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

本研究的目的是从混沌的角度理解紧致螺旋系统(CHS)中具有宽带频谱特征的边缘等离子体湍流，以便更好地了解边缘等离子体中等离子体约束与湍流结构之间的关系，为此必须计算出准确的最大Lyapunov指数，这需要较长的时间序列，因为边缘等离子体中的Lyapunov指数预计会相对较大。为此，我们完成了一个1M个数据点的时间序列的数据采集系统，并在CHS上进行了测试。我们还利用小波分析对湍流的空间结构进行了分析。该技术适用于包含脉冲或短事件的数据记录的分析，因为可以避免通过检查数据记录的大段来平均这些时间局部出现的事件，而Lyapunov指数的计算算法易于实现，即使对于高维吸引子也具有较少的限制。我们通过分析已知吸引子的数学系统的时间序列来测试我们的算法的实现，得到了已经列出的关联维和最大Lyapunov指数的值。我们使用直径1 cm的热中性锂束和八通道光学探测系统获得的16K个数据点，使我们能够测量关联维高达-12的结构，并获得了5-9的分维和正的Lyapunov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，吸引子是奇怪的。小波分析表明，湍流存在非线性弥散关系。

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.