Dust Self‐Organized Structures II. Solutions of Master Equations for Small Diffusion

Abstract

AbstractMaster equations for spherical dust structures are solved numerically using the asymptotic solutions at the center of the structures for the case of absence of external ionization and small diffusions. The structures are determined by a single parameter, the external plasma flux at the surface of the structure. The equilibrium states that are possible in a limited range of this parameter are investigated numerically. It is demonstrated that in the range of existence of equilibria the structures are changing their shapes and type of distributions inside the structures. For large external fluxes the ion and dust distributions can have peaks inside the structures while for low external fluxes the dust distribution has a single maximum at the structure center. The lower is the external flux supporting the structure the larger is its size. An increase of the external flux decreases the accumulation of dust and ions at the center. The total number of dust confined by the structure is larger for larger size structures. Estimates of dust crystallization inside structures are given. The role of diffusion is calculated by perturbations and is shown to be small in all structure regions except the structure edges. In the perturbation theory we use the exact expressions of the diffusion coefficients calculated previously numerically. The regions with dust density peaks inside the structures have been calculated with two order of magnitude larger precision that allows to resolve the structure parameter dependencies inside the peaks. It is shown that although in peaks the gradients of all parameters are increased the diffusion flux is still small and that the continuity and hydrodynamic approach are applicable within an accuracy about several %‐s (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)