[en] We have constructed a quadratic dispersion relation, in which various MHD and kinetic effects like ion diamagnetism, electron diamagnetism, electron-electron electron-ion collisions, ion Landau-damping, E x B drift and energetic particles are included and treated in a systematic way. The numerical study in which we use the formalism to investigate the two most likely instabilities in tandem mirror machines produced many quantitative and qualitative results about the two modes. We have proposed a physically motivated, non-perturbative closure scheme to deal with some problems in plasma or fluid turbulence. After discussing a few simple analytically tractable applications, we have applied our formalism to a model problem: the shear-Alfven turbulence. The problem is readily solved numerically to obtain the turbulent spectrum with the following features: the calculated spectrum has explicit frequency shift from the linear theory as well as explicit band-broadening in k, ω space; the frequency integrated spectrum obeys a power law in the intermediate k range, i.e., I/sub k/ /approximately/ K/sup -α/, where α approaches the value 2 in the case we studied; and the form of the power law is hardly influenced by changing low-k, high-k damping effects, or by changing the strength of the turbulence. It is very encouraging that this closure scheme is capable of producing essential features associated with a turbulence spectrum. 66 refs., 38 figs