Numerical study on long-wavelength drift-wave instabilities in steep gradients

Drift-wave instabilities are essential for the anomalous transport in tokamak plasmas, and the instability behaviors in steep gradients are not clearly understood yet where unconventional modes become important. Numerical study on long-wavelength drift-wave instabilities in steep gradients is conducted efficiently based on global two-dimensional eigen equations. The results show that two quantum numbers lᵣ, lθ, corresponding to radial and poloidal direction respectively, are necessary to describe the multiple branches of ITG modes and dissipative TEMs. Unlike the conventional ITG branch with ideal ballooning structure, the unconventional ITG modes have anti-ballooning structures and peaks away from the mid-plane. The TEM branches with lᵣ=0, lθ≠0 have similar anti-ballooning structures, but the TEM branches with lᵣ≠0, lθ=0 divide into two up-down symmetric parts. The steeper gradient significantly promotes the mode growth rates γ and heat diffusion coefficient χ̂, with the shrink of mode structures. However, there is a gradient turning point for the conventional ITG branch and unconventional ITG branches with lᵣ=0, lθ≠0. The gradient steepness δ ∝ kθ√Lₙ₀/R is suitable to represent the turning point with δ ≈ 1 under different toroidal mode number. In strong gradient condition, the unconventional branch with lᵣ=1, lθ=0 has the largest χ̂ among all ITG mode branches, rather than the conventional branch. For dissipative TEMs, the main driven forces originate from the collisionality and density gradient, not from temperature gradient. Proper collisionality has the largest driven force for dissipative TEMs, rather than too large collisionality. These results uncover the basic characteristics of drift-wave instabilities in steep gradients, and help to understand the pedestal-relevant experimental phenomena such as the edge coherent mode observed in EAST.