Charging and Heat Collection by a Positively Charged Dust Grain in a Plasma

Dust particulates immersed in a quasineutral plasma can emit electrons in several important applications. Once electron emission becomes strong enough, the dust enters the positively charged regime where the conventional orbital-motion-limited (OML) theory can break down due to potential-well effects on trapped electrons. A minimal modification of the trapped-passing boundary approximation in the so-called ${\mathrm{OML}}^{+}$ approach is shown to accurately predict the dust charge and heat collection flux for a wide range of dust size and temperature.

Figure 1

Dust potential (left) and power collected by the dust from the background electrons (right) versus emitted current ($T_d/T_e=0.03$, $r_d/{\lambda }_{De}=1$).

Figure 2

Potentials for various ${\widehat{J}}_{\text{th}}$ ($T_d/T_e=0.03$, $r_d/{\lambda }_{De}=1$).

Figure 3

The trapped or passing boundary of thermionic electrons for $T_d/T_e=0.03$, ${\widehat{J}}_{\text{th}}=2$, and $r_d/{\lambda }_{De}=1$.

Figure 4

Contours of ${\widehat{J}}_{\text{th}}^{*}$ and $e{\varphi }_d^{*}/T_e$ while varying $T_d/T_e$ and $r_d/{\lambda }_{De}$.