Potential around a dust grain placed in the plasma sheath

We present a theory for potential distributions around a charged dust grain in a plasma with flowing ions. For this purpose, we account for absorption of ions by the grain surface and derive a kinetic ion density response for ion flow speed lying between the electron and ion thermal speeds. Poisson's equation is then solved to obtain the potential distribution close and far from the dust grain. It is found that at distances smaller than half the Debye radius, the potential remains spherically symmetric, while at large distances the potential becomes asymmetric.