Analytic Moment Method Calculations of the Drift Wave Spectrum

A derivation and approximate solution of renormalized mode coupling equations describing the turbulent drift wave spectrum is presented. Arguments are given which indicate that a weak turbulence formulation of the spectrum equations fails for a system with negative dissipation. The inadequacy of the weak turbulence theory is circumvented by utilizing a renormalized formulation. An analytic moment method is developed to approximate the solution of the nonlinear spectrum integral equations. The solution method employs trial functions to reduce the integral equations t algebraic equations in basic parameters describing the spectrum. An approximate solution of the spectrum equations is first obtained for a model dissipation with known solution, and second for an electron dissipation in the NSA. Analytic Moment Method Calculations of the Drift Wave Spectrum