Statistical theory of subcritically-excited strong turbulence in inhomogeneous plasmas. III

A statistical theory of nonlinear-nonequilibrium plasma state with strongly developed turbulence and with strong inhomogeneity of the system has been developed. A unified theory fur both the thermally excited fluctuations and the strongly turbulent fluctuations is presented. With respect to the turbulent fluctuations, the coherent part to a certain lest mode is renormalized as the drag to the test mode: and the rest, the incoherent part, is considered Co be a random noise. The renormalized operator includes the effect of nonlinear destabilization as well as the decorrelation by turbulent fluctuations. Formulation is presented by deriving an Fokker-Planck equation for the probability distribution function. Equilibrium distribution function of fluctuations is obtained, Transition from the thermal fluctuations, that is governed by the Boltzmann distribution, to the turbulent fluctuation is clarified. The distribution function for the turbulent fluctuation has tail component and the width of which is in the same order as the mean fluctuation level itself. The Lyapunov function is constructed for the strongly turbulent plasma, and it is shown that an approach to a certain equilibrium distribution is assured. The result for the most probable state is expressed in terms of 'minimum renormalized dissipation rate', which is given by the ratio of the nonlinear decorrelation rate of fluctuation energy and the random excitation rate which includes both the thermal noise and turbulent self-noise effects. Application is made for example to the current-diffusive interchange mode turbulence in inhomogeneous plasmas. The applicability of this method covers plasma turbulences in much wider circumstance as well as neutral fluid turbulence. This method of analyzing strong turbulence has successfully extended the principles of statistical physics, i.e,, Kubo-formula, Prigogine's principle of minimum entropy production rate. The condition for the turbulence transition is analogous to the Maxwell's construction in the phase transition physics in thermodynamical equilibrium. The method provides the extension of the nonequilibrium statistical physics to the far-nonequilibrium states.