Dust Self-Organized Structures I. Role of Ion Drag and Ion Diffusion on Screened Grains

Self-organized dust structures are investigated using a Gurevich-Parker model for non-linear dust screening. The non-linear dust drag coefficients and non-linear diffusion coefficients are calculated numerically as functions of nonlinear parameter for screening, dust density and ion flux drift velocity. Nonlinear ion dust drag inside the structures creates an electric field with potential well for ions at the structure center. The equilibrium dust structures confine both the dust grains and the plasma particles, have a finite size and have inside an enhanced dust and ion densities. The necessary conditions for existence of equilibrium dust structures are found. The equilibrium dust structures are determined by two global parameters related to the external plasma flux and to the power of ionization. The equilibrium exist only in a restricted phase space of these two parameters and depends on the the drag coefficient at the structure center. The equilibrium requirements are found using non-linear drag coefficient calculated numerically. It is shown that this phase space area can be broad but it is systematically decreasing with an increase of the ionization rate. It is found that equilibrium exists for dust structures with large dust and ion density concentration at the center and that for these structures the ion diffusion is strongly suppressed by ion scattering on non-linearly screened grains. The results of the theory can be used to interpret the recently observed compact dust structures in micro-gravity experiments and can provide some recommendations for future micro-gravity experiments in spherical chambers (© 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)