Suppression of Ion-Scale Microtearing Modes by Electron-Scale Turbulence via Cross-Scale Nonlinear Interactions in Tokamak Plasmas

Gyrokinetic turbulence simulations are applied for the first time to the cross-scale interactions of microtearing modes (MTMs) and electron-temperature-gradient (ETG) modes. The investigation of the fluctuation response in a multiscale simulation including both types of instabilities indicates that MTMs are suppressed by ETG turbulence. A detailed analysis of nonlinear mode coupling reveals that radially localized current-sheet structures of MTMs are strongly distorted by fine-scale $\mathit{E}\times \mathit{B}$ flows of ETG turbulence. Consequently, electron heat transport caused by the magnetic flutter of MTMs is significantly reduced and ETG turbulence dominates electron heat transport.

Figure 1

(a) Linear growth rate ${\gamma }_{\mathit{l}}$ and real frequency ${\omega }_{\mathit{r}}$ as functions of the poloidal wave number $k_y$. (b) Time evolution of the electron heat flux caused by $\mathit{E}\times \mathit{B}$ flows and magnetic flutter, $Q_{\mathrm{eE}}$ and $Q_{\mathrm{eM}}$. We carried out a low-$k$ simulation resolving only MTM ($k_y{\rho }_a\le 2.1$) up to $t=90R/c_a$, and then refined grid sizes as a full-$k$ simulation resolving ETG/MTM ($k_y{\rho }_a\le 34.1$). (c) Poloidal-wave-number spectra of the electrostatic and magnetic-field energies, $W_{\mathrm{Ek}}$ and $W_{\mathrm{Mk}}$. Dotted (blue) and chain (red) lines plot results from the low-$k$ simulation, while solid (cyan) and dashed (pink) lines correspond to the full-$k$ simulation.

Figure 2

Structure of the electron-parallel current, $u_{\parallel e}$. Snapshots in the midplane of flux-tube $\theta =0$ (a) in the low-$k$ simulation, $t=86R/c_a$, and (b) in the full-$k$ simulation, $t=94R/c_a$. (c) Radial autocovariance of $u_{\parallel e}$ for the $k_y{\rho }_a=0.3$ mode of MTM. Dotted (green), dashed (blue), and solid (red) lines correspond to the linear eigenfunction, the low-$k$ simulation, and the full-$k$ simulation, respectively. A linear theoretical estimate, $\delta r_{\mathrm{est}}=\pm 0.096{\rho }_a$, is also plotted.

Figure 3

2D wave number spectra of nonlinear electron-entropy transfer during MTM suppression in the full-$k$ simulation (snapshots at $t=92.0R/c_a$): (a) the contribution by the high-$k_y$, high-$k_y$ coupling $J_{e\mathit{k}}^{{\mathrm{\Omega }}_H,{\mathrm{\Omega }}_H}$; (b) the contribution by the low-$k_y$, high-$k_y$ coupling $2J_{e\mathit{k}}^{{\mathrm{\Omega }}_L,{\mathrm{\Omega }}_H}=J_{e\mathit{k}}^{{\mathrm{\Omega }}_L,{\mathrm{\Omega }}_H}+J_{e\mathit{k}}^{{\mathrm{\Omega }}_H,{\mathrm{\Omega }}_L}$, as normalized by $n_0{T}_e{c}_a{\rho }_a^2/R^3$.