Nonlinear Theory of Drift-Wave Turbulence and Enhanced Diffusion

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.

Nonlinear mechanisms for drift wave saturation and induced particle transport

“…(23a) and (24c) to obtain This formula can be interpreted as saying that the growth rate vanishes when the nonlinear contribution to the ion flux T"ij balances the electron flux. This picture of the balances resulting in saturation is essentially the same as that of Dupree,9 with an additional input consisting of the knowledge that the saturated spectra are dominated by the + and -modes.…”

“…One class of approaches treats the electrons linearly and the ions nonlinearly. Examples are the work of Dupree, 9 Terry and Horton, 10,11 and Waltz. 12 In Dupree's resonance-broadening theory, applied to the particular case of the current-driven drift wave, the insta bility grows until the ion diffusion shuts off the growth.…”

“…If the inhibition of the electron E X B diffusion by both coherent effects and resonance depopulation by the parallel acceleration is negligible, then the lin ear electron phase shift used by Dupree, 9 Terry and Horton, 10 ' 11 and Waltz 12 should quite accurately give the electron flux. This will be shown in Sec.…”

“…IX. In this case, the theory of Dupree 9 (applied specifically to collisionless drift waves) would be applicable. Preliminary results from three-dimensional gyrokinetic simulations of drift waves 20 indicate a particle flux significantly enhanced over the 2 -dimensional results, but still somewhat less than the expectation from the linear electron phase shift.…”

Anomalous pinch of turbulent plasmas driven by the magnetic-drift-induced Lorentz force through the Stokes-Einstein relation

“…In the following, we shall use the constant d rr approximation [19] for mathematical simplicity. This approximation gives D = d rr , χ = 5 2 d rr , and χ φ = d rr .…”