Development of the concepts of plasma turbulence

The review is devoted to exposition of the physical principles on which the current ideas on plasma turbulence are based. A comparison is made of the results obtained in the theory of plasma turbulence and the turbulence of incompressible liquids. The basic physical differences between hydrodynamic and plasma turbulence are pointed out. It is shown how the concepts of turbulent excitations arise in the statistical description of turbulence. The fundamental difference is pointed out between turbulent elementary excitations and elementary excitations describing a state close to thermodynamic equilibrium. Special emphasis is given to explanation of the physical meaning of the concept of effective turbulent collisions. It is shown that inclusion of turbulent collisions does not make possible construction of a theory of weak turbulence on the basis of simple expansions of the interaction in the turbulence energy. Examples are presented which show that effective turbulent collisions can fundamentally change the theoretical predictions which must be compared with existing experiments. It is shown how the inclusion of effective turbulent collisions permits construction of a theory of correlation functions of turbulent plasma fields. In connection with the discussion of new approaches to the theory of weak turbulence, taking into account effective turbulent collisions, an analysis is carried out of the theories of anomalous electrical conductivity of a plasma in an external electric field.