Discharging of dust particles in the afterglow of plasma with large dust density

The discharging of dust particles in the afterglow of plasma with large dust density is studied. We used measured electron and metastable dependencies to calculate the rate describing collection of electrons by dust particles by solving the electron balance equation. This rate is compared with the rate calculated using the orbital motion limited (OML) theory. It is found that the OML theory may not be applied for description of dust charging at large afterglow times, and the energetic electrons generated in metastable-metastable collisions significantly affect charging of dust particles. The time dependence for dust charge is calculated by two different approaches: first, the “standard” approach is used, which assumes that ion and electron fluxes to the dust particles are different in the afterglow. Second, the dust charge is calculated by assuming that desorption of electrons from dust particles is very fast. Both approaches gave similar results for dust charging. In addition, the effects of secondary emission due to ion-dust and metastable-dust collisions on dust discharging are investigated. The main source of dust charging in the late afterglow of plasma with large dust density are the energetic electrons generated in Ar${}^m$ metastable-metastable collisions.

Figure 1

The time dependence for electron density. Solid line: measured electron density; dashed line: the density used in the calculations. On the measured curve, small high frequency modulation upon the much slower density variation is due to the noise.

Figure 2

(a) The time dependence for $K_d^e$. Solid line: the rate obtained using the approach (i) (from the electron balance equation); dotted line: the rate $K_d^{e\text{OML}}$; dashed line: the term $K_d^{ef}{n}_{ef}/n_e$ in Eq. (8). (b) The dust charge calculated using different approaches: dashed line: approach (ii) (using the OML theory and accounting for deposition of thermal and energetic electrons on dust particles); solid line: approach (i) (from the electron balance equation). ${\gamma }_i={\gamma }_m=0$.

Figure 3

Time dependence for the density of energetic electrons (solid line) compared with that of thermal electrons (dashed line). The dependence for $n_{ef}$ is obtained from Eq. (12) for the same conditions as in Fig. 2a.

Figure 4

The dust charge as a function of time calculated by including different groups of electrons. Dashed line: OML theory with both thermal and energetic electrons ($K_d^e=K_d^{e\text{OML}}+K_d^{ef}{n}_{ef}/n_e$); dashed-dotted line: OML theory for thermal electrons only ($K_d^e=K_d^{e\text{OML}}$); dotted line: OML theory with only energetic electrons ($K_d^e=K_d^{ef}{n}_{ef}/n_e$). Solid line is a result of using the collection rate from the approach (i).

Figure 5

The collection rate (a) and dust charge [(b) and (c)] for different ion secondary electron yields. Secondary electron yield for the Ar${}^m$ metastables is set to zero. ${\gamma }_m=0$. Solid line: ${\gamma }_i=0.4$; dashed line: ${\gamma }_i=0.25$; dotted line: ${\gamma }_i=0.1$; dashed-dotted line: ${\gamma }_i=0.01$. The curves in (a) and (b) are obtained using the approach (i) and the curves in (c) are calculated by using the OML theory [approach (ii)]. The other parameters are the same as in Fig. 2.

Figure 6

The collection rate (a) and dust charge (b) as a function of time for different metastable secondary electron yield. Secondary electron yield for the argon ions is set to zero. ${\gamma }_i=0$. Solid line: ${\gamma }_m=0.5$; dashed line: ${\gamma }_m=0.25$; dotted line: ${\gamma }_m=0.01$. The curves are calculated by the approach (i). The other parameters are the same as for Fig. 2.

Figure 7

Dust charge as a function of time calculated using the approach (ii) (dashed line) and the approach (iii) (solid line).