashed dotted line for $N_d{Z}_d;r_0=1\mu \text{m}$ and $N_g=1.75\cdot {10}^{16}{\text{cm}}^{-3}$. Helium.

Figure 3

(Color online) Dependencies of frequencies of electron-impact ionization, ${\nu }_i$, charge recombination on the dust-particle surface, ${\nu }_d$, and wall recombination, ${\nu }_w$, on the dust-particle concentration, $N_d$, for two values of initial electric field: $E_0/p=4\text{V}/\left(\text{cm}\cdot \text{Torr}\right)$ (dashed line for ${\nu }_i$, dashed dotted line for ${\nu }_d$, solid line for ${\nu }_w$) and $E_0/p=8\text{V}/\left(\text{cm}\cdot \text{Torr}\right)$ (squares for ${\nu }_i$, circles for ${\nu }_w$, triangles for ${\nu }_d$). Helium, $N_g=1.75\cdot {10}^{16}{\text{cm}}^{-3}$, $r_0=1\mu \text{m}$, and $j_z=1\text{mA}/{\text{cm}}^2$.

Figure 4

(Color online) Dust-particle surface-potential ${\phi }_s$ dependencies on the scaling parameter, $N_d{r}_0/j_z$, for different particle radii (symbols) $r_0=1,2,5\mu \text{m}$, and discharge current densities (lines): $j_z=0.1$, 1, and $10\text{mA}/{\text{cm}}^2$. $N_g=1.75\cdot {10}^{16}{\text{cm}}^{-3}$. Helium.

Figure 5

(Color online) Dust-particle surface potential (${\phi }_s$, lines) and axial electric field (symbols) dependencies on dust-particle concentration, $N_d$, for different buffer gases: solid line and circles for helium; dashed line and triangles for neon; dashed dotted line and squares for argon; $r_0=1\mu \text{m}$, $N_g=1.75\cdot {10}^{16}{\text{cm}}^{-3}$, and $j_z=1\text{mA}/{\text{cm}}^2$.

Figure 6

(Color online) Electron-energy distribution functions in dusty plasma for $E_z=8.6\text{V}/\text{cm}$, $N_g=1.75\cdot {10}^{16}{\text{cm}}^{-3}$, $j_z=0.1\text{mA}/{\text{cm}}^2$. Self-consistent solutions: $r_0=1\mu \text{m}$, $N_d=9.2\cdot {10}^6{\text{cm}}^{-3}$, and ${\phi }_s=1.82\text{eV}$ (squares); $r_0=2\mu \text{m}$, $N_d=2.7\cdot {10}^5{\text{cm}}^{-3}$, and ${\phi }_s=2.26\text{eV}$ (triangles); $r_0=5\mu \text{m}$, $N_d=5.1\cdot {10}^4{\text{cm}}^{-3}$, and ${\phi }_s=3.02\text{eV}$ (circles). Nonself-consistent solution for the given parameters ($r_0=1\mu \text{m}$, ${\phi }_s=1.82\text{eV}$, and $E_z=8.6\text{V}/\text{cm}$): $N_d=9.2\cdot {10}^5{\text{cm}}^{-3}$ (solid line); $N_d=9.2\cdot {10}^7{\text{cm}}^{-3}$ (dashed line). Helium.