Kinetic Equations for Turbulent Plasmas. II. Fluctuation Spectrum

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Abstract
When the many-particle distribution functions are constructed by summing all possible products of the single-particle distribution functions and the pair correlation functions, the BBGKY hierarchy exhibits a modification in the effective interaction owing to the presence of the finite correlations; the pair correlation function as well as the single-particle distribution develops in time with inclusion of the correlation effects in its kinetic equation. We solve the second member of the hierarchy in the fluid limit, assuming that the plasma is in a weakly turbulent stationary state. A dielectric response function of such a turbulent plasma is thereby obtained; an integral equation which self-consistently determines the energy spectrum of turbulence is then derived. A simplification of this equation arising in connection with certain experimental applications is also discussed. It is shown that the solution of the equation leads to a positive energy spectrum for both turbulent and quiescent plasmas.