Effect of electron emission on the charge and shielding of a dust grain in a plasma: A continuum theory

The continuum approximation is used to analyze the effect of electron emission from the surface of a spherical dust grain immersed in a plasma on the grain charge by assuming negligible ionization and recombination in the disturbed plasma region around the grain. A parameter is introduced that quantifies the emission intensity regardless of the emission mechanism (secondary, photoelectric, or thermionic emission). An analytical expression for the grain charge Z _d is derived, and a criterion for change in the charge sign is obtained. The case of thermionic emission is examined in some detail. It is shown that the long-distance asymptotic behavior of the grain potential follows the Coulomb law with a negative effective charge Z _eff, regardless of the sign of Z _d. Thus, the potential changes sign and has a minimum if Z _d > 0, which implies that attraction is possible between positively charged dust grains.