A scaling law for the dust cloud in radio frequency discharge under microgravity conditions

We employ the approximation of overlapped scattering potentials of charged dust particles exposed to streaming ions to deduce the "equation of state" for a stationary dust cloud in the radio frequency discharge apart from the void dust boundary. The obtained equation defines the potential of a dust particle as a function of the ion number density, the mass of a carrier gas atom, and the electron temperature. A scaling law that relates the particle number density to the particle radius and electron temperature in different systems is formulated. Based on the proposed approach the radius of a cavity around a large particle in the bulk of a cloud is estimated. The results of calculation are in a reasonable agreement with the experimental data available in literature.