Development of statistical analysis tools for global observable of fluctuation data towards optimised real-time control applications

The StatComp package is a Matlab statistical toolbox developed over the years by Dr. Testa and his students. It has been inspired by M. R. Brown’s paper Magnetohydrodynamic Turbulence: Observation and experiment [2]. It first performed the analysis of the edge magnetic turbulent field in the TCV. It started in 2015 by A. Yantchenko and has been constantly improved and supplemented since then. The last addition to the package was many separate functions for the ”big data” analysis of the results, done by S. Ogier-Collin. The entire code is currently under review for release in the MHD analysis package within the SPC’s General Analysis Toolkit. The present document reports the latest evolution of this package in the perspective of using the charac- terisation plasma turbulence to possibly provide useful information for the optimisation of real-time plasma control and the fusion performance of a tokamak. The mathematical theory of the StatComp analyses and some examples of application are presented in the section 2. The section 3 presents the evolution of the existing functions as well as the addition of the loading function for the electrostatic data from the edge of the plasma, and the multifractality and predictability analyses. These enhancements are put in the perspective of one particular usage: the characterisation of the turbulence in order optimise potentially plasma control. Then, the up-to-date running instructions and interpretation guidelines are detailed in the section 4. The latter are based on the output figures resulting of the analysis of a standard dataset constituted of a white noise sample, three fractional Brownian motions of different known Hurst index, of a linear ramp and of a sample of the solar wind. The section 5 shows the results of the test on four actual shots realised on the TCV tokamak. The varying parameters are the signs of the poloidal magnetic field and of the plasma current. The four shots are each the resultant of a positive or negative poloidal field and a positive or negative plasma current. The shape and position of the plasma in the vacuum vessel are the same for each shot as well as the amplitude of the varied parameters, i.e. the magnetic field and plasma current. The emphasis is made on the presentation and interpretation of the results obtained with the electrostatic data on the low-field side of the plasma. The obtained results are discussed along the limits of the package and its possible improvements in section 6 before concluding in section 7. In the appendix, the structures necessary to the use of the package are detailed and examples of run commands are presented. In order to offer to the reader a frame of reference for reflection, the main parameters and orders of magnitude related to the plasma shots in TCV are given. Some of the mathematical basis of the statistical theory are also elaborated to complete the description of the different tools of the package. Finally, the reduced bibliography of all the sources explicitly mentioned in this report is doubled by a second bibliography presenting a wider selection of relevant sources each accompanied with a brief description of its content and its link to the present study.