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

以宽带频谱为特征的边缘等离子体湍流的混沌行为

• 批准号: 07680547
• 负责人: KOMORI Akio
• 金额: $ 1.41万
• 依托单位: National Institute for Fusion Science
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1995
• 资助国家: 日本
• 起止时间: 1995 至 1996
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-07680547/
• 关键词: chaos; edge plasma; broadband turbulence; Compact Helical System; correlation dimension; the Lyapunov exponent; wavelet analysis

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.

从混沌的角度理解紧凑螺旋系统（CompactHelicalSystem，CHS）中具有宽带频谱特征的边缘等离子体湍流，以便更好地理解边缘等离子体中等离子体约束与湍流结构之间的关系，为此必须计算精确的最大李雅普诺夫指数，其需要长的时间序列，因为预期其在边缘等离子体中相对较大。为此，我们研制了一套数据采集系统，获得了100万个数据点的时间序列，并在CHS上进行了测试。我们还利用小波分析方法分析了湍流的空间结构。该方法适用于分析包含脉冲或短寿命事件的数据记录，因为它可以避免通过检查数据记录的大部分来平均这些时间上局部化的事件.该算法易于实现，即使对于高维吸引子也具有较小的限制.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的实现，并且已经获得了关联维数和最大李雅普诺夫指数的已经列表的值。我们使用16 K数据点，用八通道光学检测系统获得的直径为1cm的热中性锂束，允许我们测量关联维数高达-12的结构，得到了5-9的分维和正的李雅普诺夫指数。因此，CHS中的宽带湍流本质上是由相对较少的变量决定的，观察到的混沌是确定性的，吸引子是奇异的。小波分析还表明湍流存在非线性色散关系。