Trapped ion effect on shielding, current flow, and charging of a small object in a plasma

The problem of electrostatic shielding around a small spherical collector immersed in nonflowing plasma, and the related problem of electron and ion flow to the collector, date to the origins of plasma physics. Calculations have typically neglected collisions, on the grounds that the mean free path is long compared to the Debye length. However, it has long been suspected that negative-energy trapped ions, created by occasional collisions, could be important. This paper presents self-consistent analytic calculations of the density and distribution function of trapped and untrapped ions, the potential profile, the ion and electron current to the collector, and the floating potential and charge of the collector. Under typical conditions for dust grains immersed in a discharge plasma, trapped ions are found to dominate the shielding near the grain, substantially increase the ion current to the grain, and suppress the floating potential and grain charge, even when the mean free path is much greater than the Debye length.