A kinetic theory of trapped-electron-driven drift wave turbulence in a sheared magnetic field

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Abstract
A kinetic theory of collisionless and dissipative trapped-electron-driven drift wave turbulence in a sheared magnetic field is presented. Weak turbulence theory is employed to calculate the nonlinear electron and ion responses and to derive a wave kinetic equation that determines the nonlinear evolution of trapped-electron mode turbulence. The saturated fluctuation spectrum is calculated using the condition of nonlinear saturation. The turbulent transport coefficients (D, χi, χe), are, in turn, calculated using the saturated fluctuation spectrum. Because of the disparity in the three different radial scale lengths of the slab-like eigenmode: Δ (trapped-electron layer width), xt (turning point width), and xi (Landau damping point), Δ<xt<xi, it is found that ion Compton scattering rather than trapped-electron Compton scattering is the dominant nonlinear saturation mechanism. Ion Compton scattering transfers wave energy from short to long wavelengths where the wave energy is shear damped. As a consequence, a saturated fluctuation spectrum ‖φ‖2(kθ)∼k−αθ (α=2 and 3 for the dissipative and collisionless regimes, respectively) occurs for kθ ρs<1 and is heavily damped for kθ ρs>1. The predicted fluctuation level and transport coefficients are well below the ‘‘mixing length’’ estimate. This is due to the contribution of radial wave numbers x−1t<kr≤ρ−1i to the nonlinear couplings, the effect of radial localization of the trapped-electron response to a layer of width Δ, and the weak turbulence factor 〈γle/ωk〉k<1, which enters the saturation level.