Coupling transport simulations with Phase-Space-Reconstruction methods and Lyapunov exponents analyses

Nuclear fusion in tokamaks represents a promising solution for producing clean and sustainable energy. However, achieving stable and reliable operation requires controlling plasma dynamics over long periods. A crucial part of this challenge lies in the ability to predict plasma behavior from limited measurements, in order to anticipate and mitigate potential instabilities. In this context, it is particularly useful to develop tools that can evaluate the predictability horizon of a dynamic system, that is, the time during which its evolution can be predicted with acceptable accuracy. Plasmas in tokamaks can be modeled as complex dynamic systems, characterized by nonlinear interactions that can lead to chaotic phenomena. One of the most commonly used mathematical tools to analyze the predictability of such systems is the Lyapunov exponent. This indicator quantifies the rate of divergence of two initially close trajectories in phase space. A positive Lyapunov exponent is often associated with chaotic dynamics, while an exponent close to zero suggests more predictable behavior. To estimate this exponent from time series data, it is necessary to reconstruct the phase space using a dedicated algorithm, such as Phase Space Reconstruction (PSR) via the delay method. The present work aims to test the ability of a phase space reconstruction algorithm to correctly estimate Lyapunov exponents, specifically the largest Lyapunov exponent, from time series measurements. The analyses are conducted using simulated data generated by the ASTRA software, which models plasma dynamics in a tokamak. To this end, an adapted version of the statComp package was developed to perform the required analyses. This report is structured as follows: • Section 2 presents the statComp package adapted to ASTRA, describes its usage, and explains how to interpret its results. • Section 3 details the phase space reconstruction algorithm and the estimation of Lyapunov exponents using the delay method. This section includes a practical illustration on a reference system, the Lorenz attractor. • In Section 4, the algorithm is applied to simulated data from ASTRA to test its robustness and relevance. • Section 5 provides a conclusion summarizing the results and lessons learned from this work. • Finally, Section 6 explores research perspectives, followed by the acknowledgments in