标题： 高维平均场哈密顿映射模型中的自洽混沌输运 显示英文标题

标题： Self-consistent chaotic transport in a high-dimensional mean-field Hamiltonian map model

摘要： 自洽的混沌输运在哈密顿平均场模型中被研究。 该模型提供了一个对临界稳定系统中输运的简化描述，包括强剪切流中的涡度混合和等离子体中的电子动力学。 通过一个耦合所有自由度的平均场来引入自洽性。 该模型被表述为一组大数量的$N$耦合的标准类似保面积扭转映射，在这些映射中，扰动的振幅和相位而不是像标准映射中那样是常数，而是动态变量。 特别感兴趣的是研究周期轨道对混沌输运和相干结构的影响。 数值模拟表明，自洽性导致形成一个围绕系统椭圆不动点的相干宏观粒子，它同时伴随着平均场的渐近周期行为。 为了模拟这种渐近状态，我们引入了一个非自治映射，该映射允许对全局输运的开始进行详细研究。 讨论了一种类似于闸门类型的输运机制，该机制允许在非自治系统中跨瞬时KAM不变环的输运。 作为理解输运的第一步，我们研究了一种称为顺序周期轨道的特殊类型轨道。 利用对称性性质，我们证明了可以通过复制从低维周期轨道生成高维顺序周期轨道。 我们表明，在自洽映射中的顺序周期轨道可以借助数值和渐近方法从标准类似映射的平凡（未耦合）周期轨道延续而来。 正规形式用于描述这些轨道，并找到保证其存在的映射参数值。 数值模拟用于验证渐近方法的预测。 显示英文摘要

摘要： Self-consistent chaotic transport is studied in a Hamiltonian mean-field model. The model provides a simplified description of transport in marginally stable systems including vorticity mixing in strong shear flows and electron dynamics in plasmas. Self-consistency is incorporated through a mean-field that couples all the degrees-of-freedom. The model is formulated as a large set of $N$ coupled standard-like area-preserving twist maps in which the amplitude and phase of the perturbation, rather than being constant like in the standard map, are dynamical variables. Of particular interest is the study of the impact of periodic orbits on the chaotic transport and coherent structures. Numerical simulations show that self-consistency leads to the formation of a coherent macro-particle trapped around the elliptic fixed point of the system that appears together with an asymptotic periodic behavior of the mean field. To model this asymptotic state, we introduced a non-autonomous map that allows a detailed study of the onset of global transport. A turnstile-type transport mechanism that allows transport across instantaneous KAM invariant circles in non-autonomous systems is discussed. As a first step to understand transport, we study a special type of orbits referred to as sequential periodic orbits. Using symmetry properties we show that, through replication, high-dimensional sequential periodic orbits can be generated starting from low-dimensional periodic orbits. We show that sequential periodic orbits in the self-consistent map can be continued from trivial (uncoupled) periodic orbits of standard-like maps using numerical and asymptotic methods. Normal forms are used to describe these orbits and to find the values of the map parameters that guarantee their existence. Numerical simulations are used to verify the prediction from the asymptotic methods.