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

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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.