Stationary charge distribution of grains in near-earth plasma: Analytical solution of discrete population balance equations

At zero photo/secondary emission rates we present the analytical solution of the discrete population balance equations giving the stationary charge distribution on,,rains in near-Earth plasma. It is shown that the envelope of the stationary charge distribution can be described by the Gaussian function Lip to very small (similar to 10nm) dust grains. The peak position of (he enveloping curve is deviated from the charge obtained on the basis of equating primary electron and ion fluxes entering the grain. We propose an analytical dependence which is in close agreement with the exact solution in the region under study. We also demonstrate that the ratio of the mean grain surface, energy to the electron temperature in energy units is not a constant as predicted earlier. The ratio has a form of a shifted hyperbolic law and for dust grains similar to 10nm it is almost twice greater than the value obtained for micrometer-sized dust grains.