Nonlinear Theory of Drift-Wave Turbulence and Enhanced Diffusion

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Abstract
The turbulent plasma state which develops from unstable, current‐driven drift waves is analyzed. In the nonlinear theory, the wave growth predicted by the linear theory is ultimately suppressed by ion damping. Since the phase speeds of the unstable waves are much greater than the ion thermal velocity, the ions cannot absorb wave energy until they become trapped. The amplitude of the turbulent spectrum grows until trapping occurs, and a quasi‐steady state is reached in which the directed electron energy is converted into ion thermal energy at a constant rate. In this state the perturbation of the density gradient due to the turbulence is equal to the mean gradient. Nonlinear limitation due to mode coupling does not suppress the unstable wave growth until much larger density perturbations have developed. Therefore, ion trapping is established as the controlling nonlinear mechanism. In the steady state, the ions diffuse across the magnetic field with a diffusion coefficient D⊥ ≈ (k⊥ −2γ)max, where γ is the growth rate predicted by the linear theory and k⊥ is a perpendicular wavenumber. Although the detailed treatment is for a specific instability, the general conclusions appear to apply to a variety of drift waves.