Although a general description of the pair grain interaction can be directly obtained from fluctuations of grain distributions and grain pair correlation function, we prefer here to give a simple description of the collective interaction using the model of a “test” grain in a “sea” of all other grains. In the limit of linear fluctuations this can lead to a direct description of the grain interaction in the presence of many grains (with collective effects included) for β ≪ 1. But using this approach we will also be able to demonstrate how the non-linearity changes the collective interaction for β ≫ 1.

Formation of structures is one of the most general phenomenon in complex plasmas and includes ordered as well as disordered grain distributions. The universal structurization instability operates also for both ordered and disordered states. Such an instability does not exist in an ordinary plasma without dust. Contrary to ordinary plasmas, dusty plasmas have a large rate of dissipation. Let us remind that ordinary plasmas is often unstable due to low rate of binary collisions. There was a long-term investigation on ordinary plasmas which led to conclusion that almost only binary particle collisions can thermalize their particle distribution (if contacts with thermal surfaces are not important). In ordinary plasmas, even small deviations in particle distribution from thermal distributions create instabilities. Complex plasmas, contrary to ordinary plasmas, are very dissipative systems that need a constant supply of energy and particles in order to exist. This opens a door for the universal instability related to the structure formation and to self-organization processes in ordered as well as in disordered states.

The first experiments on complex plasma condensation into dust plasma crystals are [1, 2, 3, 4, 5, 6]. The physical explanation of the condensation takes into account general physical conditions met in the experiments. One can also use general features of a complex plasma as a state of matter described in details above as well as the new types of the grain attraction, collective and non-collective. Except general concepts, the detailed theory of the complex-plasma phase transition does not exist and the detailed investigation of the grain-grain interaction is still required both experimentally and theoretically. There are many steps to be done after fixing the nature of the pair grain interaction in order to obtain a complete theory of phase transitions in a complex plasma. From a general point of view, it is even difficult to introduce the concept of free energy (which is widely used in the theory of phase transitions in the ordinary matter) to begin with theoretical description of phase transitions in complex plasmas.

The material given in the previous chapter shows that recently discovered complex plasmas present a new kind of matter not previously encountered and that investigation of this new field of physics is only in its first stage. Many new discoveries can be expected in the very near future. The field is very rapidly developing and is of major importance to fundamental science. Usually, most new discoveries in fundamental science have many future applications. It is very difficult to predict such discoveries, and new discoveries usually require some time to be incorporated into everyday life. But the situation with complex plasmas is different because the recent boom in the field not only stems from scientific discoveries but was simultaneously dictated by several problems of industry.

The aim of this chapter is to demonstrate that a complex plasma requires formulation of a new ground state with the balance of fluxes as an inevitable feature. The flux variation has a strong effect on the propagation of collective modes leading not only to the mode damping but also to an instability which leads to formation of structures in complex plasmas.