A Roadmap to Recent Developments in the Theory of Turbulent Generation of Long-wavelength Flows
Author: John A. Krommes
Date of PPPL Report: March 2004
Presented at: the Thirteenth Toki International Conference on Plasma Physics and Controlled Nuclear Fusion (ITC-13), 9 - 12 December 2003, Japan.
A brief overview is given of recent results in the theory of turbulent generation of long-wavelength fluctuations; references are provided to more detailed calculations in the literature. Emphasis is placed on conceptual foundations and technical tools, which can be simply illustrated by studies of the scalar (one-field) generalized Hasegawa-Mima equation. Then a functional Hamiltonian formalism is discussed as a way of efficiently handling systems of coupled fields. Casimir invariants are shown to be the appropriate "plasmon densities"; a tensor spectral-balance equation builds in the conservation constraints automatically. A concise expression can be obtained for the nonlinear growth rate in terms of the spectral density, a tensor generalization of the triad interaction time, and the metric tensor and structure constants of the Hamiltonian structure.