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

A statistical mechanics description is extended for a self-sustained inhomogeneous turbulence, including the effects of thermal fluctuations. Interchange mode in the presence of inhomogeneous magnetic field, which reveals a subcritically-excited strong turbulence, is considered as a collective mode. A Langevin equation is formulated for a test mode, in which the coherent interactions with thermal fluctuations are kept as a collisional drag and the incoherent ones are considered to be thermal noise: The coherent nonlinear interactions are kept as a renormalized turbulent drag, and the incoherent ones are considered to be a random self-noise. Both thermal and turbulent excitations are thus included. The solutions of stationary turbulent state are obtained, provided that both noises are statistically independent. The analysis for the fluctuation level, decorrelation rate, and the correlation functions clearly shows the connection between a mode which is excited by thermal fluctuations and the one being subcritically self-excited. The level is expressed as nonlinear functions (with hysteresis) of nonequilibrium parameter (gradient). A phase diagram is obtained in the gradient-temperature space. An application of the extended fluctuation-dissipation theorem for far non-equilibrium system is explicitly made and new statistical relations are presented.