Drift-wave turbulence with wave–wave and wave–particle nonlinear effects in a sheared slab

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Abstract
Low‐β tokamaks have drift‐wave density fluctuations (ñ/n) with the characteristics of strong turbulence. To describe their spectra, earlier work [Phys. Fluids 2 6, 169 (1983)] with simple wave–wave nonlinear coupling models in two dimensions is extended to more physical electrostatic models for drift waves in three dimensions. The electrons are treated with a linear nearly Boltzmann response. The cold ions have nonlinear cross‐field drift motion and linear parallel motion. Numerical methods based on the direct interaction approximation are applied to both wave–wave and wave–particle nonlinear effects, and the spectral intensity Ikxkyk∥ω [ñ/n=(ρs/Ln)I1/2] for a sheared slab is calculated. The shear causes a linear coupling of adjacent kx and k∥ modes. A suggested extension to toroidal geometry is made. Many similarities with experiments are found: I k⊥ is nearly isotropic in k⊥ and peaked at k⊥ρs <O(1/3). Ion Compton scattering damps at large k⊥ρs and parallel ion motion provides critical damping at low ky ρs. Here I1/2∼O(3) is weakly dependent on the linear driving rate γ and best summarized by the mixing length model: ñ/n∼1/kxLn with D∼γ/k2x. The relative frequency spectral widths Δωk/ωk̃ are finite and not inconsistent with those observed experimentally.