Studies of the charging of a thin dust layer in a plasma

When an infinite plane layer of dust having a number-density profile normal to the plane is exposed to an ambient e(sup -), p(sup +) plasma, one can imagine the features of the charging process near the layer boundary. If the e(sup -), p(sup +) temperatures are equal, and the B field is normal to the dust layer, the controlling factor is the large electron relative to proton speeds. Since the collision rate between plasma particles of number density n and speed v and an uncharged dust grain of radius a is estimated as the product n v pi a(exp 2), electrons dominate the charging process. The outer edge of the layer charges negatively, setting up an electrical potential that inhibits penetration of electrons into the layer and at the same time accelerates protons inward. Interior to the outer negative region then, one would expect many energetic protons compared to a reduced number of electrons from the ambient plasma. Charge imbalances are bound to arise, but the details are not so easy to deduce from simple arguments. These details are the subject of the present study.