On How Zonal Fields Suppress Reversed Shear Alfvén Eigenmode in Tokamak Plasmas

Abstract

Employing both nonlinear gyrokinetic simulations and theoretical analyses, we have discovered the novel result that, with energetic particle dynamics kept linear, the nonlinear suppression and eventual saturation of reversed-shear Alfvén eigenmode occur via the downward frequency chirping induced by the beat-driven zonal current. More specifically, as the mode frequency chirps downward, there is enhanced mode conversion to radially propagating electron Landau-damped kinetic Alfvén waves; resulting in enhanced convective (radiative) damping and, thereby, its suppression and saturation. Theoretical results are in good agreement with simulations both qualitatively and quantitatively.

Figures (5)

• Figure 1: Saturation of the $n=4$ RSAE in GTC simulation with nonlinear thermal plasma and linear EP response. Time evolution of (a) normalized amplitude of the electrostatic parallel electric field $E_{\parallel,{\rm es}}=-\nabla_\parallel\delta\phi$, (b) normalized growth rate $\gamma/\omega_{\rm lin}$ for the dominant $m=12$ poloidal harmonic, and (c) instantaneous frequency $f$ (kHz) at the $q_{\rm m}$ surface. Vertical dot lines (I, II, III) mark distinct phases of the evolution, and $\omega_{\rm lin}=2\pi\times65.8$ kHz is the RSAE linear frequency.
• Figure 2: KAW excitation and RSAE frequency evolution. (a) Time evolution of $E_\parallel$ radial profile, with Alfvén resonance inside $q_{\rm m}$ (dashed). (b) RSAE frequency relative to Alfvén continua from MAS Bao2023; $q$ profile (orange, right axis). Horizontal lines show $E_\parallel$ structure at times I, II, III from GTC simulation (FIG. \ref{['gtc_sim_fig1']}).
• Figure 3: (a) Time evolution of normalized frequency $\Omega_r=\omega_{0r}/\omega_A$ and damping rate $\Omega_i=\omega_{0i}/\omega_A$ from the 'RSAE-ZF-MHD' model with zonal flow and zonal current. (b) Corresponding evolution with only zonal flow included.
• Figure 4: (a) Time evolution of $\Omega_r$ and $\Omega_i$ from the 'RSAE-ZF-KAW' model with zonal flow and zonal current. (b) Radial profile of the perturbed electrostatic potential $|\delta\phi_0|$ at the nonlinear saturation ($t=0.53$ ms).
• Figure 5: Quantitative comparison of the evolution of $E_\parallel/E_{\parallel,{\rm es}}$: GTC Simulation (black), 'RSAE-ZF-MHD' model (Eq. \ref{['AE_ZF_eigen_eq']}, blue circles, scaled $\times 10$), and 'RSAE-ZF-KAW' model (Eq. \ref{['RSAE_KAW_e_Landau_model']}, red squares).