Role of stochastic processes in particle charging due to photoeffect on   the Moon
  Neglecting the effects associated with the solar wind plasma, the photoelectrons are the only elementary particles which create an electrical current through sunlit surface of the moon. They are knocked off of the surface soil, rise above the surface, and then fall back. Therefore, on average, on any unit of surface area there is a positive charge, equal in magnitude to the charge of photoelectrons flying over this area. However, the charge of any small dust particle can strongly fluctuate discretely: a photoelectron can be either knocked off of the or be reacquired by the particle. The result is a "random walk" in sign and magnitude of the charge of grains. In a few minutes after sunrise, almost every dust particle on the surface has at least one extra or missing electron, and the average modulus of the charge accumulated on a particle is proportional to the square root of the number of "steps" (knocking off /returns of photoelectrons). Therefore, the average value of the modulus of the charge of a fine dust particle exceeds by several orders of magnitude the proportion of the average surface charge attributable to the particle. So dust particles that have ejected a sufficient number of photoelectrons can take off from the surface because of the electric field of the near surface charge double layer. It is shown that: (i) almost half of all dust particles on the illuminated lunar surface are missing at least one electron; (ii) a significant portion of particles up to 100 nm in size emits several photoelectrons and acquire a positive charge, sufficient to take off from the surface; (iii) above the surface there is a "boiling layer" of dust with a maximum thickness of several hundred meters where the average size of the particles and their density non-monotonically depend on the altitude. 
Eugene V. Rosenfeld, Alexander V. Zakharov
astro-ph.EP