Hamiltonian Particle Dynamics in Fusion Plasmas: Orbital Tomography and Spectrum Analysis for Energy and Momentum Transport under Resonant Non-Axisymmetric Perturbations

RESUMO

This thesis investigates the impact of resonant mode-particle interactions on transport and confinement in toroidal fusion plasmas. Using analytical and numerical approaches, we study how intrinsic and externally applied magnetic perturbations affect plasma particles with different kinetic characteristics, focusing on resonant interactions with guiding-center motion. We develop a novel, computationally efficient method based on Action-Angle variables to identify resonance locations and characterize resonances in guiding-center phase space, including the number of islands in resonance chains and the formation of transport barriers. Using the drift center (DC) approximation, we derive analytical expressions for orbital frequencies and the kinetic $q$ factor for large-aspect-ratio (LAR) equilibria. These results provide the conditions for mode-particle resonances, which can strongly influence particle, momentum, and energy transport and, consequently, plasma confinement. The analytical results are validated against numerical simulations, demonstrating an efficient tool for predicting transport barriers and energetic-particle behavior under non-axisymmetric perturbations. We further extend the orbital-frequency analysis from LAR equilibria to numerically reconstructed, realistic equilibria using a computationally efficient, semi-analytical geometrical method applicable to arbitrary unperturbed equilibria. Finally, for the LAR equilibrium, we extend the analysis to time-dependent perturbations and demonstrate the emergence of Arnold diffusion in guiding-center phase space, highlighting the role of the Arnold web in particle transport. Overall, this work advances the understanding of mode-particle resonant interactions and provides computational tools for predicting transport and confinement in realistic fusion configurations.