Chaotic behavior of edge plasma turbulence characterized by a broadband frequency spectrum

本研究旨在从混沌的角度理解致密螺旋系统（CHS）中以宽带频谱为特征的边缘等离子体湍流，从而更好地理解等离子体约束与边缘等离子体湍流结构之间的关系。为此必须计算精确的最大李雅普诺夫指数，这需要很长的时间序列，因为它在边缘等离子体中预计相对较大。因此，我们完成了一个产生1M个数据点时间序列的数据采集系统，并在CHS上进行了测试。并利用小波分析对湍流的空间结构进行了分析。该技术适用于分析包含脉冲或短期事件的数据记录，因为可以避免通过检查数据记录的大部分来平均这些暂时局部发生的事件。李雅普诺夫指数的计算算法易于实现，即使对高维吸引子也没有太多限制。我们通过分析具有已知吸引子的数学系统的时间序列来测试我们的算法实现，并获得了相关维数和最大Lyapunov指数的已制表值。我们使用直径为1cm的热中性锂束和八通道光学检测系统获得的16K数据点，使我们能够测量到相关维数高达12的结构，并获得了5-9的分形维数和正李亚普诺夫指数。因此，CHS中的宽带湍流本质上是由相对较少的变量决定的，观测到的混沌是确定性的，吸引子是奇异的。用小波分析方法证明了湍流的非线性色散关系的存在。

Aims of this study are understanding of edge plasma turbulence characterized by a broadband frequency spectrum in the Compact Helical System (CHS) from the chaotic point of view, so that the relation between plasma confinement and turbulent structure in the edge plasma will be better understood.The accurate largest Lyapunov exponent must be calculated for this purpose, which needs a long time series because it is expected to be relatively large in the edge plasma. Thus we have completed a data acquisition system which yields the time series of 1M data points, and tested it on CHS.We have also analyzed the spatial structure of the turbulence by using wavelet analysis. This technique is suitable for the analysis of data records containing pulses or short-lived events, because it is avoidable to average out these temporally localized occurrences by examining large sections of the data record.The Lyapunov exponent is calculated by the algorithm that is easy to implement and has less limitation even for high dimensional attractors. We have tested our implementation of the algorithm by analyzing time series from mathematical systems with known attractors, and have obtained the already tabulated values for the correlation dimension and largest Lyapunov exponent.Our use of 16K data points, obtained with a thermal neutral lithium beam of 1cm diameter with an eight-channel optical detection system, has allowed us to measure the structure for correlation dimensions up to-12, and the fractal dimensions of 5-9 and the positive Lyapunov exponent have been obtained. Thus the broadband turbulence in CHS is essentially determined by relatively small number of variables, and the chaos observed is deterministic and the attractor is strange. The existence of a nonlinear dispersion relation of the turbulence is also suggested by wavelet analysis.