"Data-driven discovery approach to tackle turbulence in fusion plasmas"

Abstract:

The aim of this thesis was to make a contribution to the understanding of the turbulent transport in the core of magnetically confined plasmas. Turbulent transport arises from electrostatic turbulence, with two instabilities, the ion temperature gradient (ITG) and the trapped electron modes (TEM), dominant at low wave numbers k. Distinguishing them from experimental measurements of density fluctuations and identifying their interplay with other instabilities would allow a better understanding of turbulent transport.

Algorithms have been developed to extract the different spectral components (low frequency component, broadband component, QC modes and noise) from fixed frequency conventional reflectometry (CFR). These algorithms integrate signal processing and machine learning in an intelligent way (without ad hoc constraints), preserving the statistical and physical properties of each extracted component.

The ohmic confinement regimes have been studied because of the clear link between instability and confinement regime: in the Linear Ohmic Confinement (LOC) sub-regime, TEM seems to dominate, whereas in the Saturated Ohmic Confinement (SOC) sub-regime, ITG becomes dominant, inducing then distinct turbulent transport behaviours. Furthermore, Quasi-Coherent (QC) modes emerged as a potential signature of TEM in the reflectometry frequency spectrum: they are observed in LOC and disappear at the LOC-SOC transition.

It was first verified on TEXTOR and Tore Supra data that the extracted QC modes component retains its statistical and physical properties. Under 2 different magnetic configurations: Tore Supra (limiter) and WEST (divertor). A probability map of occurrence was constructed for both tokamaks, highlighting a 'class' of QC modes in the LOC sub-regime in the LFS with a probability of 0.7 and 0.6 respectively, and in the HFS with a probability of 0.4 and 0.3. In addition, a ratio of the energy content in the QC modes to the energy content in the broadband component showed a predominance of the QC modes as they approached the LOC-SOC transition, after which the energy of the QC modes started to decrease, showing a more abrupt behaviour in the LFS.

The remaining QC modes were found in the SOC sub-regime in 2 classes, one at low current and another at high current. At the aim of discriminating the different classes of QC modes, general trends were found based on their spectral centroid and spectral bandwidth, however as it was not enough multifractal spectrum was found useful highlighnt differences in the power-scaling of classes of QC. Sub-classes were also found as one exhibiting low frequency and high frequency QC modes and another one exhibiting a degradation of the QC modes towards a broadband behaviour.

The evolution of other spectral components was also systematically studied, such as the energy content in the LF and the spectral shape of the broadband component related to microturbulence. No discriminating information between classes was obtained from these analyses.

To go further in the analysis of these different QC mode classes and sub-classes, the time evolution of the energy exchange between time scales was introduced for the first time, i.e. the dynamics of the energy exchange between the LF component and BB component versus the QC mode components.

Different signatures of QC mode dynamics were observed in different QC mode classes, especially between the LOC class and the SOC class.

Among these different QC mode dynamics, an interaction with the QC modes and the sawtooth instability belonging to the LF component was observed and analysed, possibly giving a link between the electrical turbulence and the MHD instabilities, the nature of the link between the QC modes and the MHD activities is still open. Indeed, the analysis performed using the transfer entropy shows a possible causality from the sawtooth to the QC modes.

To further investigate the link between the QC modes and the LF component, the multi-magnetic configuration study was extended to another magnetic configuration, the W7X stellarator. It showed a similar signature of QC mode dynamics for QC modes being caused by the LF and provoking the BB component (bi-directional causality), all using the transfer entropy (TE) concept. This study may reveal a universal underlying mechanism. The poloidal velocity studies  on ToreSupra and W7X goes in the same direction.

Bi-directional causality using TE allows a selection of signals from the whole database for deeper studies on universal mechanisms, possibly energy exchange between turbulence sources, etc.