Ion trapping by a charged dust grain in a plasma

Motivated by space and laboratory applications, a theory is presented for ions trapped by a charged dust grain in a plasma. The grain’s attractive Debye sphere confines ions after a collision. They shield the grain’s considerable electric charge from external fields. Their number ${\mathit{N}}_{\mathrm{trap}}$ is determined by a balance of the capture and loss rates. At steady state, ${\mathit{N}}_{\mathrm{trap}}$ is independent of the collisional mean free path and increases with the plasma ion density. Because of the density dependence, trapping is significant in laboratory plasmas but not in comparatively less dense space plasmas.