AI 中文总结
本研究采用统一框架研究托卡马克的Tokamap映射，揭示了磁力线输运的普适标度规律及磁剪切参数的影响，建立了哈密顿相空间几何与宏观输运性质的联系。
AI 中文摘要
托卡马克中的磁力线输运由混沌动力学与作为部分输运势垒的不变相空间结构之间的相互作用所支配。我们采用统一的几何、动力学与统计框架研究保守型Tokamap（托卡马克映射），这是一种适用于磁力线动力学的精确辛映射。相空间图与李雅普诺夫指数表征混合哈密顿动力学，而系综平均输运呈现出具有增长、交叉和饱和区域的普适动力学标度，这些区域通过齐次标度理论相互关联。庞加莱回归统计表明，降低磁剪切参数会系统性地减缓输运，特征输运时间遵循代数标度关系τ_c∝x_q^(-0.213)。该行为反映出与KAM岛、共振链及cantori（康托环）相关的粘性效应日益占主导地位。我们的结果建立了哈密顿相空间的几何组织与宏观输运性质之间的直接联系，为理解托卡马克及其他具有混合相空间的哈密顿系统中的长期磁力线输运提供了综合框架。
英文摘要
Magnetic field-line transport in tokamaks is governed by the interplay between chaotic dynamics and invariant phase-space structures that act as partial transport barriers. We investigate the conservative Tokamap, an exact symplectic mapping for magnetic field-line dynamics, using a unified geometrical, dynamical, and statistical framework. Phase-space portraits and Lyapunov exponents characterize the mixed Hamiltonian dynamics, while ensemble-averaged transport exhibits universal dynamic scaling with growth, crossover, and saturation regimes connected through a homogeneous scaling theory. Poincaré recurrence statistics reveal that decreasing the magnetic-shear parameter systematically slows transport, with the characteristic transport time following the algebraic scaling $τ_c\propto x_q^{-0.213}$. This behavior reflects increasingly dominant stickiness associated with KAM islands, resonance chains, and cantori. Our results establish a direct connection between the geometrical organization of Hamiltonian phase space and macroscopic transport properties, providing a comprehensive framework for understanding long-time magnetic field-line transport in tokamaks and other Hamiltonian systems with mixed phase space.
