Effects of moderate small-scale shear flow, e.g., which may be created by the trapped electron mode, on electromagnetic (EM) ion-scale turbulence in tokamak plasmas are numerically investigated via a self-consistent Landau-fluid model. A modeling analysis is carried out in slab geometry to reveal the underlying mechanism of the multi-scale multi-mode nonlinear interaction. Results show that while a Kelvin–Helmholtz (KH) instability with long wavelengths may be excited by the shear flows to dominate the multi-scale EM fluctuation, shorter wavelength ion temperature gradient (ITG) modes experience multiple quasi-steady (QS) stages with enhanced fluctuation level through different driving and saturation mechanisms. One mechanism is the secondary ITG instability due to the decrease in flow stabilization modified by the zonal flow. Meanwhile, the other one is the modulational interaction between the EM ITG and KH modes through the nonlinear mode coupling. Moreover, the synergism of these two mechanisms may sustain the final QS state near the marginal KH instability threshold. Complex linear and nonlinear interactions among multiple modes and external flow, as well as self-generated zonal flow, result in a weak dependence of the final saturation level of the dominant EM ITG mode on the small-scale flow amplitude. The turbulent heat transport is visibly suppressed by weaker shear flow, but is almost not affected by stronger shear flows. The underlying mechanism is elaborated.
Nonlinear saturation dynamics of electromagnetic turbulence and associated transport are investigated using global simulation based on the Landau-fluid model in the finite β tokamak plasmas. The focus is on the kinetic ballooning mode(KBM), while a comparison to the β stabilized ion temperature gradient(ITG) mode is carried out. Results show that the KBM turbulence creates relatively weaker zonal flows in finite β plasmas. Zonal current could be formed around the low order rational surfaces, but is too narrow and localized to affect the global transport level. It is found that the KBM turbulence is nonlinearly saturated in sequential two stages. The linear KBM instability is first saturated transiently at a low fluctuation level by weak zonal flows. Afterwards, robust, linearly stable long wavelength fluctuations are nonlinearly excited and then interact feedback with primary unstable KBM components through the modulation process. As a result, the KBM is finally saturated with a down-shifted wavenumber spectrum. The suppression of turbulent transport by long wavelength fluctuations is identified mainly resulting from the reduction of KBM turbulence intensity.
The linear eigenmode characterizations and the nonlinear turbulence energy spreading of the drift waves in a tokamak plasma with strong pedestal gradient are numerically investigated based on an electromagnetic Landau fluid model. By the linear eigenmode analysis, it is found that the dominant instability in the low $\beta$ regime is the ion-temperature-gradient (ITG$^c$) mode and the electron drift wave instability (eDWI$^p$) in the core and edge region with strong density gradient, respectively. Multiple eigenstates of the eDWI$^p$ with different peak locations in the poloidal direction can be obtained by the eigenvalue problem solver. The dominant one is the high order eDWI$^p$ corresponding to the unconventional ballooning mode structure with multiple peaks in the poloidal position, in contrast to the conventional modes that peak at the outboard mid-plane, and has been verified through initial value simulation. In the high $\beta$ regime, the dominant eigenmodes in the core and edge region are the conventional and unconventional kinetic ballooning modes respectively. In the nonlinear simulation, an inward turbulence spreading phenomenon during the quasi-saturation phase of the edge turbulence is clearly observed. The inward speed of the turbulence energy front in the high $\beta$ regime is much faster than that in the low $\beta$ regime. It is interestingly found that the speed of the turbulence energy front increases with the increase of the plasma $\beta$ in the low $\beta$ regime, while it is almost unchanged in the high $\beta$ regime. It is identified that the turbulence spreading in the low and high $\beta$ regimes are determined by the nonlinear dynamics and the linear toroidal coupling respectively.
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