Limits of validity for orbital-motion-limited theory for a small floating collector

The orbital-motion-limited (OML) theory has been widely used to calculate the ion response to a charged grain immersed in plasma. The theory assumes there are no potential barriers preventing plasma ions from reaching positive-energy points in phase space. However, Allen et al. [J. Plasma Phys. 63, 299 (2000)] have recently shown that for any finite-size negatively charged dust grain in a Maxwellian plasma, there are always potential barriers sufficient to exclude some ions. We calculate the magnitude of the potential barriers, and determine which ions are subject to barriers. The OML theory is shown to become exact in the limit of small grain size, and to be very accurate in calculating ion current to the grain for typical conditions pertinent to dusty plasma. Thus OML theory is well justified in calculating the floating potential. However, we find that potential barriers can influence the shielding of the potential at r approximate to gimel (D) under some conditions, especially large grams, high plasma density, and small T-i/T-e.