The floating potential of spherical probes and dust grains. II: Orbital motion theory

Probe theory is generally used to find the potential of dust particles immersed in plasma. The orbital motion limited theory (OML) is often used to find the potential at the probe surface, but the assumptions underlying this theory are usually not valid in the case of dust and the more general orbital motion (0111) theory, is much harder to calculate. Solutions are given for the OM theory in a range of cases applicable to dust. It is shown that the surface potential the full theory gives reduces to the OML result for small probes. Commonly in dusty plasmas the OML surface potential is used, with the surrounding distribution given by Debye-Mickel, or Yukawa theory. This form, however, neglects ion depletion due to the absorption of particles on the probe surface. In this paper a new analytical solution to the system is given which is applicable to small probes and dust. This new expression is equivalent to Yukawa form, but takes ion absorption into account.