GENE simulations of Ion-Temperature-Gradient turbulence in various stellarator configurations are conducted, using the magnetic information from an entire flux surface. The variability of the localization for the density fluctuations, according to the specific geometry, is evidently observed. The beneficial effects of the localization for the fluctuations on the ITG transport levels, compared to the local (flux-tube) estimate corresponding to the location where normal curvature is strongest, are documented in this publication.

ETG turbulence in W7-X

GENE simulations of Electron-Temperature-Gradient (ETG) driven turbulence in Wendelstein 7-X are compared, in terms of the ensuing heat flux, to a low-density discharge from the OP1.1 operational phase. These core plasma conditions, featuring cold ions and a flat density profile, can generally drive ETG turbulence. The simulations results, however, are apparently unable to explain the experimental electron heat flux in terms of ETG turbulence. Thanks to their modular design (and low shear) stellarators can break high amplitude streamers. There is, therefore, theoretical indication that ETG turbulence in W7-X may not  contribute to the transport, especially in high-performance scenarios. Details of the analysis can be found in this letter.

Ballooning stability

The GIST code has been developed further to address the calculation of the Mercier coefficient Dp, related to infinite-n ballooning instabilities. More specifically, a configuration is susceptible to this instability, in case that Dp > 0.25 holds. Thanks to a detailed analytical derivation for this criterion, we are in the possition to break down the individual factors that form Dp. Using GIST, we can calculate the Mercier criterion employing the same modules for the construction of the magnetic geometry for gyrokinetic simulations. In this respect, the relation between MHD and gyrokinetic stability (in finite beta plasmas) can be unambiguously compared.

Turbulence optimization

The STELLOPT code has been provided with several target functions relevant to turbulence transport. One of the very first attempts involves optimization of the high-mirror W7-X configuration for ITG turbulence. The target function did not rely on expensive turbulence calculations, which would make inclusion into the optimizer prohibitive. Rather, a simple geometry-specific proxy function was introduced capturing essential features of ITG turbulence, based on the magnetic field curvature and the flux expansion of magnetic surfaces. Details of a new configuration termed MPX, together with the used stochastic global optimization technique called Differential Evolution, can be found here.

Turbulence optimization

Statistics of turbulence

We have developed tools based on ARIMA models and Singular Spectrum Analysis (SSA) in order to examine statistics of gyrokinetic as well as fluid turbulence, looking for signature of intermittent transport. A basic prerequisite of this approach is the filtering of the time signals from hidden deterministic components, allowing the inspection of the stochastic part alone. For the tokamak experiment TORPEX, we perform an SSA analysis for simulations  in the scrape-off region, with and without presence of blobs, based on a Braginskii model. These  results demonstrate deviations from Gaussian distribution, as predicted by an instanton method. Details can be found in this publication.

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