聚变等离子体中的哈密顿粒子动力学：共振非轴对称扰动下能量与动量输运的轨道层析成像与频谱分析
Hamiltonian Particle Dynamics in Fusion Plasmas: Orbital Tomography and Spectrum Analysis for Energy and Momentum Transport under Resonant Non-Axisymmetric Perturbations
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中文总结 AI 辅助
本研究通过解析和数值方法，利用作用-角变量识别共振并分析轨道频率，预测了聚变等离子体中非轴对称扰动下的输运势垒和高能粒子行为。
中文摘要 AI 辅助
本论文研究了环向聚变等离子体中共振模-粒子相互作用对输运和约束的影响。利用解析和数值方法，我们研究了内在及外部施加的磁扰动如何影响具有不同动力学特性的等离子体粒子，重点关注与引导中心运动的共振相互作用。我们开发了一种基于作用-角变量的新颖、计算高效的方法，用于识别共振位置并表征引导中心相空间中的共振，包括共振链中的岛数量以及输运势垒的形成。利用漂移中心近似，我们推导了大环径比平衡下轨道频率和动力学$q$因子的解析表达式。这些结果为模-粒子共振提供了条件，而模-粒子共振可强烈影响粒子、动量和能量输运，进而影响等离子体约束。解析结果与数值模拟进行了验证，展示了一种在非轴对称扰动下预测输运势垒和高能粒子行为的有效工具。我们进一步将轨道频率分析从大环径比平衡扩展到数值重建的真实平衡，采用一种适用于任意未扰动平衡的计算高效半解析几何方法。最后，对于大环径比平衡，我们将分析扩展到含时扰动，并展示了引导中心相空间中阿诺德扩散的出现，强调了阿诺德网在粒子输运中的作用。总体而言，本工作推进了对模-粒子共振相互作用的理解，并为预测真实聚变装置中的输运和约束提供了计算工具。
英文摘要
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.
发表机构
- National Technical University of Athens（雅典国家技术大学）
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