Investigations of the Validity of Quasilinear Theory and the Dynamics of Drift Wave Turbulence

Theoretical basis for the quasilinear theory and analytical investigations of the dynamics of drift wave turbulence are presented in this dissertation. There are three main parts. In the first part, by using the analytical theory of two-point correlations, it is demonstrated that for a one-dimensional, one-species plasma system, the quasilinear theory for Langmuir wave turbulence is valid under the weak turbulence conditions. This calculation also shows that the original predictions of Adam, Laval, and Pesme (Phys. Rev. Lett. 43, 1671(1979)) are incorrect because of the use of an invalid source term for the fluctuations. In the second part, a paradigmatic, two-nonlinearity, dissipative trapped-electron drift wave model is developed to describe the dynamics of a nonuniform magnetized plasma. In this model, mode couplings by both the E times B and the polarization drift nonlinearities are present. The statistical dynamics for this system are investigated using the EDQNM closure scheme. In particular, a large nonlinear frequency shift is shown to be induced by cross coupling of the two nonlinearities. Thus, instability drive is self-consistently modified by this turbulent back reaction. The density fluctuation spectrum is further obtained in different parameter ranges. The results show that the dynamics of dissipative drift wave turbulence are fundamentally different from that of the familiar Hasegawa -Mima model, because E times B drift nonlinearity blocks the low-k condensation of fluctuation energy. The third part generalizes the second part by including the effects of a sheared magnetic field. Both the linear properties of the generalized model, and the multiple helicity nonlinear dynamics, including the interactions of the two nonlinearities, are analyzed in detail. In particular, a one-point renormalization is performed to investigate the nonlinear eigenmode properties and the saturation of the system in the multiple helicity limit. It is shown that for the moderate-to-weak magnetic shear limit, both nonlinearities and cross-coupling effects will affect the nonlinear transfer processes. An analytical explanation of previous computational observation of the suppression of magnetic shear damping by turbulence (D. Biskamp and M. Walter, Phys. Lett. 109A, 34(1985)) is also given.