Equilibrium electric potential of spherical, cylindrical, and planar dust grains moving through a plasma

The charge on a dust grain in a plasma depends on the plasma parameters and on the grain's velocity through the plasma. Intuition suggests that at high velocity the grain should sweep up equal numbers of both the positive and negative plasma species, and so it should come to zero potential with respect to the plasma. This is in fact not always the case. We have derived the equilibrium potential phi of a small conducting sphere moving at speed w through a plasma of temperature T composed of electrons with charge -e and ions with charge Ze and mass ratio M = m(i)/m(e) and find that for large w the potential goes to the finite value e phi/kT = -1/2[(M - 1)/(M + Z)]. For a conducting cylinder of infinite length in the same plasma, e phi/kT is slightly different owing to the different potential variation outside the grain, but for large cylinder speed the potential goes to the same nonzero limit as the sphere. The case of an infinite, conducting plane is quite different, and values depend on whether there is plasma on one side of the plane or on both. In the latter case, which is most analogous to those of the sphere and cylinder, phi does go to zero for large plane speed. We show equilibrium e\phi\/kT versus w curves for the three elementary shapes, in each instance for an O+ - e(-), H+ - e(-), and ''5m(e)''(+) - e(-) plasma, and comment on characteristics. The last example is a plasma of electrons and ions having the artificially small mass ratio M = 5, of interest because results can be compared with computer simulations of particle dynamics in the presence of a charged grain.