Nonlinear generation of global zonal structures in gyrokinetic simulations of TCV and ASDEX Upgrade magnetic configurations

Abstract

In tokamaks, turbulence is responsible not only for the anomalous transport of heat and particles from the core to the edge, which reduces heating efficiency, but also for the generation of zonal structures (ZSs). Examples of ZSs are those with characteristic sound frequency, like the geodesic acoustic modes (GAMs). Developing a theoretical model of ZS is essential, as they contribute to the turbulence saturation and thus indirectly influence transport. In this paper, we investigate the radial structure of ZS in the frequency range of GAMs, by means of numerical simulations using the gyrokinetic particle-in-cell code ORB5. We find that radially extended coherent ZSs (labelled here as global ZSs) are non-linearly generated by the high-n part of the turbulence spectrum (with n being the toroidal mode number) by means of self-consistent simulations. We also reproduce this generation by mimicking the turbulence modes with an antenna, thus isolating the nonlinear generation mechanism.

Figures (9)

• Figure 1: Magnetic field configuration ($|B|(T)$) in the TCV (a) and ASDEX Upgrade (b) cases. Safety factor (c): Safety factor profiles. (d): Temperature profiles. (e): Density profiles. TCV: $R_0 (m) = 0.88$, $a_0 (m) = 0.25$, $B_0 (T) = 1.44$, $\kappa = 1.44$, $L_x = 265.5$ ($\rho^* = 7.53\cdot 10^{-3}$). AUG: $R_0 (m) = 1.65$, $a_0 (m) = 0.50$, $B_0 (T) = 2.0$, $\kappa = 1.08$, $L_x = 1077.0$ ($\rho^* = 1.85\cdot 10^{-3}$).
• Figure 2: Evolution in time of the zonal radial electric field, $\overline{E}_r[a.u]$, for the TCV (a,b) and the AUG (c,d) configurations in simulations with different ITG spectra.
• Figure 3: Frequency spectra of zonal electric field in the TCV (upper row) and the AUG (bottom row) configurations in simulations with different ITG spectra. The global ZS spectra in the TCV are calculated in the time interval $t (ms) = [0.4, 5.3]$, while it is $t (ms) = [0.4, 2.6]$ for the AUG. The white dashed lines indicate the linear analytical GAM frequency Gao10. The dashed green lines in the AUG plots depict GAM frequency estimation from linear GK simulations Novikau17. The white crosses show experimental frequencies in the GAM range, in the AUG case Conway08.
• Figure 4: (a): Temporal evolution of the zonal potential and high-$n$ ITG mode in the TCV simulation with the broad range of toroidal modes $n = [0,80]$. (b): The $n = 80$ potential at different radial points in the same TCV simulation. The vertical black dashed line indicates the time instant $t = 0.109$ at which the antenna spatial profile is taken for later simulations. (c): Temporal evolution of the $n = 80$ antenna with frequency $\omega(kHz) = 15.31$, whose spatial profile is taken from the TCV simulation with $n = [0,80]$.
• Figure 5: (a): Radial structure of the $n = 80$ electric potential at the low field size at $t = 0.109$ in the TCV simulation with $n = [0, 80]$ and the antenna recreated from the this potential. (b): Poloidal structure of the antenna. The black lines indicate the flux surfaces at $s = 0.50, 0.80, 0.95$, respectively.