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

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 26, 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: Ik⊥ 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.