Multi-scale multi-mode nonlinear interaction in tokamak plasma turbulence with moderate small-scale shear flow

Abstract

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.

Role of the zonal flow in multi-scale multi-mode turbulence with small-scale shear flow in tokamak plasmas

“…[36,37] This can also consistently capture the excitation of secondary KH mode when the flow shear is larger than the stability threshold. [35] The highly complex nonlinear interaction dynamics of cross-scale turbulence with ITG as well as KH modes are governed by normalized evolution equations of perturbed density n, the vorticity ∇ 2 ⊥ φ , parallel ion velocity υ , magnetic flux ψ (corresponding to the parallel vector potential through A = −ψ), as well as ion temperature T i as follows:…”

“…The normalizations are expressed as usual. [35] The code has been well checked for the convergency with enough high resolutions in radial real space and mode number spectral space. Other main parameters used in simulations are λ = 1.5, ŝ = 0.1 and the classical cross-field dissipations are set as D U = D n = η ⊥ = χ ⊥ = 0.01 which are included to damp smaller-scale fluctuations.…”

“…Nonlinear evolution equations ( 1)-( 5) can be numerically solved by an initial value code with the same numerical setting 065207-2 as in Ref. [35]. The small-scale shear flow externally embedded in cross-scale EM system as a coherent structure is set as…”

“…Therefore, in this work, we mainly analyze the underlying mechanisms in the oscillation phase. [35] Simulations show that the odd symmetric components of zonal flow (same symmetry as the external flow) make the radial parity of the KH mode alteration through adjusting the drift velocities at two sides of the resonant surface so that the KH mode becomes bursty firstly. Afterwards, the ITG intermittency follows due to nonlinear mode coupling among the KH, EM ITG modes and the shear flows including the zonal flows and the external small-scale shear flow.…”

Features of transport induced by ion-driven trapped-electron modes in tokamak plasmas

“…In additional, several physical effects, including the collisions, magnetic shear, finite β and finite Larmor radius effects [26][27][28][29][30][31][32] and other plasma parameters are considered as well. Furthermore, the turbulent transport is determined by the type of micro-turbulence [33,34] and it has been illustrated in the experiments, theories and simulations. Additional, transitions of turbulence in plasma density limits were discussed.…”