Complex plasmas IV: Theoretical approaches to complex plasmas and their application

This paper completes a series of reviews devoted to the physics of complex plasmas, in which one of the components (dust) is in a crystalline or liquid state, while the others (electron, ions, and neutral atoms) are in a gaseous state. This review is devoted to the theoretical approaches used to describe complex plasmas so far. The main theoretical developments have been concentrated in the gaseous and weakly nonideal states of complex plasmas. Here, we describe the achievements in the new kinetic and new hydrodynamic approaches to complex plasmas. At present, only generalizations of the van der Waals approach for complex plasmas have been used to describe phase transitions and plasma condensation in complex plasmas. Here, criteria for transitions are described and compared with the existing experimental observations. Theoretical and numerical results for nonlinear structures, such as dust layers, dust voids, dust sheaths, and dust convective vortices, obtained by solving the stationary balance equations, are also discussed and compared with state-of-the-art experiments. At present, experiments in this field are progressing very fast, while theory is not advancing at the same rate of development. To further develop new theoretical models, one can use the elementary physical processes in complex plasmas described in the previous parts of the review. However, the detailed comparison of theory and experiments also needs more detailed experimental diagnostics of the phenomena observed. In the concluding part of our review, the trends in experiment and theory, as well as some existing applications, including industrial, environmental, and astrophysical ones, are described. (C) 2004 MAIK "Nauka/Interperiodica".