Zaslavsky G M, Carreras B A, Lynch V E, Garcia L, Edelman M
Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, New York 10012, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2005 Aug;72(2 Pt 2):026227. doi: 10.1103/PhysRevE.72.026227. Epub 2005 Aug 31.
The paper describes the complex topological structure of invariant surfaces that appears in a quasi-stationary regime of the tokamak plasma, and it considers in detail anomalous transport of particles along the invariant surfaces (isosurfaces) that have topological genus greater than 1. Such dynamics is pseudochaotic; i.e. it has a zero Lyapunov exponent. Simulations discover such surfaces in confined plasmas under a fairly low ratio of pressure to the magnetic field energy (beta). The isosurfaces correspond to quasi-coherent structures called "streamers" and the streamers are connected by filaments. We study distribution of time of particle separation, Poincaré; recurrences of trajectories, and first time arrival to the system's edge. A model of a multibar-in-square billiard, introduced by Carreras et al. [Chaos 13, 1175 (2003)] is studied with renormalization group method to obtain a distribution of the first time of particles arrival to the edge as a function of the number of bars, which appears to be power-like. The characteristic exponent of this distribution is discussed with respect to its dependence on the number of filaments that connect adjacent streamers.
本文描述了托卡马克等离子体准稳态中出现的不变曲面的复杂拓扑结构，并详细考虑了粒子沿拓扑亏格大于1的不变曲面（等值面）的反常输运。这种动力学是伪混沌的，即它的李雅普诺夫指数为零。模拟发现在压力与磁场能量之比（β）相当低的受限等离子体中存在这样的曲面。这些等值面对应于称为“飘带”的准相干结构，且飘带由细丝相连。我们研究了粒子分离时间的分布、庞加莱轨迹的重现以及首次到达系统边缘的时间。用重正化群方法研究了卡雷拉斯等人[《混沌》13, 1175 (2003)]引入的一个多杆方台球模型，以得到粒子首次到达边缘的时间分布作为杆数的函数，该分布似乎呈幂律形式。讨论了这种分布的特征指数对连接相邻飘带的细丝数量的依赖性。
