Nonlinear Theory of Macroinstabilities and Enhanced Transport in Plasmas

A method is described for solving the magnetohydrodynamic equations for nonlinear plasma waves and turbulence due to macroinstabilities. It is argued that the dominant nonlinear effect for macroinstabilities is the scattering of fluid elements of charge by plasma waves. The consequent wave-fluid interaction causes an enhanced diffusion coefficient in the continuity equation and an identical enhanced viscosity coefficient in the momentum equation. This enhanced plasma transport is analogous to the eddy transport and Reynolds stress of neutral turbulence. A nonlinear dispersion relation is obtained from the linear dispersion relation by simply adding the enhanced diffusion term to the frequency. It is shown that linear macroinstabilities are stabilized by the enhanced diffusion, and viscosity, terms. As examples, the enhanced diffusion coefficients, and density and electric field fluctuations are calculated for resistive instabilities.