Milestone in predicting core plasma turbulence: successful multi-channel validation of the gyrokinetic code GENE

Abstract

On the basis of several recent breakthroughs in fusion research, many activities have been launched around the world to develop fusion power plants on the fastest possible time scale. In this context, high-fidelity simulations of the plasma behavior on large supercomputers provide one of the main pathways to accelerating progress by guiding crucial design decisions. When it comes to determining the energy confinement time of a magnetic confinement fusion device, which is a key quantity of interest, gyrokinetic turbulence simulations are considered the approach of choice - but the question, whether they are really able to reliably predict the plasma behavior is still open. The present study addresses this important issue by means of careful comparisons between state-of-the-art gyrokinetic turbulence simulations with the GENE code and experimental observations in the ASDEX Upgrade tokamak for an unprecedented number of simultaneous plasma observables.

Fig. 1. Previous validation works and workflow.

(a) (Incomplete) list of previous validation works comparing several turbulence observables between experiment and gyrokinetic simulations^–. The current study compares the to date largest number of turbulence quantities simultaneously. b Flow chart describing the steps involved in comparative studies. For details, refer to the text.

Fig. 2. Experimental set up.

a Poloidal cross-section of AUG including flux surfaces (black lines) and density fluctuations from the gyrokinetic simulation. The zoomed windows show (b) density fluctuations at the measurement position. Additionally, the probing beam from ray-tracing (green) and the weighting function from 2D full-wave simulations (shades of grey) are shown. Panel (c) depicts temperature fluctuations along with the CECE measurement volumes (black ellipses) obtained from the Torbeam and ECRad codes.

Fig. 3. Input to the gyrokinetic simulations and comparison of heat fluxes.

Profiles and normalized gradients of the electron temperature (a, b), ion temperature (c, d) and electron density (e, f). The points in (a, c, e) indicate experimental measurement data. The lines and uncertainties are output of Bayesian analysis in (a–f). Radial profiles of (g) electron and (h) ion surface-integrated heat fluxes: transport analysis results are shown as solid lines with uncertainty bands from Markov Chain Monte Carlo modeling, gyrokinetic simulation results are plotted as symbols x.

Fig. 4. Comparison of fluctuation amplitudes.

a, b Electron temperature fluctuation spectra including statistical uncertainties (square root of the statistical variance) measured by CECE (solid line) and through synthetic diagnostic analysis on gyrokinetic data (dashed line). Experimental wavenumber spectra measured with DBS ((c) two in O-mode, (d) one in X-mode) for the flat (blue) and steep (red) scenarios and comparison with two-dimenstional full-wave simulation (black, dark red). e Wavenumber spectra calculated directly from the turbulence field from the gyrokinetic simulations.

Fig. 5. Comparison of cross-phase α_nT between density and electron temperature fluctuations.

The frequency region with significant coherence between the n_e and T_e signals is shown in stronger colors than regions with no coherence. The error bars indicate the statistical uncertainty (square root of the statistical variance) For more details, refer to the text.

Fig. 6. Comparison of radial correlation lengths.

a Radial correlation length of electron density fluctuation $l_{\mathrm{r},n_{\mathrm{e}}}$ versus inverse perpendicular structure size k_⊥ for both steep (red) and flat (blue) scenarios. Experimental data (full symbols) and fits (solid lines) compared to synthetic diagnostic analyses of gyrokinetic simulations (symbol x) and fits (dashed lines). b Maximum of the normalized cross-correlation between adjacent CECE channels (circles) and between simulated electron temperature fluctuations averaged in the corresponding plasma volumes (symbols x) for the steep (red) and flat (blue) scenario.