Theory of Strong Turbulence in Plasmas

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Abstract
A theory of fluctuations which may be applicable to a plasma in any of the three states, namely, the quiescent, weakly turbulent, and strongly turbulent states, is obtained from an exact solution of the second equation of the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy for the stationary values of the pair correlation function. A salient feature of the theory is an explicit recognition of the fact that the effective interactions between two particles may be drastically modified because of the presence of strong correlations in a turbulent plasma. As a consequence of such a modification a significant change in the frequency wavenumber dispersion relationship of the collective mode may take place in such a way that the fluctuations with macroscopic intensities can coexist in a stable manner with the given single-particle distributions; this point is specifically illustrated by means of two examples (the cold beam-plasma system and the ion-acoustic wave instability) of turbulent plasmas. The possible existence of size effects in the plasma turbulence is also discussed.