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Abstract
A new approach to the problem of turbulent transport in plasmas is formulated, based upon the constraints imposed by boundary conditions and conservation laws. This approach is consistent with several recent phenomenological studies of global confinement scalings in magnetically confined fusion plasmas. It implies that the edge regions of such configurations are particularly important in determining fluxes of particles and thermal energy. A general method for studying turbulent transport from this point of view is elaborated. The method is applied to a simple model, which shares some salient features with the fluctuations that account for transport in the edge regions of experimental plasmas; these features include wavelike behavior on large scales and a self-consistent relation between mean quantities and the fluctuations in dynamic equilibrium. A mixing-length analysis is presented, based upon these general properties and a small number of additional physical assumptions. The mixing-length theory, which accounts for phase relations, transport, and the mean density gradient in the nonlinear state, emphasizes the balance between turbulent and classical transport mechanisms in the edge region. It requires input from a weakly nonlinear theory, which is developed in the form of a rigorous bifurcation analysis. The perturbative treatment shows that the model system undergoes a supercritical Hopf bifurcation. A nonlinear stability calculation using the energy method indicates that nonlinear instabilities are unlikely for the model. A rigourous bound on the particle transport consistent with the model is obtained, and methods for improving this bound are outlined.
